review article charge radii and quadrupole moments of the low … · 2019. 7. 31. · eld theories,...

Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2013 Article ID 756847 17 pageshttpdxdoiorg1011552013756847

Review ArticleCharge Radii and Quadrupole Moments ofthe Low-Lying Baryons in the Chiral Constituent Quark Model

Neetika Sharma and Harleen Dahiya

Department of Physics Dr BR Ambedkar National Institute of Technology Jalandhar 144011 India

Correspondence should be addressed to Harleen Dahiya dahiyahnitjacin

Received 16 December 2012 Revised 15 April 2013 Accepted 13 May 2013

Academic Editor Jan E Alam

Copyright copy 2013 N Sharma and H Dahiya This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The chiral constituent quark model (120594CQM) with general parameterization method (GPM) has been formulated to calculate thecharge radii of the spin (12)

+ octet and (32)+ decuplet baryons and quadrupole moments of the spin (32)

+ decuplet baryons andspin (32)

+

rarr (12)+ transitions The implications of such a model have been investigated in detail for the effects of symmetry

breaking and GPM parameters pertaining to the one- two- and three-quark contributions Our results are not only comparablewith the latest experimental studies but also agree with other phenomenological models It is found that the 120594CQM is successful ingiving a quantitative and qualitative description of the charge radii and quadrupole moments

1 Introduction

The internal structure of baryons is determined in termsof electromagnetic Dirac and Pauli form factors 119865

1(119876

2)

and 1198652(119876

2) or equivalently in terms of the electric and

magnetic Sachs form factors 119866119864(119876

2) and 119866

119872(119876

2) [1] The

electromagnetic form factors are the fundamental quantitiesof theoretical and experimental interest which are furtherrelated to the static low energy observables of charge radiiand magnetic moments One of the main challenges in thetheoretical and experimental hadronic physics is to under-stand the structure of hadrons within the quantum chromo-dynamics (QCD) in terms of these moments AlthoughQCDis accepted as the fundamental theory of strong interactionsthe direct prediction of these kinds of observables from thefirst principle of QCD still remains a theoretical challenge asthey lie in the nonperturbative regime of QCD

Following the discoveries that the quarks and antiquarkscarry only 30 of the total proton spin [2 3] the orbitalangular momentum of quarks and gluons is expected tomake a significant contribution In addition to this there isa significant contribution coming from the strange quarksin the nucleon which are otherwise not present in thevalence structure It therefore becomes interesting to discuss

the interplay between the spin of nonvalence quark andthe orbital angular momentum in understanding the spinstructure of baryons Further the experimental developments[4ndash6] providing information on the radial variation of thecharge and magnetization densities of the proton give theevidence for the deviation of the charge distribution fromspherical symmetry On the other hand it is well knownthat the quadrupole moment of the nucleon should vanishon account of its spin-12 nature This observation hasnaturally turned to be the subject of intense theoretical andexperimental activity

The mean square charge radius (1199032B) giving the possibleldquosizerdquo of baryon has been investigated experimentally withthe advent of new facilities at JLAB SELEX Collaborations[7ndash13] Several measurements have been made for the chargeradii of 119901 119899 and Σ

minus in electron-baryon scattering experi-ments [13 14] giving 119903

119901= 0877 plusmn 0007 fm (1199032

119901= 0779 plusmn

0025 fm2 [15]) and 1199032

119899= minus01161plusmn00022 fm2 [12]The recent

measurement of 1199032

Σminus

[13 14] is particularly interesting as itgives the first estimate for the charge form factor of a strangebaryon at low momentum transfer

The Δ(1232) resonance is the lowest-lying excited stateof the nucleon in which the search for quadrupole strength

2 Advances in High Energy Physics

has been carried out [16ndash19] The spin and parity selectionrules in the 120574 + 119901 rarr Δ

+ transition allow three contributingphoton absorption amplitudes the magnetic dipole 119866

1198721 the

electric quadrupole moment1198661198642 and the charge quadrupole

moment 1198661198622 The 119866

1198721amplitude gives us information on

magnetic moment whereas the information on the intrinsicquadrupolemoment can be obtained from themeasurementsof 119866

1198642and 119866

1198622amplitudes [12] If the charge distribution

of the initial and final three-quark states was sphericallysymmetric the 119866

1198642and 119866

1198622amplitudes of the multipole

expansion would be zero [20] However the recent experi-ments at Mainz Bates Bonn and JLab Collaborations [7ndash11 21 22] reveal that these quadrupole amplitudes are clearlynonzero [12] The ratio of electric quadrupole amplitude tothe magnetic dipole amplitude is at least 11986421198721 equiv minus0025 plusmn

0005 and a comparable value of same sign and magnitudehas been measured for the 11986221198721 ratio [12] Further thequadrupole transition moment (119876Δ

+

119873) measured by LEGSand Mainz collaborations (minus0108 plusmn 0009 plusmn 0034 fm2 [16ndash18] and minus00846 plusmn 00033 fm2 [19] resp) also leads to theconclusion that the nucleon and the Δ

+ are intrinsicallydeformed

The naive quark model (NQM) [23ndash27] is one of thesimplest model to describe the hadron properties and inter-actions in the low energy regime This model is able toprovide a simple intuitive picture of the hadron structure interms of three valence quarks (119902119902119902) for baryons and quarkantiquark (119902119902) for mesons It allows the direct calculationsof the low energy hadronic matrix elements including theirspectra and successfully accounts for many of the low energyproperties of the hadrons in terms of the valence quarks[28ndash32] Interestingly with the inclusion of the spin-spininteractions generated configurationmixing [28] between thevalence quarks the NQM has not only given an accuratedescription of the hadron spectroscopy data but also has beenable to describe some subtle features of the data including the119873minusΔmass difference photohelicity amplitudes and baryonmagnetic moments [29ndash36] However some major findingson the experimental front discussed below have brought intoprominence the inadequacies of the NQM

The measurements in the deep inelastic scattering (DIS)experiments [2 3] indicate that the valence quarks of theproton carry only about 30 of its spin and also establishethe asymmetry of the quark distribution functions [37ndash41]This is referred to as the ldquoproton spin problemrdquo in NQMSeveral effective and phenomenological models have beendeveloped to explain the ldquoproton spin problemrdquo by includingspontaneous breaking of chiral symmetry and have beenfurther applied to study the electromagnetic properties ofbaryons

For the calculations pertaining to the baryon chargeradii NQM leads to vanishing charge radii for the neutralbaryons like 119899 Σ0 Ξ0 and Λ This is in contradiction tothe experimental data The inclusion of quark spin-spininteractions in NQM modify the baryon wavefunction tosome extent leading to the breaking of the SU(3) symmetryand a nonvanishing neutron charge mean square radius[29ndash32] A likely cause of these dynamical shortcomings

is that the NQM does not respect chiral symmetry whosespontaneous breaking leads to the emission of Goldstonebosons (GBs) In this context it becomes important toincorporate the effect of chiral symmetry breaking (120594SB)in the phenomenological models to obtain a reasonableagreement with the data On the other hand a wide varietyof accurately measured data have been accumulated forthe static low energy properties of baryons for examplemasses electromagnetic moments charge radii and lowenergy dynamical properties such as scattering lengths anddecay rates which has renewed considerable interest in thelow energy baryon spectroscopy The direct calculations ofthese quantities from the first principle of QCD are extremelydifficult as they require the nonperturbativemethods Severaleffective and phenomenological models such as Lattice QCDeffective field theories QCD sum rules and variants ofquark models have been developed to explain the failuresof the NQM and further applied to study the properties ofbaryons

Some of the important models measuring the chargeradii of octet baryon are the Skyrme model with bound stateapproach [42ndash44] slow-rotor approach [45] semibosonizedSU(3) NJL model [46] cloudy bag model [47] variants ofconstituent quark models [48ndash54] 1119873

119888expansion approach

[55ndash58] perturbative chiral quark model (P120594QM) [59]heavy-baryon chiral perturbation theory (HB120594PT) [60]chiral perturbation theory (120594PT) [61 62] Lattice QCD [63]and so forth The charge radii of decuplet baryons havebeen studied within the framework of Lattice QCD [64ndash66]quark model [67] 1119873

119888expansion [55 56] chiral pertur-

bation theory [68] and so forth The results for differenttheoretical models are however not consistent with eachother

There have been a lot of theoretical investigations inunderstanding the implications of the 11986221198721 and 11986421198721

ratios in finding out the exact sign of deformation in thespin (12)

+ octet baryons However there is a little consensusbetween the results even with respect to the sign of thenucleon deformation Some of the models predict the defor-mation in nucleon as oblate [69 70] some predict a prolatenucleon deformation [71ndash80] whereas others speak aboutldquodeformationrdquo without specifying the sign The quadrupolemoment of the (32)+ decuplet baryons has also been studiedusing the variants of the constituent quark model (CQM)[81ndash84] chiral quark soliton model (120594QSM) [85] spectatorquark model [86ndash88] slow-rotator approach (SRA) [89 90]skyrme model [91 92] general parametrization method[93 94] light cone QCD sum rules (QCDSR) [95 96]large 119873

119888[97 98] chiral perturbation theory (120594PT) [99ndash

103] Lattice QCD (LQCD) [104ndash108] and so forth In thiscase also the results for different theoretical models arenot consistent in terms of sign and magnitude with eachother

As the hadron structure is sensitive to the pion cloudin the low energy regime a coherent understanding isnecessary as it will provide a test for the QCD-inspiredeffective field theories One of the important nonperturbativeapproaches which finds its application in the low energyregime is the chiral constituent quark model (120594CQM) [109

Advances in High Energy Physics 3

110] It is one of the most convenient languages for thetreatment of light hadrons at low energies using the effectiveinteraction Lagrangian approach of the strong interactionsThe 120594CQM coupled with the ldquoquark seardquo generation throughthe chiral fluctuation of a constituent quark GBs [111ndash119] successfully explains the ldquoproton spin problemrdquo [117ndash119] hyperon 120573 decay parameters [120 121] strangenesscontent in the nucleon [122ndash124] magnetic moments of octetand decuplet baryons including their transitions [125ndash127]magnetic moments of (12)minus octet baryon resonances [128]magnetic moments of (12)minus and (32)

minus

Λ resonances [129]charge radii [130] quadrupole moment [131] and so forthThe model is successfully extended to predict the importantrole played by the small intrinsic charm (IC) content in thenucleon spin in the SU(4) 120594CQM [132] and to the calculatethe magnetic moment of spin (12)

+ and spin (32)+ charm

baryons including their radiative decays [133] In view of theabove developments in the 120594CQM it become desirable toextend themodel to calculate the charge radii and quadrupolemoment of the spin (12)

+ octet and spin (32)+ decuplet

baryonsThe purpose of the present communication is to cal-

culate the charge radii of the spin (12)+ octet and spin

(32)+ decuplet baryons and quadrupole moment of the

spin (32)+ decuplet baryons including the spin (32)

+

rarr

(12)+ transitions within the framework of 120594CQM using a

general parametrization method (GPM) [134ndash138] In orderto understand the role of pseudoscalar mesons in the baryoncharge radii and quadrupole moment we will compare ourresults with NQMas well as other phenomenological modelsThe detailed analysis of SU(3) symmetry breaking would alsobe carried out in the 120594CQM Further we aim to discuss theimplications of GPM parameters by calculating the extent towhich the three-quark term contributes

2 Charge Radii and Quadrupole Moments

Themean square charge radii (1199032B) and quadrupole moments(119876B) are the lowest order moments of the charge density120588 in a low-momentum expansion The charge radii containfundamental information about the possible ldquosizerdquo of thebaryons whereas the ldquoshaperdquo of a spatially extended particleis determined by its quadrupole moment [139ndash142]

The mean square charge radius 1199032

B of a given baryon is ascalar under spatial rotation and is defined as

⟨1199032

⟩ = int1198893

119903120588 (r) 1199032 (1)

where 120588(r) is the charge density The intrinsic quadrupolemoment with respect to the body frame of axis is defined as

1198760= int119889

3r120588 (r) (31199112 minus 1199032

) (2)

For the charge density concentrated along the 119911-direction theterm proportional to 3119911

2 dominates 1198760is positive and the

particle is prolate shaped If the charge density is concentratedin the equatorial plane perpendicular to 119911 axis the term

proportional to 1199032 dominates119876

0is negative and the particle

is oblate shapedThe most general form of the multipole expansion of

the nucleon charge density 120588 in the spin-flavor space can beexpressed as

120588 = A1015840

3

sum

119894=1

1198901198941 minus B1015840

3

sum

119894 = 119895

119890119894[2120590

119894sdot 120590

119895minus (3120590

119894119911120590119895119911

minus 120590119894sdot 120590

119895)]

minus C1015840

3

sum

119894 = 119895 = 119896

119890119894[2120590

119895sdot 120590

119896minus (3120590

119895119911120590119896119911

minus 120590119895sdot 120590

119896)]

(3)

The charge radii operator composed of the sum of one- two-and three-quark terms is expressed as

1199032 = A3

sum

119894=1

1198901198941 + B

3

sum

119894 = 119895

119890119894120590119894sdot 120590

119895+ C

3

sum

119894 = 119895 = 119896

119890119894120590119895sdot 120590

119896 (4)

whereas the quadrupole moment operator composed of atwo- and three-quark term can be expressed as

119876 = B1015840

3

sum

119894 = 119895

119890119894(3120590

119894119911120590119895119911

minus 120590119894sdot 120590

119895)

+ C1015840

3

sum

119894 = 119895 = 119896

119890119894(3120590

119895119911120590119896119911

minus 120590119895sdot 120590

119896)

(5)

The coefficients called GPM parameters of the charge radiiand quadrupole moments are related to each other as A =

A1015840 B = minus2B1015840 and C = minus2C1015840 These GPM parameters are tobe determined from the experimental observations on chargeradii and quadrupole moment

Before calculating the matrix elements corresponding tothe charge radii and quadrupole moment it is essential tosimplify various operator terms involved in (4) It can beeasily shown that

sum

119894 = 119895

119890119894(120590i sdot 120590j) = 2J sdot sum

119894

119890119894120590i minus 3sum

119894

119890119894

sum

119894 = 119895 = 119896

119890119894(120590j sdot 120590k) = plusmn3sum

119894

119890119894minus sum

119894 = 119895

119890119894(120590i sdot 120590j)

(6)

where +ve sign holds for 119869 = 32 and minusve sign for 119869 = 12

states leading to different operators for spin (12)+ and spin

(32)+ baryons

Operator sum119894 = 119895

119890119894(120590i sdot 120590j) sum

119894 = 119895 = 119896

119890119894(120590j sdot 120590k)

119869 =1

23sum

119894

119890119894120590iz minus 3sum

119894

119890119894

minus3sum119894

119890119894120590iz

119869 =3

25sum

119894

119890119894120590iz minus 3sum

119894

119890119894

6sum119894

119890119894minus 5sum

119894

119890119894120590iz

(7)


The charge radii operators for the spin (12)+ octet and

spin (32)+ decuplet baryons can now be expressed as

1199032B = (A minus 3B)sum119894

119890119894+ 3 (B minus C)sum

119894

119890119894120590119894119911 (8)

1199032Blowast = (A minus 3B + 6C)sum

119894

119890119894+ 5 (B minus C)sum

119894

119890119894120590iz (9)

It is clear from the above equations that the determinationof charge radii basically reduces to the evaluation of theflavor (sum

119894119890119894) and spin (sum

119894119890119894120590119894119911) structure of a given baryon

The charge radii squared 1199032

B(Blowast) for the octet (decuplet)baryons can now be calculated by evaluatingmatrix elementscorresponding to the operators in (8) and (9) and are given as

1199032

B = ⟨B1003816100381610038161003816100381610038161199032B

100381610038161003816100381610038161003816B⟩ 119903

2

119861lowast

= ⟨Blowast1003816100381610038161003816100381610038161199032Blowast

100381610038161003816100381610038161003816Blowast

⟩ (10)

Here |B⟩ and |Blowast⟩ respectively denote the spin-flavor wave-

functions for the spin (12)+ octet and the spin (32)

+

decuplet baryonsThe quadrupole moment operators for the spin (12)

+spin (32)

+ baryons and spin (32)+

rarr (12)+ transitions

can be calculated from the operator in (5) and are expressedas

119876B = B1015840

(3sum

119894 = 119895

119890119894120590iz120590jz minus 3sum

119894

119890119894120590iz + 3sum

119894

119890119894)

+ C1015840

(3 sum

119894 = 119895 = 119896

119890119894120590jz120590kz + 3sum

119894

119890119894120590iz)

119876Blowast = B1015840

(3sum

119894 = 119895

119890119894120590iz120590jz minus 5sum

119894

119890119894120590iz + 3sum

119894

119890119894)

+ C1015840

(3 sum

119894 = 119895 = 119896

119890119894120590jz120590kz + 5sum

119894

119890119894120590iz minus 6sum

119894

119890119894)

119876BlowastB = 3B1015840

sum

119894 = 119895

119890119894120590iz120590jz + 3C1015840

sum

119894 = 119895 = 119896

119890119894120590jz120590kz

(11)

It is clear from the above equations that the determination ofquadrupolemoment basically reduces to the evaluation of theflavor (sum

119894119890119894) spin (sum

119894119890119894120590iz) and tensor terms (sum

119894119890119894120590iz120590jz)

and (sum119894119890119894120590jz120590kz) for a given baryon

Using the three-quark spin-flavor wavefunctions for thespin (12)

+ octet and spin (32)+ decuplet baryons the

quadrupole moment can now be calculated by evaluating thematrix elements of operators in (11) We now have

119876B = ⟨B 10038161003816100381610038161003816119876B

10038161003816100381610038161003816B⟩ 119876Blowast = ⟨Blowast 10038161003816100381610038161003816

119876Blowast10038161003816100381610038161003816Blowast

⟩

119876BrarrBlowast = ⟨Blowast 10038161003816100381610038161003816119876BlowastB

10038161003816100381610038161003816B⟩

(12)

3 Naive Quark Model (NQM)

The appropriate operators for the spin and flavor structure ofbaryons in NQM are defined as

sum

119894

119890119894= sum

119902=119906119889119904

119899B119902119902 + sum

119902=119906119889119904

119899B119902119902

= 119899B119906119906 + 119899

B119889119889 + 119899

B119904119904 + 119899

B119906119906 + 119899

B119889119889 + 119899

B119904119904

sum

119894

119890119894120590119894119911

= sum

119902=119906119889119904

(119899B119902+

119902++ 119899

B119902minus

119902minus)

= 119899B119906+

119906++ 119899

B119906minus

119906minus+ 119899

B119889+

119889++ 119899

B119889minus

119889minus+ 119899

B119904+

119904++ 119899

B119904minus

119904minus

(13)

where 119899B119902(119899

B119902) is the number of quarks with charge 119902 (119902) and

119899B119902+

(119899B119902minus

) is the number of polarized quarks 119902+(119902

minus) For a

given baryon 119906 = minus119906 and 119906+= minus119906

minus with similar relations for

the 119889 and 119904 quarksThe general expression for the charge radiiof any of the spin (12)

+ octet baryon in (4) can be expressedas

1199032B = (A minus 3B)(sum

119906119889119904

119899119902minus sum

119906119889119904

119899119902)119902

+ 3 (B minus C) (sum

119906119889119904

119899119902+

minus sum

119906119889119904

119899119902minus

)119902+

(14)

Before we discuss the details of the charge radii cal-culations it is essential to define the octet and decupletwavefunctions The ldquomixedrdquo state octet baryon wavefunctiongenerated by the spin-spin forces [33 34] which improves thepredictions of the various spin-related properties [117ndash119] isexpressed as

|B⟩ equiv

100381610038161003816100381610038161003816100381610038168

1

2

+

⟩ = cos 120579100381610038161003816100381656 0+

⟩119873=0

+ sin 120579100381610038161003816100381670 0

+

⟩119873=2

(15)

with

100381610038161003816100381656 0+

⟩119873=0

=1

radic2(120593

1015840

1205941015840

+ 12059310158401015840

12059410158401015840

) 120595119904

(0+

)

100381610038161003816100381670 0+

⟩119873=2

=1

2[(120593

1015840

12059410158401015840

+ 12059310158401015840

1205941015840

) 1205951015840

(0+

)

+ (1205931015840

1205941015840

minus 12059310158401015840

12059410158401015840

) 12059510158401015840

(0+

)]

(16)

Here 120579 is the mixing angle and 120594 120593 and 120595 are the spinisospin and spatial wavefunctions For the details of thewavefunction we refer the readers to [33 34] Using the


Table 1 Charge radii of octet baryons in NQMconfig in terms of the GPM parameters The results in NQM without configuration can easilybe calculated by substituting 120579 = 0

Charge radii NQMconfig

1199032

119901(A minus 3B)[2119906 + 119889] + (B minus C) [cos2120579(4119906

+minus 119889

+) + sin2

120579 (2119906++ 119889

+)]

1199032

119899(A minus 3B)[119906 + 2119889] + (B minus C) [cos2120579(minus119906

++ 4119889

+) + sin2

120579 (119906++ 2119889

+)]

1199032

Σ+

(A minus 3B)[2119906 + 119904] + (B minus C) [cos2120579(4119906+minus 119904

+) + sin2

120579 (2119906++ 119904

+)]

1199032

Σminus

minus(A minus 3B)[2119889 + 119904] minus (B minus C) [cos2120579(4119889+minus 119904

+) + sin2

120579 (2119889++ 119904

+)]

1199032

Σ0

(A minus 3B)[119906 + 119889 + 119904] + (B minus C) [cos2120579(2119906++ 2119889

+minus 119904

+) + sin2

120579 (119906++ 119889

++ 119904

+)]

1199032

Ξ0

(A minus 3B)[119906 + 2119904] + (B minus C) [cos2120579(minus119906++ 4119904

+) + sin2

120579 (119906++ 2119904

+)]

1199032

Ξminus

minus(A minus 3B)[119889 + 2119904] + (B minus C) [cos2120579(minus119889++ 4119904

+) + sin2

120579 (119889++ 2119904

+)]

1199032

Λ(A minus 3B)[119906 + 119889 + 119904] + (B minus C) [cos2120579(3119904

+) + sin2

120579 (119906++ 119889

++ 119904

+)]

1199032

ΣΛ(A minus 3B)[119906 + 119889 + 119904] + radic3(B minus C) [119906

+minus 119889

+]

Table 2 Charge radii of decuplet baryons in NQM in terms of GPMparameters

Chargeradii NQM

1199032

Δ++

1

2[(A minus 3B + 6C)(3119906) + 5(B minus C)(3119906

+)]

1199032

Δ+ (A minus 3B + 6C)(2119906 + 119889) + 5(B minus C)(2119906

++ 119889

+)

1199032

Δ0 (A minus 3B + 6C)(119906 + 2119889) + 5(B minus C)(119906

++ 2119889

+)

1199032

Δminus minus(A minus 3B + 6C)(3119889) minus 5(B minus C)(3119889

+)

1199032

Σlowast+ (A minus 3B + 6C)(2119906 + 119904) + 5(B minus C)(2119906

++ 119904

+)

1199032

Σlowastminus minus(A minus 3B + 6C)(2119889 + 119904) minus 5(B minus C)(2119889

++ 119904

+)

1199032

Σlowast0 (A minus 3B + 6C)(119906 + 119889 + 119904) + 5(B minus C)(119906

++ 119889

++ 119904

+)

1199032

Ξlowast0 (A minus 3B + 6C)(119906 + 2119904) + 5(B minus C)(119906

++ 2119904

+)

1199032

Ξlowastminus minus(A minus 3B + 6C)(119889 + 2119904) minus 5(B minus C)(119889

++ 2119904

+)

1199032

Ωminus

minus(A minus 3B + 6C)(3119904) minus 5(B minus C)(3119904+)

ldquomixedrdquo wavefunction (15) the charge radii for the 119901 and Σ+

from (14) can now be expressed as

1199032

119901= (A minus 3B) (2119906 + 119889) + 3 (B minus C)

times [cos2120579 (4

3119906+minus

1

3119889+) + sin2

120579 (2

3119906++

1

3119889+)]

1199032

Σ+

= (A minus 3B) (2119906 + 119904) + 3 (B minus C)


3119906+minus

1

3119904+) + sin2

120579 (2

3119906++

1

3119904+)]

(17)

The expressions for the charge radii of other octet baryons inNQM with configuration mixing (NQMconfig) are presentedin Table 1The results without configurationmixing can easilybe obtained by taking the mixing angle 120579 = 0

Configuration mixing generated by the spin-spin forcesdoes not affect the spin (32)

+ decuplet baryons The wave-function in this case is given as

1003816100381610038161003816Blowast

⟩ equiv

1003816100381610038161003816100381610038161003816100381610

3

2

+

⟩ =100381610038161003816100381656 0

+

⟩119873=0

= 120594119904

120593119904

120595119904

(0+

) (18)

Using the baryon wavefunction from the above equation andthe charge radii operator from (9) the general expression forthe charge radii of spin (32)

+ baryons can be expressed as

1199032Blowast = (A minus 3B + 6C)(sum

119906119889119904

119899119902minus sum

119906119889119904

119899119902)119902


119906119889119904

119899119902+

minus sum

119906119889119904

119899119902minus

)119902+

(19)

As an example the charge radii for Δ+ baryon can be

expressed as

1199032

Δ+

= (A minus 3B + 6C) (2119906 + 119889) + 5 (B minus C) (2119906++ 119889

+) (20)

The expressions for the charge radii of other decuplet baryonsin NQM are presented in Table 2

For the spin (12)+ octet baryons the quadrupole

moment of 119901 and Σ+ in NQM can be expressed as

119876119901= 3B1015840

(2119906 + 119889 minus 2119906+minus 119889

+)

+ C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119876Σ+ = 3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+)

+ C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

(21)


For the spin (32)+ decuplet baryons the quadrupole

moment of Δ+ and Ξlowastminus can be expressed as

119876Δ+ = B1015840

(6119906 + 3119889 + 2119906++ 119889

+)

+ C1015840

(minus6119906 minus 3119889 + 10119906++ 5119889

+)

119876Ξlowastminus = B1015840

(3119889 + 6119904 + 119889++ 2119904

+)

+ C1015840

(minus3119889 minus 6119904 + 5119889++ 10119904

+)

(22)

Similarly for the spin (32)+

rarr (12)+ transitions the

quadrupole moment of the Δ+119901 and Σ

lowastminusΣminus transitions can

be expressed as

119876Δ+

119901= 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889)

119876Σlowastminus

Σminus = 2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)

(23)

The expressions for quadrupole moment of the other (12)+octet and (32)

+ decuplet baryons and for spin (32)+

rarr

(12)+ transitions in NQM can similarly be calculated The

results are presented in Tables 7 8 and 9

4 Chiral Constituent Quark Model (120594CQM)

In light of the recent developments and successes of the120594CQM in explaining the low energy phenomenology [117ndash127] we formulate the quadrupole moments for the (32)

+

decuplet baryons and spin (32)+


The basic process in the 120594CQM is the Goldstone boson (GB)

emission by a constituent quark which further splits into a 119902119902pair as

119902plusmn997888rarr GB0

+ 1199021015840

∓997888rarr (119902119902

1015840

) + 1199021015840

∓ (24)

where 1199021199021015840

+ 1199021015840 constitute the ldquoquark seardquo [111ndash116] The effec-

tive Lagrangian describing the interaction between quarksand a nonet of GBs is

L = 1198928119902Φ

1015840

119902 (25)

with

119902 = (

119906

119889

119904

)

Φ1015840

= (

1205870

radic2

+120573

120578

radic6

+ 120577

1205781015840

radic3

120587+

120572119870+

120587minus

minus

1205870

radic2

+ 120573

120578

radic6

+ 120577

1205781015840

radic3

1205721198700

120572119870minus

120572119870

0

minus120573

2120578

radic6

+ 120577

1205781015840

radic3

)

(26)

where 120577 = 1198921119892

8 119892

1and 119892

8are the coupling constants for

the singlet and octet GBs respectively If the parameter 119886 (=

|1198928|2) denotes the transition probability of chiral fluctuation

of the splitting 119906(119889) rarr 119889(119906) + 120587+(minus) then 120572

2119886 1205732

119886 and 1205772119886

respectively denote the probabilities of transitions of 119906(119889) rarr

119904 + 119870minus(0) 119906(119889 119904) rarr 119906(119889 119904) + 120578 and 119906(119889 119904) rarr 119906(119889 119904) +

1205781015840 SU(3) symmetry breaking is introduced by considering

119872119904gt 119872

119906119889as well as by considering the masses of GBs to

be nondegenerate (119872119870120578

gt 119872120587and119872

1205781015840 gt 119872

119870120578) [111ndash119]

In terms of the quark contents the GB field can beexpressed as

Φ1015840

= (

120601119906119906

119906119906 + 120601119906119889

119889119889 + 120601119906119904119904119904 120593

119906119889119906119889 120593

119906119904119906119904

120593119889119906

119889119906 120601119889119906

119906119906 + 120601119889119889

119889119889 + 120601119889119904119904119904 120593

119889119904119889119904

120593119904119906119904119906 120593

119904119889119904119889 120601

119904119906119906119906 + 120601

119904119889119889119889 + 120601

119904119904119904119904) (27)

where

120601119906119906

= 120601119889119889

=1

2+

120573

6+

120577

3 120601

119904119904=

2120573

3+

120577

3

120601119906119904

= 120601119889119904

= 120601119904119906

= 120601119904119889

= minus120573

3+

120577

3

120601119889119906

= 120601119906119889

= minus1

2+

120573

6+

120577

3 120593

119906119889= 120593

119889119906= 1

120593119906119904

= 120593119889119904

= 120593119904119906

= 120593119904119889

= 120572

(28)

A redistribution of flavor and spin structure takes place inthe interior of baryon due to the chiral symmetry breaking

and the modified flavor and spin content of the baryon canbe calculated by substituting for every constituent quark

119902 997888rarr 119875119902119902 +

1003816100381610038161003816120595 (119902)10038161003816100381610038162

119902plusmn997888rarr 119875

119902119902plusmn+1003816100381610038161003816120595 (119902

plusmn)10038161003816100381610038162

(29)

Here119875119902= 1minussum119875

119902is the transition probability of no emission

of GB from any of the 119902 quark with

sum119875119906= 119886 (120601

2

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904)

sum119875119889= 119886 (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904)


sum119875119904= 119886 (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889)

(30)

and |120595(119902)|2 (|120595(119902

plusmn)|2) are the transition probabilities of the

emission of 119902 (119902plusmn) quark

1003816100381610038161003816120595 (119906)10038161003816100381610038162

= 119886 [(21206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904) 119906 + 120601

2

119906119906119906

+ (1206012

119906119889+ 120593

2

119906119889) (119889 + 119889) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119889)10038161003816100381610038162

= 119886 [(1206012

119889119906+ 2120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904) 119889 + 120601

2

119889119889119889

+ (1206012

119889119906+ 120593

2

119889119906) (119906 + 119906) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119904)10038161003816100381610038162

= 119886 [(1206012

119904119906+ 120601

2

119904119889+ 2120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889) 119904 + 120601

2

119904119904119904

+ (1206012

119904119906+ 120593

2

119904119906) (119906 + 119906) + (120601

2

119904119889+ 120593

2

119904119889) (119889 + 119889)]

1003816100381610038161003816120595 (119906plusmn)10038161003816100381610038162

= 119886 [(1206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904) 119906

∓+ 120593

2

119906119889119889∓+ 120593

2

119906119904119904∓]

1003816100381610038161003816120595 (119889plusmn)10038161003816100381610038162

= 119886 [1205932

119889119906119906∓+ (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904) 119889

∓+ 120593

2

119889119904119904∓]

1003816100381610038161003816120595 (119904plusmn)10038161003816100381610038162

= 119886 [1205932

119904119906119906∓+ 120593

2

119904119889119889∓+ (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904) 119904

∓]

(31)

After the inclusion of ldquoquark seardquo the charge radii forthe spin (12)

+ octet baryons in 120594CQM with configurationmixing (120594CQMconfig) can be obtained by substituting (29) foreach quark in (17) The charge radii for the case of 119901 and Σ

+

are now expressed as

1199032

119901= (A minus 3B) (2119875

119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

minus1

3119875119889119889+minus

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119889119889++

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)]

1199032

Σ+

= (A minus 3B) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119904119904 +

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906)10038161003816100381610038162

minus1

3119875119904119904+minus

1

3

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119904119904++

1

3

1003816100381610038161003816120595 (119904+)10038161003816100381610038162

)]

(32)

The charge radii in the 120594CQMconfig for other spin (12)+

octet baryons are presented in Table 3 The results without

configuration mixing can easily be obtained by taking themixing angle 120579 = 0

Similarly for the spin (32)+ decuplet baryons the charge

radii are modified on substituting for each quark from (29)For example the charge radii for Δ

+ in 120594CQM can beexpressed as

1199032

Δ+

= (A minus 3B + 6C) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 5 (B minus C) (2119875119906119906++ 2

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+ 119875119889119889++1003816100381610038161003816120595 (119889

+)10038161003816100381610038162

)

(33)

The charge radii of the other decuplet baryons can becalculated similarly and are detailed in Table 4

After the inclusion of ldquoquark seardquo the quadrupolemoment for the spin (12)

+ octet baryons vanishes onaccount of the effective cancelation of contribution comingfrom the ldquoquark seardquo and the orbital angular momentumas observed spectroscopically For the spin (32)

+ decupletbaryons the quadrupole moment in 120594CQM can be obtainedby substituting (29) for each quark in (21) The quadrupolemoment of Δ+ and Ξ

lowastminus in 120594CQM can be expressed as

119876Δ+

= 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

) 119886(2 +1205732

3+

21205772

3)

119876Ξlowastminus

= minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

) 119886(4120572

2

3+ 120573

2

+2120577

2

3)

(34)

Similarly the quadrupole moment of Δ+119901 and Σ

lowastminusΣminus

transitions in 120594CQM can be expressed as

119876Δ+

119901

= 2radic2[B1015840

(1 minus 119886(1 + 1205722

+1205732

3+

21205772

3)) minus C1015840

]

119876Σlowastminus

Σminus

= 2radic2B1015840

119886(1205722

3minus

1205732

3)

(35)

The expressions for the quadrupole moment of other (32)+decuplet baryons and spin (32)

+

rarr (12)+ transitions in

120594CQM can similarly be calculated The results are presentedin Tables 8 and 9

5 Results and Discussion

The calculations of charge radii and quadrupole moment ofoctet and decuplet baryons involve two set of parametersthe SU(3) symmetry breaking parameters of 120594CQM and theGPM parameters The 120594CQM parameters 119886 1198861205722 1198861205732 and119886120577

2 represent respectively the probabilities of fluctuations topions 119870 120578 and 120578

1015840 A best fit of 120594CQM parameters can beobtained by carrying out a fine grained analysis of the spinand flavor distribution functions [117ndash119] leading to

119886 = 012 120572 = 07 120573 = 04 120577 = minus015 (36)


Table 3 Charge radii of octet baryons in 120594CQMconfig in terms of SU(3) symmetry breaking parameters and GPM parameters These resultsare obtained by substituting 119902 rarr 119875

119902119902 + |120595(119902)|

2 and 119902plusmn

rarr 119875119902119902plusmn+ |120595(119902

plusmn)|2 for every constituent quark in NQM Results in 120594CQM without

configuration mixing can easily be obtained by substituting the mixing angle 120579 = 0

Charge radii 120594CQMconfig

1199032

119901 A minus 3B + (B minus C) [cos2120579 (3 minus 119886 (4 + 21205722

+ 1205732

+ 21205772

)) + sin2

120579 (1 minus119886

3(6 + 120573

2

+ 21205772

))]

1199032

119899 (B minus C) [cos2120579 (minus2 +119886

3(3 + 9120572

2

+ 21205732

+ 41205772

)) + sin2

120579 (119886 (minus1 + 1205722

))]

1199032

Σ+ A minus 3B + (B minus C) [cos2120579 (3 minus

119886

3(12 + 5120572

2

+ 41205732

+ 61205772

)) + sin2

120579 (1 minus119886

3(6 + 120572

2

+ 21205772

))]

1199032

Σminus A minus 3B + (B minus C) [cos2120579 (minus1 +

119886

3(7120572

2

+ 21205772

)) + sin2

120579 (minus1 +119886

3(5120572

2

+ 21205732

+ 21205772

))]

1199032

Σ0 (B minus C) [cos2120579 (1 minus

119886

3(6 minus 120572

2

+ 21205732

+ 21205772

)) + sin2

120579 (119886

3(minus3 + 2120572

2

+ 1205732

))]

1199032

Ξ0 (B minus C) [cos2120579 (minus2 +

119886

3(3 + 5120572

2

+ 61205732

+ 41205772

)) + sin2

120579 (119886

3(minus3 + 120572

2

+ 21205732

))]

1199032

Ξminus A minus 3B + (B minus C) [cos2120579 (minus1 +

119886

3(2120572

2

+ 51205732

+ 21205772

)) + sin2

120579 (minus1 +119886

3(4120572

2

+ 31205732

+ 21205772

))]

1199032

Λ (B minus C) [cos2120579 (minus1 +119886

3(3120572

2

+ 41205732

+ 21205772

)) + sin2

120579 (119886

9(minus9 + 6120572

2

+ 71205732

+ 21205772

))]

1199032

ΣΛ (B minus C) [radic3 minus119886

radic3(3 + 3120572

2

+ 1205732

+ 21205772

)]

Table 4 Charge radii of decuplet baryons in 120594CQM in terms ofSU(3) symmetry breaking parameters and GPM parameters Theseresults are obtained by substituting 119902 rarr 119875

119902119902 + |120595(119902)|

2 and 119902plusmn

rarr

119875119902119902plusmn+ |120595(119902

plusmn)|2 for every constituent quark in NQM

Charge radii 120594CQM

1199032

Δ++

A + 2B + C minus5119886

6(B minus C)(9 + 3120572

2

+ 21205732

+ 41205772

)

1199032

Δ+

A + 2B + C minus5119886

3(B minus C)(6 + 120573

2

+ 21205772

)

1199032

Δ0 5119886(B minus C)(minus1 + 120572

2

)

1199032

Δminus

A + 2B + C minus5119886

3(B minus C)(6120572

2

+ 1205732

+ 21205772

)

1199032

Σlowast+

A + 2B + C minus5119886

3(B minus C)(6 + 120572

2

+ 21205772

)

1199032

Σlowastminus

A + 2B + C minus5119886

3(B minus C)(5120572

2

+ 21205732

+ 21205772

)

1199032

Σlowast0

5119886

3(B minus C)(minus3 + 2120572

2

+ 1205732

)

1199032

Ξlowast0

5119886


2

+ 21205732

)

1199032

Ξlowastminus A + 2B + C minus

5119886

3(B minus C)(4120572

2

+ 31205732

+ 21205772

)

1199032

Ωminus

A + 2B + C minus5119886

3(B minus C)(3120572

2

+ 41205732

+ 21205772

)

Themixing angle 120579 is fixed from the consideration of neutroncharge radius [28] This set of parameters has already beentested for a wide variety of low energy matrix elementsand has been able to give a simultaneous fit to the quan-tities describing proton spin and flavor structure [117ndash119]weak vector-axial vector form factors [120 121] strangeness

content in the nucleon [122ndash124] octet and decuplet baryonsmagnetic moments [125ndash127] and so forth

The order of GPM parameters corresponding to the one-two- and three-quark terms decreases with the increasingcomplexity of terms and obeys the hierarchy A gt B gt C[143 144]These are fitted by using the available experimentalvalues for the charge radii and quadrupole moment ofnucleon as input In the present case we have used 119903

119901=

0877 plusmn 0007 fm [12] 1199032

119899= minus01161 plusmn 00022 fm2 [12]

and 119876Δ+

119873= minus00846 plusmn 00033 fm2 [19] The set of GPM

parameters obtained after 1205942 minimization are as follows

A = 0879 B = 0094 C = 0016 (37)

For the quadrupole moment calculations best fit set ofparameters obtained after 1205942 minimization are as follows

B1015840

= minus0047 C1015840

= minus0008 (38)

obeying the hierarchy B1015840gt C1015840 [143 144] corresponding

to the two- and three-quark contribution Since we alsointend to investigate the extent to which the three-quark termcontributes we calculate the charge radii corresponding tothe one- and two-quark terms only by taking C = 0 Similarlyif we intend to calculate the charge radii corresponding to justthe one-quark term we can take B = C = 0

Using the set of parameters discussed above we havecalculated the numerical values for the charge radii of octetand decuplet baryons in120594CQMconfig and presented the resultsin Tables 5 and 6 respectively To understand the implicationsof chiral symmetry breaking and ldquoquark seardquo we have alsopresented the results ofNQMaswell as comparing our resultswith the predictions of other available phenomenologicalmodels Since the calculations in 120594CQM have been carried


Table 5 Charge radii of octet baryons calculated in 120594CQM in comparison with other phenomenological models (in units of fm2)

Charge radii NQM RCQM[51]

HB120594PT[60]

120594PT [61 62] CCQM[52]

P120594QM [59] 1119873119888

[57 58]Lattice[63]

120594CQMconfig

With SU(3)

symmetryWith SU(3) symmetry breaking

A = 0879

B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

1199010813 mdash 0735 0717 082 072 plusmn 009 0779 0685 0732 0801 0766

119903119901=

0877 plusmn 0007

1199032

119899minus0138 mdash minus0113 minus0113 minus013 minus0111plusmn 0014 minus0116 minus0158 minus0087 minus0140 minus0116

minus01161plusmn 000221199032

Σ+

0813 079 1366 060 plusmn 002 113 081 plusmn 010 0928 0749 0732 0802 07671199032

Σminus

0675 049 0798 067 plusmn 003 072 071 plusmn 007 0672 0657 0646 0678 0664061 plusmn 021 [13]1199032

Σ0

0069 015 mdash minus003plusmn 001 020 005 plusmn 001 0128 mdash 0043 0062 00521199032

Ξ0

minus0138 014 minus0122 013 plusmn 003 minus019 014 plusmn 002 0132 minus0082 minus0087 minus0145 minus01201199032

Ξminus

0675 047 0997 049 plusmn 005 054 062 plusmn 007 0520 0502 0646 0683 06691199032

Λminus0069 0038 minus0284 011 plusmn 002 003 005 plusmn 001 0050 0010 minus0042 minus0076 minus0063

1199032

ΣΛ0135 minus012 0074 003 plusmn 001 mdash 00 minus0066 mdash 0085 0132 0109

Table 6 Charge radii of decuplet baryons calculated in 120594CQM in comparison with other phenomenological models (in units of fm2)

Charge radii NQM FTQM [67] CCQM [52] 1119873119888[57 58] Lattice [64ndash66]

120594CQMWith SU(3)

symmetryWith SU(3) symmetry breakingA = 0879

B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

Δ++

1084 118 043 1011 mdash 0938 0961 09961199032

Δ+

1084 082 043 1011 0410 (57) 0938 0946 09831199032

Δ0

00 016 000 00 mdash 00 minus0030 minus00251199032

Δminus

1084 084 043 1011 minus0410 (57) 0938 1006 10331199032

Σlowast+

1084 097 042 1086 0399 (45) 0938 0940 09781199032

Σlowastminus

1084 084 037 0845 minus0360 (32) 0938 1013 10381199032

Σlowast0

00 034 003 0127 0020 (7) 00 minus0036 minus00301199032

Ξlowast0

00 049 006 0244 0043 (10) 00 minus0043 minus00351199032

Ξlowastminus

1084 082 033 0692 minus0330 (20) 0938 1019 10431199032

Ωminus

0390 078 029 0553 mdash 0245 0429 0355

out using theGPM theNQMresults have also beenpresentedby including the one- two- and three-quark contributionsof the GPM parameters It is clear from Tables 1 and 2that if we consider the contribution coming from one-quark term only the charge radii of the charged baryonsare equal whereas all neutral baryons have zero charge radiiThese predictions are modified on the inclusion of two- andthree-quark terms of GPM and are further modified on theinclusion of ldquoquark seardquo and SU(3) symmetry breaking effectsThus it seems that the GPM parameters alone are able toexplain the experimentally observed nonzero charge radii ofthe neutral baryons However NQM is unable to account forthe ldquoproton spin problemrdquo and other related quantities theresults have been presented for 120594CQM The importance of

strange quark mass has been investigated by comparing the120594CQM results with and without SU(3) symmetry breakingThe SU(3) symmetry results can be easily derived fromTables3 and 4 by considering 120572 = 120573 = 1 and 120577 = minus1 The SU(3)

breaking results are in general higher in magnitude than theSU(3) symmetric results and the values obtained are also inagreement with the other models

For the case of octet baryons it can be easily shown fromTable 5 that in the SU(3) symmetric limit octet baryon chargeradii can be expressed in terms of the nucleon charge radiileading to the following relations

1199032

Σ+

= 1199032

119901 119903

2

Ξminus

= 1199032

Σminus

= 1199032

119901+ 119903

2

119899 (39)


Table 7 Quadrupole moments of the octet baryons in NQM usingthe GPM

Baryons NQM119901 3B1015840

(2119906 + 119889 minus 2119906+minus 119889

+) + C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119899 3B1015840

(119906 + 2119889 minus 119906+minus 2119889

+) + C1015840

(119906 minus 4119889 minus 119906++ 4119889

+)

Σ+

3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+) + C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

Σminus

3B1015840

(2119889 + 119904 minus 2119889+minus 119904

+) + C1015840

(minus4119889 + 119904 + 4119889+minus 119904

+)

Σ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+)

+C1015840

(minus2119906 minus 2119889 + 119904 + 2119906++ 2119889

+minus 119904

+)

Ξ0

3B1015840

(119906 + 2119904 minus 119906+minus 2119904

+) + C1015840

(119906 minus 4119904 minus 119906++ 4119904

+)

Ξminus

3B1015840

(119889 + 2119904 minus 119889+minus 2119904

+) + C1015840

(119889 minus 4119904 minus 119889++ 4119904

+)

Λ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+) + 3C1015840

(minus119904 + 119904+)

The inclusion of SU(3) symmetry breaking changes thispattern considerably and we get

1199032

Σ+

gt 1199032

119901 119903

2

Ξminus

gt 1199032

Σminus

gt 1199032

119901+ 119903

2

119899 (40)

Also we have

21199032

Λ= minus2119903

2

Σ0

= 1199032

Ξ0

= 1199032

119899 (41)

which has its importance in the isospin limit where the three-quark core in neutral baryons does not contribute to thecharge radii In the limit of SU(3) symmetry breaking anonvanishing value for the neutral baryons charge radii isgenerated by the ldquoquark seardquo through the chiral fluctuationsof constituent quarks leading to

1199032

Λgt minus119903

2

Σ0

1199032

Ξ0

gt 1199032

119899 (42)

The exact order of SU(3) symmetry breaking effects can beeasily found from Table 3 Since experimental information isnot available for some of these octet charge radii the accuracyof these relations can be tested by the future experiments Itis interesting to note that the relation for the Σ baryon chargeradii

1199032

Σ+

minus 21199032

Σ0

minus 1199032

Σminus

= 0 (43)

holds good even after incorporating SU(3) symmetry break-ing Since this relation is independent of SU(3) symmetrybreaking parameters any refinement in the Σ baryon chargeradii data would have important implications for SU(3)

symmetry breaking Further our predicted value 1199032

Σminus

=

0664 is clearly of the order of proton charge radius andis also in agreement with the recent SELEX collaborationexperimental results [12] It would be important to mentionhere that the 120594CQM parameters play an important role inthe SU(3) symmetry breaking effects whereas the assumedparametrization plays a dominant role in the valence quarkdistributions

In Table 3 we have presented the results for the case withconfiguration mixing generated by the spin-spin forces Wehave not presented the results without configuration mixingwhich can easily be obtained by taking the mixing angle 120579 =

0 It has been observed that configuration mixing decreasesthe overall magnitudes of the charge radii in 120594CQM but

the change is very small as compared to the other lowenergy properties like spin distribution function magneticmoments and so forth [117ndash127]

On comparing our results with the other phenomenolog-icalmodels we find that for the case of charged octet baryonsour results are in fair agreement in sign and magnitude withthe other model predictions However for the neutral octetbaryons 119899 Σ0 Ξ0 and Λ different models show oppositesign For example if we consider the charge radii for the Λ

baryon our model prediction (minus0063) is opposite in signto the predictions of the relativistic constituent quark model(RCQM) [51] covariant constituent quark model (CCQM)[52] 1119873

119888expansion [55 56] and P120594QM [59] On the other

hand it is in agreement with the sign of HB120594PT [60] Asimilar trend has been observed for the charge radii of ΣΛtransitionThe difference in the sign may be due to the chiralfluctuation of a constituent quark leading to the reversalof sign in case of neutral octet baryons This can perhapsbe substantiated by a measurement of charge radii of otherbaryons

The spin (32)+ decuplet baryon charge radii presented

in Table 6 are in general higher than the octet baryon chargeradii which are in line with the trend followed by the octetand decuplet baryons for the other low energy hadronicmatrix elements such as magnetic moments In this casealso the inclusion of SU(3) symmetry breaking increases thepredictions of charge radii It can be easily shown that SU(3)

symmetry results in the following relations for the decupletbaryons

1199032

Δ++

= 1199032

Δ+

= 1199032

Δminus

= 1199032

Σlowast+

= 1199032

Σlowastminus

= 1199032

Ξlowastminus

(44)

These results are affected by the inclusion of SU(3) symmetrybreaking and give

1199032

Ξlowastminus

gt 1199032

Σlowastminus

gt 1199032

Δminus

gt 1199032

Δ++

gt 1199032

Δ+

gt 1199032

Σlowast+

(45)

Some relations derived in 1119873119888expansion of QCD [55ndash58]

are found to be independent of SU(3) symmetry breakingparameters in 120594CQM Even though the individual chargeradii are affected by SU(3) symmetry breaking the effects arecanceled exactly for the following relations

21199032

Δ++

minus 1199032

Δ+

minus 1199032

Δ0

minus 1199032

Δminus

= 0

21199032

Δ++

minus 31199032

Δ+

+ 31199032

Δ0

+ 1199032

Δminus

= 0

1199032

Σlowast+

minus 21199032

Σlowast0

minus 1199032

Σlowastminus

= 0

(46)

In this case also SU(3) symmetry breaking is expected toreduce the charge radii with increasing strangeness contentAs a consequence Δminus Σminus and Ξ

minus should have successivelydecreasing charge radiiHowever this suppression disappearsin 120594CQM due to the effect of ldquoquark seardquo and the chargeradii of Δ

+ Σlowastminus and Ξlowast0 are of almost the same order as

that of Σlowast+ Ξlowastminus and Σlowast0 respectively Again the sign and

magnitude of the decuplet baryon charge radii in 120594CQM arein fair agreement with the other phenomenological modelswith the exception for neutral baryons One of the importantpredictions in 120594CQM is a nonzero Δ

0 charge radii which


Table 8 Quadrupole moments of the decuplet baryons in NQM and 120594CQM using the GPM

Baryon NQM 120594CQM

Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)

Σlowastminus B1015840

(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)

Ξlowastminus B1015840

(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)

Table 9 Quadrupole moments of the spin (32)+

rarr (12)+ transitions in NQM and 120594CQM using the GPM

Baryon NQM 120594CQMΔ

+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772

)) minus 2radic2C1015840

Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840

(minus119906 minus 119889 + 2119904) radic2B1015840

(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772

)) minus radic2C1015840

Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


vanishes in NQM as well as in some other models This isfurther endorsed by the predictions of the field theoreticalquark model (FTQM) calculations [67] The contribution ofthe three-quark term in the case of decuplet baryons is exactlyopposite to that for the octet baryons Unlike the octet baryoncase the inclusion of the three-quark term increases the valueof the baryon charge radii

For the sake of completeness certain relations betweenthe octet and decuplet baryon charge radii can also be testedfor the spacing between the levels In NQM we have

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)

In 120594CQM the inclusion of SU(3) symmetry breaking effectscreates a spacing between the octet and decuplet baryoncharge radii as

1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)

We have calculated the numerical values for thequadrupole moment for the (32)

+ decuplet baryons in120594CQM and presented the results in Table 10 The results ofthe spin (32)

+

rarr (12)+ transitions have been presented in

Table 11 To understand the implications of chiral symmetrybreaking and ldquoquark seardquo we have also presented the results ofNQM Since the calculations in 120594CQMhave been carried outusing the GPM the NQM results have also been presentedby including the two- and three- quark term contributions ofthe GPM parameters so that the contribution of the ldquoquarkseardquo effects can be calculated explicitly For the case of spin(12)

+ octet baryons we find that the quadrupole momentsare zero for all the cases in NQM Even if we considerthe contribution coming from two-quark terms with the


Table 10 Quadrupole moments of the spin (32)+ decuplet baryons in 120594CQM using GPM and SU(3) symmetry breaking

120594CQM with SU(3)

Baryon NQM fm2 CQM [84] 120594PT [99ndash103] SRA[89 90]

Skyrme[91 92]

GPM[93 94] Symmetry Symmetry breaking

10minus2 fm2

10minus1 fm2

10minus1 fm2

10minus2 fm2 fm2 fm2 fm2

Δ++

minus0409 minus93 minus08 plusmn 05 minus087 minus88 minus012 minus03437 minus03695Δ

+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ

minus 0204 46 06 plusmn 03 080 88 006 01719 01930Σlowast+

minus0204 minus54 minus07 plusmn 03 minus042 minus71 minus0069 minus01719 minus01808Σlowastminus 0204 40 40 plusmn 02 052 71 0039 01719 01942

Σlowast0 00 minus07 minus013 plusmn 007 005 00 0014 00 00067

Ξlowast0 00 minus13 minus035 plusmn 02 minus007 minus46 minus01719 00 00079

Ξlowastminus 0204 34 02 plusmn 01 035 46 0024 01719 01954

Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966

inclusion of ldquoquark seardquo and SU(3) symmetry breakingeffects the quadrupole moments still remain zero In thecase of (32)+ decuplet baryons the quadrupole moments ofthe charged baryons are equal whereas all neutral baryonshave zero quadrupole moment

For the (32)+ decuplet and radiative decays of baryons

it can be easily shown that in the SU(3) symmetric limit themagnitude of quadrupole moments can be expressed by thefollowing relations

119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+

= 119876Σlowastminus

= 119876Ξlowastminus

= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)

The inclusion of SU(3) symmetry breaking changes thispattern considerably and we obtain

119876Ωminus

gt 119876Ξlowastminus

gt 119876Σlowastminus

gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)

which has its importance in the isospin limit where thethree-quark core in neutral baryons does not contribute tothe quadrupole moment In the limit of SU(3) symmetrybreaking a nonvanishing value for the neutral baryonsquadrupole moment is generated by the ldquoquark seardquo throughthe chiral fluctuations of constituent quarks leading to

119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)

In the SU(3) limit the transition moments involving thenegatively charged baryons are zero

119876Ξlowastminus

Ξminus


Σminus

= 0 (53)

This is because if flavor symmetry is exact U-spin conser-vation forbids such transitions The exact order of SU(3)

symmetry breaking effects can be easily found from Tables 10and 11 Since there is no experimental or phenomenologicalinformation available for any of these quadrupole momentsthe accuracy of these relations can be tested by the futureexperiments

For the spin (32)+ decuplet baryons presented in

Table 10 quadrupole moments results in NQM using theGPM predict an oblate shape for all positively chargedbaryons (Δ++ Δ

+ and Σlowast+) prolate shape for negatively

charged baryons (Δminus Σlowastminus Ξ

lowastminus and Ωminus) It is important

to mention here that the NQM is unable to explain thedeformation in neutral baryons (Δ0 Σlowast0 and Ξ

lowast0) On incor-porating the effects of chiral symmetry breaking and ldquoquarkseardquo in the 120594CQM a small amount of prolate deformationin neutral baryons (Δ0 Σlowast0 and Ξ

lowast0) is observed The trendof deformations is however the same for the positively andnegatively charged baryons in 120594CQM and NQM The otherphenomenological models also observe a similar trend forexample light cone QCD sum rules [95 96] spectator quarkmodel [86ndash88] Lattice QCD [104ndash108] 120594PT [99ndash103] chiralquark soliton model (120594QSM) [85] and so forth

For the case of spin (32)+


Table 11 it is observed that quadrupole moments of all thetransitions are oblate in shapeThis result is further endorsedby the predictions of Skyrme model [91 92] The effects ofchiral symmetry breaking can further be substantiated by ameasurement of the other transition quadrupole moments

6 Summary and Conclusion

To summarize 120594CQM is able to provide a fairly gooddescription of the charge radii of spin (12)

+ octet andspin (32)

+ decuplet baryons and quadrupole moments ofspin (32)

+ decuplet baryons and spin (32)+

rarr (12)+

transitions using general parameterization method (GPM)The most significant prediction of the model for the charge



rarr (12)+ decuplet to octet transitions in 120594CQM using GPM and SU(3) symmetry

breaking

Baryon NQM fm2 Skyrme [91 92] 10minus2 fm2 GPM [93 94] fm2 120594CQM with SU(3)

Symmetry fm2 Symmerty breaking fm2

Δ+

119901 minus0110 minus52 minus0082 minus00608 minus00846minus00846 plusmn 00033

Σlowast+

Σ+

minus0110 minus093 minus0076 minus00608 minus00864Σlowastminus

Σminus 00 093 0014 minus00608 minus00018

Σlowast0

Σ0

minus0055 00 minus0031 00 minus00441Ξlowast0

Ξ0

minus0110 291 minus0031 minus00608 minus00864Ξlowastminus

Ξminus 00 minus291 0007 00 minus00018

Σlowast0

Λ minus0096 minus483 minus0041 minus00526 minus00733

radii is the nonzero value pertaining to the neutral octetbaryons (119899 Σ0 Ξ0 and Λ) and decuplet baryons (Δ0 Σlowast0Ξlowast0) For the quadrupole moment prolate shape is observed

for the spin (32)+ neutral decuplet baryons (Δ0 Σlowast0 and

Ξlowast0) The effects of SU(3) symmetry breaking have also been

investigated and the results show considerable improvementover the SU(3) symmetric case We have also studied theimplications of GPM parameters particularly the contribu-tion of the three-quark term in the octet and decuplet baryonWe find that the sign of the three-quark term contributionis opposite in the case of octet and decuplet baryons chargeradii New experiments aimed at measuring the charge radiiand quadrupole moment of the other baryons are neededfor a profound understanding of the hadron structure in thenonperturbative regime of QCD

In conclusion we would like to state that at-the-leading-order constituent quarks and the weakly interacting Gold-stone bosons constitute the appropriate degrees of freedomin the nonperturbative regime of QCDThe SU(3) symmetrybreaking parameters pertaining to the strangeness contribu-tion and the GPM parameters pertaining to the one- two-and three-quark contributions are the key in understandingthe octet and decuplet baryon charge radii and quadrupolemoment

Acknowledgments

The authors would like to thank the Department of AtomicEnergy Government of India for the financial supportthrough Grant no 201037P48BRNS1445

References

[1] R G Sachs ldquoHigh-energy behavior of nucleon electromagneticform factorsrdquo Physical Review vol 126 no 6 pp 2256ndash22601962

[2] J Ashman B Badelek G Baum et al ldquoA measurement ofthespin asymmetry and determination of the structure function g

1

in deep inelastic muon-proton scatteringrdquo Physics Letters B vol206 no 2 pp 364ndash370 1988

[3] J Ashman B Badelek G Baum et al ldquoAn investigation ofthe spin structure of the proton in deep inelastic scattering of

polarised muons on polarised protonsrdquo Nuclear Physics B vol328 no 1 pp 1ndash35 1989

[4] J J Kelly ldquoNucleon charge and magnetization densities fromSachs form factorsrdquo Physical Review C vol 66 no 6 Article ID065203 2002

[5] J Friedrich and T Walcher ldquoA coherent interpretation of theform factors of the nucleon in terms of a pion cloud andconstituent quarksrdquoTheEuropean Physical Journal A vol 17 pp607ndash623 2003

[6] S L Glashow ldquoTheunmellisonant quarkrdquo Physica A vol 96 no1-2 pp 27ndash30 1979

[7] S Taylor G S Mutchler G Adams et al ldquoRadiative decays ofthe Σ

0(1385) and Λ(1520) hyperonsrdquo Physical Review C vol 71no 5 Article ID 054609 2005

[8] O Gayou K Wijesooriya A Afanasev et al ldquoMeasurementsof the elastic electromagnetic form factor ratio 120583

119901119866

119864119901119866

119872119901via

polarization transferrdquo Physical Review C vol 64 no 3 ArticleID 038202 2001

[9] O Gayou K A Aniol T Averett et al ldquoMeasurement of119866

119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876

2 = 5 6GeV2 rdquo Physical ReviewLetters vol 88 no 9 Article ID 092301 2002

[10] V Punjabi C F Perdrisat K A Aniol et al ldquoProton elastic formfactor ratios to Q2=3 5 GeV2 by polarization transferrdquo PhysicalReview C vol 71 Article ID 055202 2005

[11] C B Crawford A Sindile T Akdogan et al ldquoMeasurementof the protonrsquos electric to magnetic form factor ratio from1

119867rarr (119890rarr 119890

1015840

119901)rdquo Physical Review Letters vol 98 no 5 ArticleID 052301 2007

[12] K Nakamura ldquoReview of particle physicsrdquo Journal of Physics Gvol 37 no 7 Article ID 075021 2010

[13] I Eschrich H Krugeri J Simon et al ldquoMeasurement of the 119878minus

charge radius by 119878minus-electron elastic scatteringrdquo Physics Letters

B vol 522 no 3-4 pp 233ndash239 2001[14] M I Adamovich Y A Alexandrov S P Baranov et al ldquoFirst

observation of 119878minus minus 119890minus elastic scattering in the hyperon beam

experiment WA89 at CERNrdquoThe European Physical Journal Cvol 8 no 1 pp 59ndash66 1999

[15] R Rosenfelder ldquoCoulomb corrections to elastic electron-protonscattering and the proton charge radiusrdquo Physics Letters B vol479 no 4 pp 381ndash386 2000

[16] G Blanpied M Blecher A Caracappa et al ldquo119873 rarr Δ

Transition from simultaneous measurements of 119901(120574rarr

120587) and119901(120574

rarr

120574)rdquo Physical Review Letters vol 79 pp 4337ndash4340 1997


[17] R Beck H P Krahn J Ahrens et al ldquoMeasurement of the11986421198721 Ratio in the 119873 rarr Δ Transition using the reaction119901(120574

rarr

119901)120587119900rdquoPhysical Review Letters vol 78 no 4 pp 606ndash609

1997[18] G Blanpied M Blecher A Caracappa et al ldquo119873 rarr Δ

transition and proton polarizabilities from measurements of119901(120574

rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+

)rdquo Physical ReviewC vol 64no 2 Article ID 025203 2001

[19] L Tiator D Drechsel S S Kamalov and S N Yang ldquoElectro-magnetic form factors of the Δ (1232) excitationrdquoThe EuropeanPhysical Journal A vol 17 no 3 pp 357ndash363 2003

[20] C Becchi and G Morpurgo ldquoVanishing of the E2 part of theNlowast33 rarr N + 120574 amplitude in the non-relativistic quark modelof ldquoelementaryrdquo particlesrdquo Physics Letters vol 17 no 3 pp 352ndash354 1965

[21] AM Bernstein ldquoDeviation of the nucleon shape from sphericalsymmetry experimental statusrdquoThe European Physical JournalA vol 17 no 3 pp 349ndash355 2003

[22] C N Papanicolas ldquoNucleon deformation a status reportrdquo TheEuropean Physical Journal A vol 18 no 2-3 pp 141ndash145 2003

[23] M Gell-Mann ldquoA schematic model of baryons and mesonsrdquoPhysics Letters vol 8 no 3 pp 214ndash215 1964

[24] R P FeynmanMGell-Mann andG Zweig ldquoGroupU(6)aU(6)generated by current componentsrdquo Physical Review Letters vol13 no 22 pp 678ndash680 1964

[25] G Zweig ldquoAn model for strong interaction symmetry and itsbreaking Irdquo CERN Reports 8182TH401 1964

[26] G Zweig ldquoAn model for strong interaction symmetry and itsbreaking IIrdquo CERN Reports 8419TH412 1964

[27] G Morpurgo ldquoIs a nonrelativistic approximation possible forthe internal dynamics of lsquoelementaryrsquo particlesrdquo Physics vol 2pp 95ndash104 1965

[28] A De Rujula H Georgi and S L Glashow ldquoHadron massesin a gauge theoryrdquo Physical Review D vol 12 no 1 pp 147ndash1621975

[29] N Isgur and G Karl ldquoGround-state baryon magneticmomentsrdquo Physical Review D vol 21 no 11 pp 3175ndash31791980

[30] N Isgur G Karl and D W L Sprung ldquoNeutron charge formfactor in a quark model with hyperfine interactionsrdquo PhysicalReview D vol 23 pp 163ndash164 1981

[31] N Isgur G Karl and R Koniuk ldquoD waves in the nucleon atest of color magnetismrdquo Physical Review D vol 25 no 9 pp2394ndash2398 1982

[32] P Geiger and N Isgur ldquoStrange hadronic loops of the proton aquark model calculationrdquo Physical Review D vol 55 no 1 pp299ndash310 1997

[33] A L Yaouanc L Oliver O Pene and J C Raynal ldquoCombinedeffects of internal quark motion and SU(6) breaking on theproperties of the baryon ground staterdquo Physical Review D vol15 no 3 pp 844ndash853 1977

[34] M Gupta and A N Mitra ldquoEven-wave harmonic-oscillatortheory of baryonic states IV Structure functions versus slopeof neutron charge form factorrdquo Physical Review D vol 18 no 5pp 1585ndash1590 1978

[35] M Gupta S K Sood and A N Mitra ldquoResonance photocou-plings with a ldquomixedrdquo nucleon and the even-wave harmonic-oscillator theory of baryonic statesrdquo Physical Review D vol 16no 1 pp 216ndash219 1977

[36] M Gupta S K Sood and A N Mitra ldquoEven-wave harmonic-oscillator theory of baryonic states V Polarized photoproduc-tion of single pionsrdquo Physical ReviewD vol 19 pp 104ndash111 1979

[37] P Amaudruz M Arneodo A Arvidson et al ldquoGottfried sumfrom the ratio119865

119899

2119865

119901

2rdquo Physical Review Letters vol 66 no 21 pp

2712ndash2715 1991[38] M Arneodo A Arvidson B Badelek et al ldquoReevaluation of

the Gottfried sumrdquo Physical Review D vol 50 no 1 pp R1ndashR31994

[39] E A Hawker T C Awes M E Beddo et al ldquoMeasurementof the light antiquark flavor asymmetry in the nucleon seardquoPhysical Review Letters vol 80 no 17 pp 3715ndash3718 1998

[40] J C Peng G T Garvey T C Awes et al ldquo119889119906 asymmetry andthe origin of the nucleon seardquo Physical Review D vol 58 no 9Article ID 092004 1998

[41] R S Towell P L McGaughey T C Awes et al ldquoImprovedmeasurement of the 119889119906 asymmetry in the nucleon seardquoPhysical Review D vol 64 no 5 Article ID 052002 2001

[42] J Kunz and P J Mulders ldquoElectromagnetic properties ofhypersons in the bound-state approach to the Skyrme modelrdquoPhysical Review D vol 41 no 5 pp 1578ndash1585 1990

[43] J Kunz P J Mulders and G A Miller ldquoCharge distributions ofhyperonsrdquo Physics Letters B vol 255 no 1 pp 11ndash17 1991

[44] C Gobbi S Boffi and D O Riska ldquoMean square radii ofhyperons in the bound-state soliton modelrdquo Nuclear Physics Avol 547 no 4 pp 633ndash644 1992

[45] B Schwesinger and H Weigel ldquoSU(3) symmetry breakingfor masses magnetic moments and sizes of baryonsrdquo NuclearPhysics A vol 540 no 3-4 pp 461ndash477 1992

[46] H Kim A Blotz M V Polyakov and K Goeke ldquoElec-tromagnetic form factors of the SU(3) octet baryons in thesemibosonized SU(3) Nambu-Jona-Lasinio modelrdquo PhysicalReview D vol 53 no 7 pp 4013ndash4029 1996

[47] D H Lu A W Thomas and A G Williams ldquoElectromagneticform factors of the nucleon in an improved quark modelrdquoPhysical Review C vol 57 no 5 pp 2628ndash2637 1998

[48] GWagner A J Buchmann andA Faessler ldquoExchange currentsin octet hyperon charge radiirdquo Physical Review C vol 58 no 6pp 3666ndash3669 1998

[49] N Barik S N Jena and D P Rath ldquoNucleon form factors andstatic properties of baryons in a quark modelrdquo Physical ReviewD vol 41 no 5 pp 1568ndash1577 1990

[50] MWarnsW Pfeil andH Rollnik ldquoElectromagnetic propertiesof hyperons in a relativised quark modelrdquo Physics Letters B vol258 no 3-4 pp 431ndash440 1991

[51] T V Cauteren D Merten T Corthals et al ldquoElectric and mag-netic form factors of strange baryonsrdquo The European PhysicalJournal A vol 20 no 2 pp 283ndash291 2004

[52] K Berger R FWagenbrunn andW Plessas ldquoCovariant baryoncharge radii and magnetic moments in a chiral constituent-quark modelrdquo Physical Review D vol 70 no 9 Article ID094027 2004

[53] B J Diaz D O Riska and F Coester ldquoBaryon form factors ofrelativisitic constituent-quark modelsrdquo Physical Review C vol69 Article ID 035212 2004

[54] B J Diaz D O Riska and F Coester ldquoErratum baryonform factors of relativisitic constituent-quark modelsrdquo PhysicalReview C vol 75 Article ID 069902 2007

[55] A J Buchmann and R F Lebed ldquoLarge119873119888 constituent quarks

and N Δ charge radiirdquo Physical Review D vol 62 no 9 ArticleID 096005 2000

[56] A J Buchmann ldquoCharge form factors and nucleon shaperdquo AIPConference Proceedings vol 904 pp 110ndash125


[57] A J Buchmann and R F Lebed ldquoBaryon charge radii andquadrupole moments in the 1N

119888expansion the 3-flavor caserdquo

Physical Review D vol 67 Article ID 016002 17 pages 2003[58] A J Buchmann ldquoStructure of strange baryonsrdquo in Proceedings

of the International Conference on Hypernuclear and StrangeParticle Physics (HYP rsquo06) Mainz Germany October 2006

[59] S Cheedket V E Lyubovitskij T Gutsche A Faessler KPumsa-Ard and Y Yan ldquoElectromagnetic form factors of thebaryon octet in the perturbative chiral quark modelrdquo TheEuropean Physical Journal A vol 20 no 2 pp 317ndash327 2004

[60] S J Puglia M J R Musolf and S L Zhu ldquoOctet baryoncharge radii chiral symmetry and decuplet intermediate statesrdquoPhysical Review D vol 36 Article ID 034014 2001

[61] B Kubis and U G Meissner ldquoBaryon form factors in chiralperturbation theoryrdquo The European Physical Journal C vol 18no 4 pp 747ndash756 2001

[62] D Arndt and B C Tiburzi ldquoCharge radii of the mesonand baryon octets in quenched and partially quenched chiralperturbation theoryrdquo Physical Review D vol 68 no 9 ArticleID 094501 2003

[63] P Wang D B Leinweber A W Thomas and R D YoungldquoChiral extrapolation of octet-baryon charge radiirdquo PhysicalReview D vol 79 no 9 Article ID 094001 2009

[64] D B Leinweber T Draper and R M Woloshyn ldquoDecupletbaryon structure from lattice QCDrdquo Physical Review D vol 46no 7 pp 3067ndash3085 1992

[65] D Arndt and B C Tiburzi ldquoElectromagnetic properties of thebaryon decuplet in quenched and partially quenched chiralperturbation theoryrdquo Physical Review D vol 68 Article ID114503 2003

[66] S Boinepalli D B Leinweber P J Moran A G Williams J MZanotti and J B Zhang ldquoElectromagnetic structure of decupletbaryons towards the chiral regimerdquo Physical Review D vol 80no 5 Article ID 054505 2009

[67] R K Sahoo A R Panda and A Nath ldquoMagnetic momentsand charge radii of decuplet baryons in a field-theoretic quarkmodelrdquo Physical Review D vol 52 no 7 pp 4099ndash4105 1995

[68] L S Geng J M Camalich andM J V Vacas ldquoElectromagneticstructure of the lowest-lying decuplet resonances in covariantchiral perturbation theoryrdquo Physical Review D vol 80 no 3Article ID 034027 2009

[69] C Alexandrou P de Forcrand T Lippert et al ldquoN to Δ

electromagnetic transition form factors from lattice QCDrdquoPhysical Review D vol 69 no 11 Article ID 114506 2004

[70] C Alexandrou P de Forcrand H Neff et al ldquoN to Δ

electromagnetic-transition form factors from lattice QCDrdquoPhysical Review Letters vol 94 no 2 Article ID 021601 2005

[71] G Clement andMMaamache ldquoAre theN andΔ deformedMITbagsrdquo Annals of Physics vol 165 no 1 pp 1ndash16 1985

[72] A B Migdal ldquoTraektorii Redzhe i forma adronovrdquo PisrsquoMa VZhETF vol 46 no 7 pp 256ndash258 1987

[73] A B Migdal ldquoRegge trajectories and the shape of hadronsrdquoJETP Letters vol 46 no 7 pp 322ndash325 1987

[74] A J Buchmann ldquoN-to-Δ quadrupole transition in the con-stituent quark modelrdquo in Proceedings of the 8th InternationalConference on the Structure of Baryons (Baryonsrsquo 98) D WMenze and B Metsch Eds p 731 World Scientific Singapore1999

[75] A J Buchmann E Hernandez and A Faessler ldquoElectromag-netic properties of the Δ (1232)rdquo Physical Review C vol 55 no1 pp 448ndash463 1997

[76] A J Buchmann and E M Henley ldquoIntrinsic quadrupolemoment of the nucleonrdquo Physical Review D vol 63 Article ID015202 2001

[77] A J Buchmann and E M Henley ldquoQuadrupole moments ofbaryonsrdquo Physical Review D vol 65 no 7 Article ID 0730172002

[78] A J Buchmann J A Hester and R F Lebed ldquoQuadrupolemoments of N and Δ in the 1N

119888expansionrdquo Physical Review

D vol 66 no 5 Article ID 056002 2002[79] A J Buchmann ldquoSize and shape of baryons in a large N

119888

quark modelrdquo in Proceedings of the Institute for Nuclear TheoryPhenomenology of Large NcQCD R F Lebed Ed vol 12 p 224World Scientific 2002



Physical Review D vol 67 Article ID 016002 2003[81] N Isgur G Karl and R Koniuk ldquoDwaves in the nucleon a test

of color magnetismrdquo Physical Review D vol 25 pp 2394ndash23981982

[82] W J Leonard and W J Gerace ldquoQuark-meson coupling modelfor baryon wave functions and propertiesrdquo Physical Review Dvol 41 pp 924ndash936 1990

[83] G Wagner A J Buchmann and A Faessler ldquoElectromagneticproperties of decuplet hyperons in a chiral quark model withexchange currentsrdquo Journal of Physics G vol 26 no 3 article267 2000

[84] M I Krivoruchenko and M M Giannini ldquoQuadrupolemoments of the decuplet baryonsrdquo Physical Review D vol 43no 11 pp 3763ndash3765 1991

[85] T Ledwig A Silva and M Vanderhaeghen ldquoElectromagneticproperties of the Δ(1232) and decuplet baryons in the self-consistent SU(3) chiral quark-soliton modelrdquo Physical ReviewD vol 79 no 9 Article ID 094025 2009

[86] G Ramalho and M T Pena ldquoElectromagnetic form factors ofthe Δ in an S-wave approachrdquo Journal of Physics G vol 36 no8 Article ID 085004 2009

[87] G Ramalho M T Pena and F Gross ldquoElectric quadrupole andmagnetic octupolemoments of theΔrdquoPhysics Letters B vol 678no 4 pp 355ndash358 2009

[88] G Ramalho M T Pena and F Gross ldquoElectromagnetic formfactors of the Δwith D-wavesrdquo Physical Review D vol 81 no 11Article ID 113011 2010


[90] J Kroll and B Schwesinger ldquoElectric quadrupole moments ofthe decuplet and the strangeness content of the protonrdquo PhysicsLetters B vol 334 pp 287ndash289 1994

[91] YOh ldquoElectric quadrupolemoments of the decuplet baryons inthe Skyrme modelrdquoModern Physics Letters A vol 10 pp 1027ndash1034 1995

[92] A Abada H Weigel and H Reinhardt ldquoRadiative decaysof hyperons in the Skyrme model view the MathML sourcetransitions ratios E2M1rdquo Physics Letters B vol 366 pp 26ndash311996


[94] A J Buchmann and EM Henley ldquoBaryon octupole momentsrdquoThe European Physical Journal A vol 35 no 3 pp 267ndash2692008


[95] K Azizi ldquoMagnetic dipole electric quadrupole and magneticoctupole moments of the Δ baryons in light cone QCD sumrulesrdquo The European Physical Journal C vol 61 no 2 pp 311ndash319 2009

[96] T M Aliev K Azizi and M Savci ldquoElectric quadrupole andmagnetic octupole moments of the light decuplet baryonswithin light cone QCD sum rulesrdquo Physics Letters vol 681 no3 pp 240ndash246 2009



D vol 66 no 5 Article ID 056002 2002[98] A J Buchmann and R F Lebed ldquoBaryon charge radii and

quadrupole moments in the 1N119888expansion the 3-flavor caserdquo

Physical Review D vol 67 Article ID 016002 2003[99] M N Butler M J Savage and R P Springer ldquoElectromagnetic

moments of the baryon decupletrdquo Physical ReviewD vol 49 pp3459ndash3465 1994

[100] M K Banerjee and J Milana ldquoDecuplet reexamined in chiralperturbation theoryrdquo Physical ReviewD vol 54 no 9 pp 5804ndash5811 1996

[101] D Arndt and B C Tiburzi ldquoElectromagnetic properties of thebaryon decuplet in quenched and partially quenched chiralperturbation theoryrdquo Physical Review D vol 68 no 11 ArticleID 114503 2003

[102] D Arndt and B C Tiburzi ldquoErratum electromagnetic proper-ties of the baryon decuplet in quenched and partially quenchedchiral perturbation theoryrdquo Physical Review D vol 65 no 5Article ID 059904 2004

[103] L S Geng J M Camalich andM J V Vacas ldquoElectromagneticstructure of the lowest-lying decuplet resonances in covariantchiral perturbation theoryrdquo Physical Review D vol 80 ArticleID 034027 2009

[104] D B Leinweber T Draper and R M Woloshyn ldquoDecupletbaryon structure from lattice QCDrdquo Physical Review D vol 46pp 3067ndash3085 1992

[105] C Alexandrou T Korzec T Leontiou J W Negele and ATsapalis ldquoElectromagnetic form factors of the Delta baryonrdquoPoSLATTICE 2007 p 149 2006

[106] C Alexandrou T Korzec G Koutsou et al ldquoQuark transversecharge densities in the delta-(1232) from lattice QCDrdquo NuclearPhysics A vol 825 no 1-2 pp 115ndash144 2009

[107] C Alexandrou T Korzec G Koutsou et al ldquoDelta-baryonelectromagnetic form factors in lattice QCDrdquo Physical ReviewD vol 79 Article ID 014507 2009

[108] S Boinepalli D B Leinweber P J Moran A G Williams J MZanotti and J B Zhang ldquoElectromagnetic structure of decupletbaryons towards the chiral regimerdquo Physical Review D vol 80Article ID 054505 2009

[109] S Weinberg ldquoPhenomenological lagrangiansrdquo Physica A vol96 no 1-2 pp 327ndash340 1979

[110] A Manohar and H Georgi ldquoChiral quarks and the non-relativistic quark modelrdquo Nuclear Physics B vol 234 no 1 pp189ndash212 1984

[111] T P Cheng and L F Li ldquoFlavor and spin contents of the nucleonin the quark model with chiral symmetryrdquo Physical ReviewLetters vol 74 pp 2872ndash2875 1995

[112] T P Cheng and L F Li ldquoChiral quark model of nucleon spin-flavor structure with SU(3) and axial-U(1) breakingsrdquo PhysicalReview D vol 57 pp 344ndash349 1998

[113] X Song J S McCarthy and H J Weber ldquoNucleon spin-flavorstructure in the SU(3)-breaking chiral quark modelrdquo PhysicalReview D vol 55 no 5 pp 2624ndash2629 1997

[114] X Song ldquoNew relations and constraints on quark spin-flavorcontent in the symmetry-breaking chiral quarkmodelrdquo PhysicalReview D vol 57 pp 4114ndash4123 1998

[115] J Linde T Ohlsson and H Snellman ldquoOctet baryon magneticmoments in the chiral quarkmodel with configurationmixingrdquoPhysical Review D vol 57 pp 452ndash464 1998

[116] J Linde T Ohlsson and H Snellman ldquoDecuplet baryonmagnetic moments in the chiral quark modelrdquo Physical ReviewD vol 57 no 9 pp 5916ndash5919 1998

[117] H Dahiya and M Gupta ldquoChiral quark model with configura-tionmixingrdquo Physical ReviewD vol 64 Article ID 014013 2001

[118] H Dahiya and M Gupta ldquoChiral quark model (120594QM) and thenucleon spinrdquo International Journal ofModern Physics A vol 19no 29 Article ID 5027 2004

[119] H Dahiya and M Gupta ldquoChiral constituent quark model andthe coupling strength of 120578rdquo International Journal of ModernPhysics A vol 21 no 21 Article ID 4255 2006

[120] N Sharma H Dahiya P K Chatley and M Gupta ldquoWeakvector and axial-vector form factors in the chiral constituentquarkmodelwith configurationmixingrdquoPhysical ReviewD vol79 Article ID 077503 2009

[121] N Sharma H Dahiya and P K Chatley ldquoExtraction of theCKM matrix element Vus from the hyperon semileptonicdecaysrdquoThe European Physical Journal A vol 44 no 1 pp 125ndash128 2010

[122] H Dahiya andM Gupta ldquox-dependence of the quark distribu-tion functions in the 120594CQMrdquoThe European Physical Journal Cvol 52 no 3 pp 571ndash579 2007

[123] HDahiya andMGupta ldquoSpin and flavor strange quark contentof the nucleonrdquo Physical Review D vol 78 Article ID 0140012008

[124] N Sharma and H Dahiya ldquoQuark sea asymmetries of the octetbaryonsrdquo Physical Review D vol 81 Article ID 114003 2010

[125] H Dahiya and M Gupta ldquoOctet magnetic moments andthe Coleman-Glashow sum rule violation in the chiral quarkmodelrdquo Physical Review D vol 66 Article ID 051501 2002

[126] H Dahiya andM Gupta ldquoOctet and decuplet baryonmagneticmoments in the chiral quark modelrdquo Physical Review D vol 67p 114015 2003

[127] H Dahiya and M Gupta ldquoSU(4) chiral quark model withconfiguration mixingrdquo Physical Review D vol 67 Article ID074001 2003

[128] N Sharma A M Torres K P Khemchandani and H DahiyaldquoMagnetic moments of the low-lying (12)minus octet baryon reso-nancesrdquoTheEuropean Physical Journal A vol 49 article 11 2013

[129] A M Torres K P Khemchandani N Sharma and H DahiyaldquoMagnetic moments of the low-lying JP = (12)minus (32)minus⋀resonances within the framework of the chiral quark modelrdquoThe European Physical Journal A vol 48 article 185 2012

[130] N Sharma and H Dahiya ldquoCharge radii of octet and decupletbaryonsrdquo inAIP Conference Proceedings vol 1388 pp 458ndash4602011

[131] N Sharma and H Dahiya ldquoQuadrupole moments of low-lyingbaryons with spin-(12)+ spin-(32)+ and spin- (32)+to(12)+transitionsrdquo Pramana vol 80 no 2 pp 237ndash249 2013

[132] H Dahiya and M Gupta ldquoSU(4) chiral quark model withconfiguration mixingrdquo Physical Review D vol 67 no 7 ArticleID 074001 2003

[133] N SharmaHDahiya P K Chatley andMGupta ldquoSpin (12)+spin (32)+ and transition magnetic moments of low lying and


charmed baryonsrdquo Physical Review D vol 81 no 7 Article ID073001 2010

[134] G Morpurgo ldquoField theory and the nonrelativistic quarkmodel a parametrization of the baryonmagnetic moments andmassesrdquo Physical Review D vol 40 pp 2997ndash3011 1989

[135] G Morpurgo ldquoField theory and the nonrelativistic quarkmodel a parametrization of themesonmassesrdquo Physical ReviewD vol 41 no 9 pp 2865ndash2870 1990

[136] G Dillon and G Morpurgo ldquoRelation of constituent quarkmodels to QCD why several simple models work lsquoso wellrsquordquoPhysical Review D vol 53 pp 3754ndash3769 1996

[137] G Dillon and G Morpurgo ldquoChiral QCD general QCDparametrization and constituent quark modelsrdquo PhysicalReview D vol 68 Article ID 014001 2003

[138] G Dillon and G Morpurgo ldquoBaryon octet magnetic momentsto all orders in flavor breaking an application to the problem ofthe strangeness in the nucleonrdquo Physical Review D vol 75 no7 Article ID 073007 2007

[139] A J Buchmann and E M Henley ldquoIntrinsic quadrupolemoment of the nucleonrdquo Physical ReviewC vol 63 no 1 ArticleID 015202 8 pages 2000

[140] A J Buchmann ldquoElectromagnetic 119873 rarr Δ transition andneutron form factorsrdquo Physical Review Letters vol 93 ArticleID 212301 4 pages 2004

[141] A J Buchmann ldquoStructure of strange baryonsrdquo in Proceedingsof the Shape of Hadrons Workshop C N Papanicolas and A MBernstein Eds Athens Greece 2006

[142] A J Buchmann ldquoCharge form factors and nucleon shaperdquo AIPConference Proceedings vol 904 pp 110ndash125 2007

[143] G Morpurgo ldquoSmallness of gluon coupling to constituentquarks in baryons and validity of nonrelativistic quark modelrdquoPhysical Review D vol 46 no 9 pp 4068ndash4075 1992

[144] G Dillon and G Morpurgo ldquoGeneral QCD parametrization ofthe charge radii of p n and Δ

+rdquo Physics Letters B vol 448 no1-2 pp 107ndash110 1999

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


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Statistical MechanicsInternational Journal of


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Journal of



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AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


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Biophysics


ThermodynamicsJournal of


has been carried out [16ndash19] The spin and parity selectionrules in the 120574 + 119901 rarr Δ

+ transition allow three contributingphoton absorption amplitudes the magnetic dipole 119866

1198721 the

electric quadrupole moment1198661198642 and the charge quadrupole

moment 1198661198622 The 119866

1198721amplitude gives us information on

magnetic moment whereas the information on the intrinsicquadrupolemoment can be obtained from themeasurementsof 119866

1198642and 119866

1198622amplitudes [12] If the charge distribution

of the initial and final three-quark states was sphericallysymmetric the 119866

1198642and 119866

1198622amplitudes of the multipole

expansion would be zero [20] However the recent experi-ments at Mainz Bates Bonn and JLab Collaborations [7ndash11 21 22] reveal that these quadrupole amplitudes are clearlynonzero [12] The ratio of electric quadrupole amplitude tothe magnetic dipole amplitude is at least 11986421198721 equiv minus0025 plusmn

0005 and a comparable value of same sign and magnitudehas been measured for the 11986221198721 ratio [12] Further thequadrupole transition moment (119876Δ

+

119873) measured by LEGSand Mainz collaborations (minus0108 plusmn 0009 plusmn 0034 fm2 [16ndash18] and minus00846 plusmn 00033 fm2 [19] resp) also leads to theconclusion that the nucleon and the Δ

+ are intrinsicallydeformed

The naive quark model (NQM) [23ndash27] is one of thesimplest model to describe the hadron properties and inter-actions in the low energy regime This model is able toprovide a simple intuitive picture of the hadron structure interms of three valence quarks (119902119902119902) for baryons and quarkantiquark (119902119902) for mesons It allows the direct calculationsof the low energy hadronic matrix elements including theirspectra and successfully accounts for many of the low energyproperties of the hadrons in terms of the valence quarks[28ndash32] Interestingly with the inclusion of the spin-spininteractions generated configurationmixing [28] between thevalence quarks the NQM has not only given an accuratedescription of the hadron spectroscopy data but also has beenable to describe some subtle features of the data including the119873minusΔmass difference photohelicity amplitudes and baryonmagnetic moments [29ndash36] However some major findingson the experimental front discussed below have brought intoprominence the inadequacies of the NQM

The measurements in the deep inelastic scattering (DIS)experiments [2 3] indicate that the valence quarks of theproton carry only about 30 of its spin and also establishethe asymmetry of the quark distribution functions [37ndash41]This is referred to as the ldquoproton spin problemrdquo in NQMSeveral effective and phenomenological models have beendeveloped to explain the ldquoproton spin problemrdquo by includingspontaneous breaking of chiral symmetry and have beenfurther applied to study the electromagnetic properties ofbaryons

For the calculations pertaining to the baryon chargeradii NQM leads to vanishing charge radii for the neutralbaryons like 119899 Σ0 Ξ0 and Λ This is in contradiction tothe experimental data The inclusion of quark spin-spininteractions in NQM modify the baryon wavefunction tosome extent leading to the breaking of the SU(3) symmetryand a nonvanishing neutron charge mean square radius[29ndash32] A likely cause of these dynamical shortcomings

is that the NQM does not respect chiral symmetry whosespontaneous breaking leads to the emission of Goldstonebosons (GBs) In this context it becomes important toincorporate the effect of chiral symmetry breaking (120594SB)in the phenomenological models to obtain a reasonableagreement with the data On the other hand a wide varietyof accurately measured data have been accumulated forthe static low energy properties of baryons for examplemasses electromagnetic moments charge radii and lowenergy dynamical properties such as scattering lengths anddecay rates which has renewed considerable interest in thelow energy baryon spectroscopy The direct calculations ofthese quantities from the first principle of QCD are extremelydifficult as they require the nonperturbativemethods Severaleffective and phenomenological models such as Lattice QCDeffective field theories QCD sum rules and variants ofquark models have been developed to explain the failuresof the NQM and further applied to study the properties ofbaryons

Some of the important models measuring the chargeradii of octet baryon are the Skyrme model with bound stateapproach [42ndash44] slow-rotor approach [45] semibosonizedSU(3) NJL model [46] cloudy bag model [47] variants ofconstituent quark models [48ndash54] 1119873

119888expansion approach

[55ndash58] perturbative chiral quark model (P120594QM) [59]heavy-baryon chiral perturbation theory (HB120594PT) [60]chiral perturbation theory (120594PT) [61 62] Lattice QCD [63]and so forth The charge radii of decuplet baryons havebeen studied within the framework of Lattice QCD [64ndash66]quark model [67] 1119873

119888expansion [55 56] chiral pertur-

bation theory [68] and so forth The results for differenttheoretical models are however not consistent with eachother

There have been a lot of theoretical investigations inunderstanding the implications of the 11986221198721 and 11986421198721

ratios in finding out the exact sign of deformation in thespin (12)

+ octet baryons However there is a little consensusbetween the results even with respect to the sign of thenucleon deformation Some of the models predict the defor-mation in nucleon as oblate [69 70] some predict a prolatenucleon deformation [71ndash80] whereas others speak aboutldquodeformationrdquo without specifying the sign The quadrupolemoment of the (32)+ decuplet baryons has also been studiedusing the variants of the constituent quark model (CQM)[81ndash84] chiral quark soliton model (120594QSM) [85] spectatorquark model [86ndash88] slow-rotator approach (SRA) [89 90]skyrme model [91 92] general parametrization method[93 94] light cone QCD sum rules (QCDSR) [95 96]large 119873

119888[97 98] chiral perturbation theory (120594PT) [99ndash

103] Lattice QCD (LQCD) [104ndash108] and so forth In thiscase also the results for different theoretical models arenot consistent in terms of sign and magnitude with eachother

As the hadron structure is sensitive to the pion cloudin the low energy regime a coherent understanding isnecessary as it will provide a test for the QCD-inspiredeffective field theories One of the important nonperturbativeapproaches which finds its application in the low energyregime is the chiral constituent quark model (120594CQM) [109



minus









+

rarr







⟨1199032

⟩ = int1198893

119903120588 (r) 1199032 (1)


1198760= int119889

3r120588 (r) (31199112 minus 1199032

) (2)








120588 = A1015840

3

sum

119894=1

1198901198941 minus B1015840

3

sum

119894 = 119895

119890119894[2120590

119894sdot 120590

119895minus (3120590

119894119911120590119895119911

minus 120590119894sdot 120590

119895)]

minus C1015840

3

sum

119894 = 119895 = 119896

119890119894[2120590

119895sdot 120590

119896minus (3120590

119895119911120590119896119911

minus 120590119895sdot 120590

119896)]

(3)


1199032 = A3

sum

119894=1

1198901198941 + B

3

sum

119894 = 119895

119890119894120590119894sdot 120590

119895+ C

3

sum

119894 = 119895 = 119896

119890119894120590119895sdot 120590

119896 (4)


119876 = B1015840

3

sum

119894 = 119895

119890119894(3120590

119894119911120590119895119911

minus 120590119894sdot 120590

119895)

+ C1015840

3

sum

119894 = 119895 = 119896

119890119894(3120590

119895119911120590119896119911

minus 120590119895sdot 120590

119896)

(5)




sum

119894 = 119895

119890119894(120590i sdot 120590j) = 2J sdot sum

119894

119890119894120590i minus 3sum

119894

119890119894

sum

119894 = 119895 = 119896


119894

119890119894minus sum

119894 = 119895

119890119894(120590i sdot 120590j)

(6)



(32)+ baryons


119890119894(120590i sdot 120590j) sum

119894 = 119895 = 119896

119890119894(120590j sdot 120590k)

119869 =1

23sum

119894

119890119894120590iz minus 3sum

119894

119890119894

minus3sum119894

119890119894120590iz

119869 =3

25sum

119894

119890119894120590iz minus 3sum

119894

119890119894

6sum119894

119890119894minus 5sum

119894

119890119894120590iz

(7)




1199032B = (A minus 3B)sum119894

119890119894+ 3 (B minus C)sum

119894

119890119894120590119894119911 (8)


119894

119890119894+ 5 (B minus C)sum

119894

119890119894120590iz (9)


119894119890119894) and spin (sum




1199032

B = ⟨B1003816100381610038161003816100381610038161199032B

100381610038161003816100381610038161003816B⟩ 119903

2

119861lowast

= ⟨Blowast1003816100381610038161003816100381610038161199032Blowast

100381610038161003816100381610038161003816Blowast

⟩ (10)



+


+spin (32)




119876B = B1015840

(3sum

119894 = 119895

119890119894120590iz120590jz minus 3sum

119894

119890119894120590iz + 3sum

119894

119890119894)

+ C1015840

(3 sum

119894 = 119895 = 119896

119890119894120590jz120590kz + 3sum

119894

119890119894120590iz)

119876Blowast = B1015840

(3sum

119894 = 119895

119890119894120590iz120590jz minus 5sum

119894

119890119894120590iz + 3sum

119894

119890119894)

+ C1015840

(3 sum

119894 = 119895 = 119896

119890119894120590jz120590kz + 5sum

119894

119890119894120590iz minus 6sum

119894

119890119894)

119876BlowastB = 3B1015840

sum

119894 = 119895

119890119894120590iz120590jz + 3C1015840

sum

119894 = 119895 = 119896

119890119894120590jz120590kz

(11)


119894119890119894) spin (sum


119894119890119894120590iz120590jz)





119876B = ⟨B 10038161003816100381610038161003816119876B


119876Blowast10038161003816100381610038161003816Blowast

⟩


10038161003816100381610038161003816B⟩

(12)



sum

119894

119890119894= sum

119902=119906119889119904

119899B119902119902 + sum

119902=119906119889119904

119899B119902119902

= 119899B119906119906 + 119899

B119889119889 + 119899

B119904119904 + 119899

B119906119906 + 119899

B119889119889 + 119899

B119904119904

sum

119894

119890119894120590119894119911

= sum

119902=119906119889119904

(119899B119902+

119902++ 119899

B119902minus

119902minus)

= 119899B119906+

119906++ 119899

B119906minus

119906minus+ 119899

B119889+

119889++ 119899

B119889minus

119889minus+ 119899

B119904+

119904++ 119899

B119904minus

119904minus

(13)

where 119899B119902(119899


119899B119902+

(119899B119902minus


minus) For a






119906119889119904

119899119902minus sum

119906119889119904

119899119902)119902


119906119889119904

119899119902+

minus sum

119906119889119904

119899119902minus

)119902+

(14)


|B⟩ equiv

100381610038161003816100381610038161003816100381610038168

1

2

+

⟩ = cos 120579100381610038161003816100381656 0+

⟩119873=0

+ sin 120579100381610038161003816100381670 0

+

⟩119873=2

(15)

with

100381610038161003816100381656 0+

⟩119873=0

=1

radic2(120593

1015840

1205941015840

+ 12059310158401015840

12059410158401015840

) 120595119904

(0+

)

100381610038161003816100381670 0+

⟩119873=2

=1

2[(120593

1015840

12059410158401015840

+ 12059310158401015840

1205941015840

) 1205951015840

(0+

)

+ (1205931015840

1205941015840

minus 12059310158401015840

12059410158401015840

) 12059510158401015840

(0+

)]

(16)





1199032


+minus 119889

+) + sin2

120579 (2119906++ 119889

+)]

1199032


++ 4119889

+) + sin2

120579 (119906++ 2119889

+)]

1199032

Σ+


+) + sin2

120579 (2119906++ 119904

+)]

1199032

Σminus


+) + sin2

120579 (2119889++ 119904

+)]

1199032

Σ0


+minus 119904

+) + sin2

120579 (119906++ 119889

++ 119904

+)]

1199032

Ξ0


+) + sin2

120579 (119906++ 2119904

+)]

1199032

Ξminus


+) + sin2

120579 (119889++ 2119904

+)]

1199032


+) + sin2

120579 (119906++ 119889

++ 119904

+)]

1199032


+minus 119889

+]


Chargeradii NQM

1199032

Δ++

1


+)]

1199032


++ 119889

+)

1199032


++ 2119889

+)

1199032


+)

1199032


++ 119904

+)

1199032


++ 119904

+)

1199032


++ 119889

++ 119904

+)

1199032


++ 2119904

+)

1199032


++ 2119904

+)

1199032

Ωminus




1199032

119901= (A minus 3B) (2119906 + 119889) + 3 (B minus C)


3119906+minus

1

3119889+) + sin2

120579 (2

3119906++

1

3119889+)]

1199032

Σ+

= (A minus 3B) (2119906 + 119904) + 3 (B minus C)


3119906+minus

1

3119904+) + sin2

120579 (2

3119906++

1

3119904+)]

(17)




1003816100381610038161003816Blowast

⟩ equiv

1003816100381610038161003816100381610038161003816100381610

3

2

+

⟩ =100381610038161003816100381656 0

+

⟩119873=0

= 120594119904

120593119904

120595119904

(0+

) (18)




119906119889119904

119899119902minus sum

119906119889119904

119899119902)119902


119906119889119904

119899119902+

minus sum

119906119889119904

119899119902minus

)119902+

(19)


expressed as

1199032

Δ+


+) (20)




119876119901= 3B1015840

(2119906 + 119889 minus 2119906+minus 119889

+)

+ C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119876Σ+ = 3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+)

+ C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

(21)




119876Δ+ = B1015840

(6119906 + 3119889 + 2119906++ 119889

+)

+ C1015840

(minus6119906 minus 3119889 + 10119906++ 5119889

+)


(3119889 + 6119904 + 119889++ 2119904

+)

+ C1015840

(minus3119889 minus 6119904 + 5119889++ 10119904

+)

(22)





be expressed as

119876Δ+

119901= 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889)

119876Σlowastminus


(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)

(23)



rarr





+






+ 1199021015840

∓997888rarr (119902119902

1015840

) + 1199021015840

∓ (24)

where 1199021199021015840



L = 1198928119902Φ

1015840

119902 (25)

with

119902 = (

119906

119889

119904

)

Φ1015840

= (

1205870

radic2

+120573

120578

radic6

+ 120577

1205781015840

radic3

120587+

120572119870+

120587minus

minus

1205870

radic2

+ 120573

120578

radic6

+ 120577

1205781015840

radic3

1205721198700

120572119870minus

120572119870

0

minus120573

2120578

radic6

+ 120577

1205781015840

radic3

)

(26)

where 120577 = 1198921119892

8 119892

1and 119892





2119886 1205732

119886 and 1205772119886




119872119904gt 119872



gt 119872120587and119872

1205781015840 gt 119872

119870120578) [111ndash119]


Φ1015840

= (

120601119906119906

119906119906 + 120601119906119889

119889119889 + 120601119906119904119904119904 120593

119906119889119906119889 120593

119906119904119906119904

120593119889119906

119889119906 120601119889119906

119906119906 + 120601119889119889

119889119889 + 120601119889119904119904119904 120593

119889119904119889119904

120593119904119906119904119906 120593

119904119889119904119889 120601

119904119906119906119906 + 120601

119904119889119889119889 + 120601

119904119904119904119904) (27)

where

120601119906119906

= 120601119889119889

=1

2+

120573

6+

120577

3 120601

119904119904=

2120573

3+

120577

3

120601119906119904

= 120601119889119904

= 120601119904119906

= 120601119904119889

= minus120573

3+

120577

3

120601119889119906

= 120601119906119889

= minus1

2+

120573

6+

120577

3 120593

119906119889= 120593

119889119906= 1

120593119906119904

= 120593119889119904

= 120593119904119906

= 120593119904119889

= 120572

(28)



119902 997888rarr 119875119902119902 +

1003816100381610038161003816120595 (119902)10038161003816100381610038162

119902plusmn997888rarr 119875

119902119902plusmn+1003816100381610038161003816120595 (119902

plusmn)10038161003816100381610038162

(29)

Here119875119902= 1minussum119875



sum119875119906= 119886 (120601

2

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904)

sum119875119889= 119886 (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904)


sum119875119904= 119886 (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889)

(30)

and |120595(119902)|2 (|120595(119902



1003816100381610038161003816120595 (119906)10038161003816100381610038162

= 119886 [(21206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904) 119906 + 120601

2

119906119906119906

+ (1206012

119906119889+ 120593

2

119906119889) (119889 + 119889) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119889)10038161003816100381610038162

= 119886 [(1206012

119889119906+ 2120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904) 119889 + 120601

2

119889119889119889

+ (1206012

119889119906+ 120593

2

119889119906) (119906 + 119906) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119904)10038161003816100381610038162

= 119886 [(1206012

119904119906+ 120601

2

119904119889+ 2120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889) 119904 + 120601

2

119904119904119904

+ (1206012

119904119906+ 120593

2

119904119906) (119906 + 119906) + (120601

2

119904119889+ 120593

2

119904119889) (119889 + 119889)]

1003816100381610038161003816120595 (119906plusmn)10038161003816100381610038162

= 119886 [(1206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904) 119906

∓+ 120593

2

119906119889119889∓+ 120593

2

119906119904119904∓]

1003816100381610038161003816120595 (119889plusmn)10038161003816100381610038162

= 119886 [1205932

119889119906119906∓+ (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904) 119889

∓+ 120593

2

119889119904119904∓]

1003816100381610038161003816120595 (119904plusmn)10038161003816100381610038162

= 119886 [1205932

119904119906119906∓+ 120593

2

119904119889119889∓+ (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904) 119904

∓]

(31)



+


1199032

119901= (A minus 3B) (2119875

119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

minus1

3119875119889119889+minus

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119889119889++

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)]

1199032

Σ+

= (A minus 3B) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119904119904 +

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906)10038161003816100381610038162

minus1

3119875119904119904+minus

1

3

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119904119904++

1

3

1003816100381610038161003816120595 (119904+)10038161003816100381610038162

)]

(32)







1199032

Δ+

= (A minus 3B + 6C) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 5 (B minus C) (2119875119906119906++ 2

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+ 119875119889119889++1003816100381610038161003816120595 (119889

+)10038161003816100381610038162

)

(33)






119876Δ+

= 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

) 119886(2 +1205732

3+

21205772

3)

119876Ξlowastminus

= minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

) 119886(4120572

2

3+ 120573

2

+2120577

2

3)

(34)


lowastminusΣminus


119876Δ+

119901

= 2radic2[B1015840

(1 minus 119886(1 + 1205722

+1205732

3+

21205772

3)) minus C1015840

]

119876Σlowastminus

Σminus

= 2radic2B1015840

119886(1205722

3minus

1205732

3)

(35)


+







119886 = 012 120572 = 07 120573 = 04 120577 = minus015 (36)



119902119902 + |120595(119902)|

2 and 119902plusmn

rarr 119875119902119902plusmn+ |120595(119902




1199032


+ 1205732

+ 21205772

)) + sin2

120579 (1 minus119886

3(6 + 120573

2

+ 21205772

))]

1199032


3(3 + 9120572

2

+ 21205732

+ 41205772

)) + sin2

120579 (119886 (minus1 + 1205722

))]

1199032


119886

3(12 + 5120572

2

+ 41205732

+ 61205772

)) + sin2

120579 (1 minus119886

3(6 + 120572

2

+ 21205772

))]

1199032


119886

3(7120572

2

+ 21205772

)) + sin2

120579 (minus1 +119886

3(5120572

2

+ 21205732

+ 21205772

))]

1199032


119886

3(6 minus 120572

2

+ 21205732

+ 21205772

)) + sin2

120579 (119886

3(minus3 + 2120572

2

+ 1205732

))]

1199032


119886

3(3 + 5120572

2

+ 61205732

+ 41205772

)) + sin2

120579 (119886

3(minus3 + 120572

2

+ 21205732

))]

1199032


119886

3(2120572

2

+ 51205732

+ 21205772

)) + sin2

120579 (minus1 +119886

3(4120572

2

+ 31205732

+ 21205772

))]

1199032


3(3120572

2

+ 41205732

+ 21205772

)) + sin2

120579 (119886

9(minus9 + 6120572

2

+ 71205732

+ 21205772

))]

1199032


radic3(3 + 3120572

2

+ 1205732

+ 21205772

)]


119902119902 + |120595(119902)|

2 and 119902plusmn

rarr

119875119902119902plusmn+ |120595(119902



1199032

Δ++

A + 2B + C minus5119886

6(B minus C)(9 + 3120572

2

+ 21205732

+ 41205772

)

1199032

Δ+

A + 2B + C minus5119886

3(B minus C)(6 + 120573

2

+ 21205772

)

1199032

Δ0 5119886(B minus C)(minus1 + 120572

2

)

1199032

Δminus

A + 2B + C minus5119886

3(B minus C)(6120572

2

+ 1205732

+ 21205772

)

1199032

Σlowast+

A + 2B + C minus5119886

3(B minus C)(6 + 120572

2

+ 21205772

)

1199032

Σlowastminus

A + 2B + C minus5119886

3(B minus C)(5120572

2

+ 21205732

+ 21205772

)

1199032

Σlowast0

5119886


2

+ 1205732

)

1199032

Ξlowast0

5119886


2

+ 21205732

)

1199032


5119886

3(B minus C)(4120572

2

+ 31205732

+ 21205772

)

1199032

Ωminus

A + 2B + C minus5119886

3(B minus C)(3120572

2

+ 41205732

+ 21205772

)




119901=

0877 plusmn 0007 fm [12] 1199032

119899= minus01161 plusmn 00022 fm2 [12]

and 119876Δ+



A = 0879 B = 0094 C = 0016 (37)


B1015840

= minus0047 C1015840

= minus0008 (38)







HB120594PT[60]

120594PT [61 62] CCQM[52]

P120594QM [59] 1119873119888

[57 58]Lattice[63]

120594CQMconfig

With SU(3)


A = 0879

B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

1199010813 mdash 0735 0717 082 072 plusmn 009 0779 0685 0732 0801 0766

119903119901=

0877 plusmn 0007

1199032


minus01161plusmn 000221199032

Σ+

0813 079 1366 060 plusmn 002 113 081 plusmn 010 0928 0749 0732 0802 07671199032

Σminus


Σ0


Ξ0


Ξminus

0675 047 0997 049 plusmn 005 054 062 plusmn 007 0520 0502 0646 0683 06691199032


1199032




120594CQMWith SU(3)


B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

Δ++

1084 118 043 1011 mdash 0938 0961 09961199032

Δ+

1084 082 043 1011 0410 (57) 0938 0946 09831199032

Δ0


Δminus

1084 084 043 1011 minus0410 (57) 0938 1006 10331199032

Σlowast+

1084 097 042 1086 0399 (45) 0938 0940 09781199032

Σlowastminus

1084 084 037 0845 minus0360 (32) 0938 1013 10381199032

Σlowast0

00 034 003 0127 0020 (7) 00 minus0036 minus00301199032

Ξlowast0

00 049 006 0244 0043 (10) 00 minus0043 minus00351199032

Ξlowastminus

1084 082 033 0692 minus0330 (20) 0938 1019 10431199032

Ωminus

0390 078 029 0553 mdash 0245 0429 0355





1199032

Σ+

= 1199032

119901 119903

2

Ξminus

= 1199032

Σminus

= 1199032

119901+ 119903

2

119899 (39)




(2119906 + 119889 minus 2119906+minus 119889

+) + C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119899 3B1015840

(119906 + 2119889 minus 119906+minus 2119889

+) + C1015840

(119906 minus 4119889 minus 119906++ 4119889

+)

Σ+

3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+) + C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

Σminus

3B1015840

(2119889 + 119904 minus 2119889+minus 119904

+) + C1015840

(minus4119889 + 119904 + 4119889+minus 119904

+)

Σ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+)

+C1015840

(minus2119906 minus 2119889 + 119904 + 2119906++ 2119889

+minus 119904

+)

Ξ0

3B1015840

(119906 + 2119904 minus 119906+minus 2119904

+) + C1015840

(119906 minus 4119904 minus 119906++ 4119904

+)

Ξminus

3B1015840

(119889 + 2119904 minus 119889+minus 2119904

+) + C1015840

(119889 minus 4119904 minus 119889++ 4119904

+)

Λ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+) + 3C1015840

(minus119904 + 119904+)


1199032

Σ+

gt 1199032

119901 119903

2

Ξminus

gt 1199032

Σminus

gt 1199032

119901+ 119903

2

119899 (40)

Also we have

21199032

Λ= minus2119903

2

Σ0

= 1199032

Ξ0

= 1199032

119899 (41)


1199032

Λgt minus119903

2

Σ0

1199032

Ξ0

gt 1199032

119899 (42)


1199032

Σ+

minus 21199032

Σ0

minus 1199032

Σminus

= 0 (43)



Σminus

=












1199032

Δ++

= 1199032

Δ+

= 1199032

Δminus

= 1199032

Σlowast+

= 1199032

Σlowastminus

= 1199032

Ξlowastminus

(44)


1199032

Ξlowastminus

gt 1199032

Σlowastminus

gt 1199032

Δminus

gt 1199032

Δ++

gt 1199032

Δ+

gt 1199032

Σlowast+

(45)



21199032

Δ++

minus 1199032

Δ+

minus 1199032

Δ0

minus 1199032

Δminus

= 0

21199032

Δ++

minus 31199032

Δ+

+ 31199032

Δ0

+ 1199032

Δminus

= 0

1199032

Σlowast+

minus 21199032

Σlowast0

minus 1199032

Σlowastminus

= 0

(46)










Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)


(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)


(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)




+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840


(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772


Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772




1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)


1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)



+








Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





minus









+

rarr







⟨1199032

⟩ = int1198893

119903120588 (r) 1199032 (1)


1198760= int119889

3r120588 (r) (31199112 minus 1199032

) (2)








120588 = A1015840

3

sum

119894=1

1198901198941 minus B1015840

3

sum

119894 = 119895

119890119894[2120590

119894sdot 120590

119895minus (3120590

119894119911120590119895119911

minus 120590119894sdot 120590

119895)]

minus C1015840

3

sum

119894 = 119895 = 119896

119890119894[2120590

119895sdot 120590

119896minus (3120590

119895119911120590119896119911

minus 120590119895sdot 120590

119896)]

(3)


1199032 = A3

sum

119894=1

1198901198941 + B

3

sum

119894 = 119895

119890119894120590119894sdot 120590

119895+ C

3

sum

119894 = 119895 = 119896

119890119894120590119895sdot 120590

119896 (4)


119876 = B1015840

3

sum

119894 = 119895

119890119894(3120590

119894119911120590119895119911

minus 120590119894sdot 120590

119895)

+ C1015840

3

sum

119894 = 119895 = 119896

119890119894(3120590

119895119911120590119896119911

minus 120590119895sdot 120590

119896)

(5)




sum

119894 = 119895

119890119894(120590i sdot 120590j) = 2J sdot sum

119894

119890119894120590i minus 3sum

119894

119890119894

sum

119894 = 119895 = 119896


119894

119890119894minus sum

119894 = 119895

119890119894(120590i sdot 120590j)

(6)



(32)+ baryons


119890119894(120590i sdot 120590j) sum

119894 = 119895 = 119896

119890119894(120590j sdot 120590k)

119869 =1

23sum

119894

119890119894120590iz minus 3sum

119894

119890119894

minus3sum119894

119890119894120590iz

119869 =3

25sum

119894

119890119894120590iz minus 3sum

119894

119890119894

6sum119894

119890119894minus 5sum

119894

119890119894120590iz

(7)




1199032B = (A minus 3B)sum119894

119890119894+ 3 (B minus C)sum

119894

119890119894120590119894119911 (8)


119894

119890119894+ 5 (B minus C)sum

119894

119890119894120590iz (9)


119894119890119894) and spin (sum




1199032

B = ⟨B1003816100381610038161003816100381610038161199032B

100381610038161003816100381610038161003816B⟩ 119903

2

119861lowast

= ⟨Blowast1003816100381610038161003816100381610038161199032Blowast

100381610038161003816100381610038161003816Blowast

⟩ (10)



+


+spin (32)




119876B = B1015840

(3sum

119894 = 119895

119890119894120590iz120590jz minus 3sum

119894

119890119894120590iz + 3sum

119894

119890119894)

+ C1015840

(3 sum

119894 = 119895 = 119896

119890119894120590jz120590kz + 3sum

119894

119890119894120590iz)

119876Blowast = B1015840

(3sum

119894 = 119895

119890119894120590iz120590jz minus 5sum

119894

119890119894120590iz + 3sum

119894

119890119894)

+ C1015840

(3 sum

119894 = 119895 = 119896

119890119894120590jz120590kz + 5sum

119894

119890119894120590iz minus 6sum

119894

119890119894)

119876BlowastB = 3B1015840

sum

119894 = 119895

119890119894120590iz120590jz + 3C1015840

sum

119894 = 119895 = 119896

119890119894120590jz120590kz

(11)


119894119890119894) spin (sum


119894119890119894120590iz120590jz)





119876B = ⟨B 10038161003816100381610038161003816119876B


119876Blowast10038161003816100381610038161003816Blowast

⟩


10038161003816100381610038161003816B⟩

(12)



sum

119894

119890119894= sum

119902=119906119889119904

119899B119902119902 + sum

119902=119906119889119904

119899B119902119902

= 119899B119906119906 + 119899

B119889119889 + 119899

B119904119904 + 119899

B119906119906 + 119899

B119889119889 + 119899

B119904119904

sum

119894

119890119894120590119894119911

= sum

119902=119906119889119904

(119899B119902+

119902++ 119899

B119902minus

119902minus)

= 119899B119906+

119906++ 119899

B119906minus

119906minus+ 119899

B119889+

119889++ 119899

B119889minus

119889minus+ 119899

B119904+

119904++ 119899

B119904minus

119904minus

(13)

where 119899B119902(119899


119899B119902+

(119899B119902minus


minus) For a






119906119889119904

119899119902minus sum

119906119889119904

119899119902)119902


119906119889119904

119899119902+

minus sum

119906119889119904

119899119902minus

)119902+

(14)


|B⟩ equiv

100381610038161003816100381610038161003816100381610038168

1

2

+

⟩ = cos 120579100381610038161003816100381656 0+

⟩119873=0

+ sin 120579100381610038161003816100381670 0

+

⟩119873=2

(15)

with

100381610038161003816100381656 0+

⟩119873=0

=1

radic2(120593

1015840

1205941015840

+ 12059310158401015840

12059410158401015840

) 120595119904

(0+

)

100381610038161003816100381670 0+

⟩119873=2

=1

2[(120593

1015840

12059410158401015840

+ 12059310158401015840

1205941015840

) 1205951015840

(0+

)

+ (1205931015840

1205941015840

minus 12059310158401015840

12059410158401015840

) 12059510158401015840

(0+

)]

(16)





1199032


+minus 119889

+) + sin2

120579 (2119906++ 119889

+)]

1199032


++ 4119889

+) + sin2

120579 (119906++ 2119889

+)]

1199032

Σ+


+) + sin2

120579 (2119906++ 119904

+)]

1199032

Σminus


+) + sin2

120579 (2119889++ 119904

+)]

1199032

Σ0


+minus 119904

+) + sin2

120579 (119906++ 119889

++ 119904

+)]

1199032

Ξ0


+) + sin2

120579 (119906++ 2119904

+)]

1199032

Ξminus


+) + sin2

120579 (119889++ 2119904

+)]

1199032


+) + sin2

120579 (119906++ 119889

++ 119904

+)]

1199032


+minus 119889

+]


Chargeradii NQM

1199032

Δ++

1


+)]

1199032


++ 119889

+)

1199032


++ 2119889

+)

1199032


+)

1199032


++ 119904

+)

1199032


++ 119904

+)

1199032


++ 119889

++ 119904

+)

1199032


++ 2119904

+)

1199032


++ 2119904

+)

1199032

Ωminus




1199032

119901= (A minus 3B) (2119906 + 119889) + 3 (B minus C)


3119906+minus

1

3119889+) + sin2

120579 (2

3119906++

1

3119889+)]

1199032

Σ+

= (A minus 3B) (2119906 + 119904) + 3 (B minus C)


3119906+minus

1

3119904+) + sin2

120579 (2

3119906++

1

3119904+)]

(17)




1003816100381610038161003816Blowast

⟩ equiv

1003816100381610038161003816100381610038161003816100381610

3

2

+

⟩ =100381610038161003816100381656 0

+

⟩119873=0

= 120594119904

120593119904

120595119904

(0+

) (18)




119906119889119904

119899119902minus sum

119906119889119904

119899119902)119902


119906119889119904

119899119902+

minus sum

119906119889119904

119899119902minus

)119902+

(19)


expressed as

1199032

Δ+


+) (20)




119876119901= 3B1015840

(2119906 + 119889 minus 2119906+minus 119889

+)

+ C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119876Σ+ = 3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+)

+ C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

(21)




119876Δ+ = B1015840

(6119906 + 3119889 + 2119906++ 119889

+)

+ C1015840

(minus6119906 minus 3119889 + 10119906++ 5119889

+)


(3119889 + 6119904 + 119889++ 2119904

+)

+ C1015840

(minus3119889 minus 6119904 + 5119889++ 10119904

+)

(22)





be expressed as

119876Δ+

119901= 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889)

119876Σlowastminus


(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)

(23)



rarr





+






+ 1199021015840

∓997888rarr (119902119902

1015840

) + 1199021015840

∓ (24)

where 1199021199021015840



L = 1198928119902Φ

1015840

119902 (25)

with

119902 = (

119906

119889

119904

)

Φ1015840

= (

1205870

radic2

+120573

120578

radic6

+ 120577

1205781015840

radic3

120587+

120572119870+

120587minus

minus

1205870

radic2

+ 120573

120578

radic6

+ 120577

1205781015840

radic3

1205721198700

120572119870minus

120572119870

0

minus120573

2120578

radic6

+ 120577

1205781015840

radic3

)

(26)

where 120577 = 1198921119892

8 119892

1and 119892





2119886 1205732

119886 and 1205772119886




119872119904gt 119872



gt 119872120587and119872

1205781015840 gt 119872

119870120578) [111ndash119]


Φ1015840

= (

120601119906119906

119906119906 + 120601119906119889

119889119889 + 120601119906119904119904119904 120593

119906119889119906119889 120593

119906119904119906119904

120593119889119906

119889119906 120601119889119906

119906119906 + 120601119889119889

119889119889 + 120601119889119904119904119904 120593

119889119904119889119904

120593119904119906119904119906 120593

119904119889119904119889 120601

119904119906119906119906 + 120601

119904119889119889119889 + 120601

119904119904119904119904) (27)

where

120601119906119906

= 120601119889119889

=1

2+

120573

6+

120577

3 120601

119904119904=

2120573

3+

120577

3

120601119906119904

= 120601119889119904

= 120601119904119906

= 120601119904119889

= minus120573

3+

120577

3

120601119889119906

= 120601119906119889

= minus1

2+

120573

6+

120577

3 120593

119906119889= 120593

119889119906= 1

120593119906119904

= 120593119889119904

= 120593119904119906

= 120593119904119889

= 120572

(28)



119902 997888rarr 119875119902119902 +

1003816100381610038161003816120595 (119902)10038161003816100381610038162

119902plusmn997888rarr 119875

119902119902plusmn+1003816100381610038161003816120595 (119902

plusmn)10038161003816100381610038162

(29)

Here119875119902= 1minussum119875



sum119875119906= 119886 (120601

2

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904)

sum119875119889= 119886 (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904)


sum119875119904= 119886 (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889)

(30)

and |120595(119902)|2 (|120595(119902



1003816100381610038161003816120595 (119906)10038161003816100381610038162

= 119886 [(21206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904) 119906 + 120601

2

119906119906119906

+ (1206012

119906119889+ 120593

2

119906119889) (119889 + 119889) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119889)10038161003816100381610038162

= 119886 [(1206012

119889119906+ 2120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904) 119889 + 120601

2

119889119889119889

+ (1206012

119889119906+ 120593

2

119889119906) (119906 + 119906) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119904)10038161003816100381610038162

= 119886 [(1206012

119904119906+ 120601

2

119904119889+ 2120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889) 119904 + 120601

2

119904119904119904

+ (1206012

119904119906+ 120593

2

119904119906) (119906 + 119906) + (120601

2

119904119889+ 120593

2

119904119889) (119889 + 119889)]

1003816100381610038161003816120595 (119906plusmn)10038161003816100381610038162

= 119886 [(1206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904) 119906

∓+ 120593

2

119906119889119889∓+ 120593

2

119906119904119904∓]

1003816100381610038161003816120595 (119889plusmn)10038161003816100381610038162

= 119886 [1205932

119889119906119906∓+ (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904) 119889

∓+ 120593

2

119889119904119904∓]

1003816100381610038161003816120595 (119904plusmn)10038161003816100381610038162

= 119886 [1205932

119904119906119906∓+ 120593

2

119904119889119889∓+ (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904) 119904

∓]

(31)



+


1199032

119901= (A minus 3B) (2119875

119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

minus1

3119875119889119889+minus

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119889119889++

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)]

1199032

Σ+

= (A minus 3B) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119904119904 +

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906)10038161003816100381610038162

minus1

3119875119904119904+minus

1

3

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119904119904++

1

3

1003816100381610038161003816120595 (119904+)10038161003816100381610038162

)]

(32)







1199032

Δ+

= (A minus 3B + 6C) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 5 (B minus C) (2119875119906119906++ 2

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+ 119875119889119889++1003816100381610038161003816120595 (119889

+)10038161003816100381610038162

)

(33)






119876Δ+

= 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

) 119886(2 +1205732

3+

21205772

3)

119876Ξlowastminus

= minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

) 119886(4120572

2

3+ 120573

2

+2120577

2

3)

(34)


lowastminusΣminus


119876Δ+

119901

= 2radic2[B1015840

(1 minus 119886(1 + 1205722

+1205732

3+

21205772

3)) minus C1015840

]

119876Σlowastminus

Σminus

= 2radic2B1015840

119886(1205722

3minus

1205732

3)

(35)


+







119886 = 012 120572 = 07 120573 = 04 120577 = minus015 (36)



119902119902 + |120595(119902)|

2 and 119902plusmn

rarr 119875119902119902plusmn+ |120595(119902




1199032


+ 1205732

+ 21205772

)) + sin2

120579 (1 minus119886

3(6 + 120573

2

+ 21205772

))]

1199032


3(3 + 9120572

2

+ 21205732

+ 41205772

)) + sin2

120579 (119886 (minus1 + 1205722

))]

1199032


119886

3(12 + 5120572

2

+ 41205732

+ 61205772

)) + sin2

120579 (1 minus119886

3(6 + 120572

2

+ 21205772

))]

1199032


119886

3(7120572

2

+ 21205772

)) + sin2

120579 (minus1 +119886

3(5120572

2

+ 21205732

+ 21205772

))]

1199032


119886

3(6 minus 120572

2

+ 21205732

+ 21205772

)) + sin2

120579 (119886

3(minus3 + 2120572

2

+ 1205732

))]

1199032


119886

3(3 + 5120572

2

+ 61205732

+ 41205772

)) + sin2

120579 (119886

3(minus3 + 120572

2

+ 21205732

))]

1199032


119886

3(2120572

2

+ 51205732

+ 21205772

)) + sin2

120579 (minus1 +119886

3(4120572

2

+ 31205732

+ 21205772

))]

1199032


3(3120572

2

+ 41205732

+ 21205772

)) + sin2

120579 (119886

9(minus9 + 6120572

2

+ 71205732

+ 21205772

))]

1199032


radic3(3 + 3120572

2

+ 1205732

+ 21205772

)]


119902119902 + |120595(119902)|

2 and 119902plusmn

rarr

119875119902119902plusmn+ |120595(119902



1199032

Δ++

A + 2B + C minus5119886

6(B minus C)(9 + 3120572

2

+ 21205732

+ 41205772

)

1199032

Δ+

A + 2B + C minus5119886

3(B minus C)(6 + 120573

2

+ 21205772

)

1199032

Δ0 5119886(B minus C)(minus1 + 120572

2

)

1199032

Δminus

A + 2B + C minus5119886

3(B minus C)(6120572

2

+ 1205732

+ 21205772

)

1199032

Σlowast+

A + 2B + C minus5119886

3(B minus C)(6 + 120572

2

+ 21205772

)

1199032

Σlowastminus

A + 2B + C minus5119886

3(B minus C)(5120572

2

+ 21205732

+ 21205772

)

1199032

Σlowast0

5119886


2

+ 1205732

)

1199032

Ξlowast0

5119886


2

+ 21205732

)

1199032


5119886

3(B minus C)(4120572

2

+ 31205732

+ 21205772

)

1199032

Ωminus

A + 2B + C minus5119886

3(B minus C)(3120572

2

+ 41205732

+ 21205772

)




119901=

0877 plusmn 0007 fm [12] 1199032

119899= minus01161 plusmn 00022 fm2 [12]

and 119876Δ+



A = 0879 B = 0094 C = 0016 (37)


B1015840

= minus0047 C1015840

= minus0008 (38)







HB120594PT[60]

120594PT [61 62] CCQM[52]

P120594QM [59] 1119873119888

[57 58]Lattice[63]

120594CQMconfig

With SU(3)


A = 0879

B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

1199010813 mdash 0735 0717 082 072 plusmn 009 0779 0685 0732 0801 0766

119903119901=

0877 plusmn 0007

1199032


minus01161plusmn 000221199032

Σ+

0813 079 1366 060 plusmn 002 113 081 plusmn 010 0928 0749 0732 0802 07671199032

Σminus


Σ0


Ξ0


Ξminus

0675 047 0997 049 plusmn 005 054 062 plusmn 007 0520 0502 0646 0683 06691199032


1199032




120594CQMWith SU(3)


B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

Δ++

1084 118 043 1011 mdash 0938 0961 09961199032

Δ+

1084 082 043 1011 0410 (57) 0938 0946 09831199032

Δ0


Δminus

1084 084 043 1011 minus0410 (57) 0938 1006 10331199032

Σlowast+

1084 097 042 1086 0399 (45) 0938 0940 09781199032

Σlowastminus

1084 084 037 0845 minus0360 (32) 0938 1013 10381199032

Σlowast0

00 034 003 0127 0020 (7) 00 minus0036 minus00301199032

Ξlowast0

00 049 006 0244 0043 (10) 00 minus0043 minus00351199032

Ξlowastminus

1084 082 033 0692 minus0330 (20) 0938 1019 10431199032

Ωminus

0390 078 029 0553 mdash 0245 0429 0355





1199032

Σ+

= 1199032

119901 119903

2

Ξminus

= 1199032

Σminus

= 1199032

119901+ 119903

2

119899 (39)




(2119906 + 119889 minus 2119906+minus 119889

+) + C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119899 3B1015840

(119906 + 2119889 minus 119906+minus 2119889

+) + C1015840

(119906 minus 4119889 minus 119906++ 4119889

+)

Σ+

3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+) + C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

Σminus

3B1015840

(2119889 + 119904 minus 2119889+minus 119904

+) + C1015840

(minus4119889 + 119904 + 4119889+minus 119904

+)

Σ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+)

+C1015840

(minus2119906 minus 2119889 + 119904 + 2119906++ 2119889

+minus 119904

+)

Ξ0

3B1015840

(119906 + 2119904 minus 119906+minus 2119904

+) + C1015840

(119906 minus 4119904 minus 119906++ 4119904

+)

Ξminus

3B1015840

(119889 + 2119904 minus 119889+minus 2119904

+) + C1015840

(119889 minus 4119904 minus 119889++ 4119904

+)

Λ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+) + 3C1015840

(minus119904 + 119904+)


1199032

Σ+

gt 1199032

119901 119903

2

Ξminus

gt 1199032

Σminus

gt 1199032

119901+ 119903

2

119899 (40)

Also we have

21199032

Λ= minus2119903

2

Σ0

= 1199032

Ξ0

= 1199032

119899 (41)


1199032

Λgt minus119903

2

Σ0

1199032

Ξ0

gt 1199032

119899 (42)


1199032

Σ+

minus 21199032

Σ0

minus 1199032

Σminus

= 0 (43)



Σminus

=












1199032

Δ++

= 1199032

Δ+

= 1199032

Δminus

= 1199032

Σlowast+

= 1199032

Σlowastminus

= 1199032

Ξlowastminus

(44)


1199032

Ξlowastminus

gt 1199032

Σlowastminus

gt 1199032

Δminus

gt 1199032

Δ++

gt 1199032

Δ+

gt 1199032

Σlowast+

(45)



21199032

Δ++

minus 1199032

Δ+

minus 1199032

Δ0

minus 1199032

Δminus

= 0

21199032

Δ++

minus 31199032

Δ+

+ 31199032

Δ0

+ 1199032

Δminus

= 0

1199032

Σlowast+

minus 21199032

Σlowast0

minus 1199032

Σlowastminus

= 0

(46)










Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)


(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)


(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)




+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840


(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772


Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772




1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)


1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)



+








Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






1199032B = (A minus 3B)sum119894

119890119894+ 3 (B minus C)sum

119894

119890119894120590119894119911 (8)


119894

119890119894+ 5 (B minus C)sum

119894

119890119894120590iz (9)


119894119890119894) and spin (sum




1199032

B = ⟨B1003816100381610038161003816100381610038161199032B

100381610038161003816100381610038161003816B⟩ 119903

2

119861lowast

= ⟨Blowast1003816100381610038161003816100381610038161199032Blowast

100381610038161003816100381610038161003816Blowast

⟩ (10)



+


+spin (32)




119876B = B1015840

(3sum

119894 = 119895

119890119894120590iz120590jz minus 3sum

119894

119890119894120590iz + 3sum

119894

119890119894)

+ C1015840

(3 sum

119894 = 119895 = 119896

119890119894120590jz120590kz + 3sum

119894

119890119894120590iz)

119876Blowast = B1015840

(3sum

119894 = 119895

119890119894120590iz120590jz minus 5sum

119894

119890119894120590iz + 3sum

119894

119890119894)

+ C1015840

(3 sum

119894 = 119895 = 119896

119890119894120590jz120590kz + 5sum

119894

119890119894120590iz minus 6sum

119894

119890119894)

119876BlowastB = 3B1015840

sum

119894 = 119895

119890119894120590iz120590jz + 3C1015840

sum

119894 = 119895 = 119896

119890119894120590jz120590kz

(11)


119894119890119894) spin (sum


119894119890119894120590iz120590jz)





119876B = ⟨B 10038161003816100381610038161003816119876B


119876Blowast10038161003816100381610038161003816Blowast

⟩


10038161003816100381610038161003816B⟩

(12)



sum

119894

119890119894= sum

119902=119906119889119904

119899B119902119902 + sum

119902=119906119889119904

119899B119902119902

= 119899B119906119906 + 119899

B119889119889 + 119899

B119904119904 + 119899

B119906119906 + 119899

B119889119889 + 119899

B119904119904

sum

119894

119890119894120590119894119911

= sum

119902=119906119889119904

(119899B119902+

119902++ 119899

B119902minus

119902minus)

= 119899B119906+

119906++ 119899

B119906minus

119906minus+ 119899

B119889+

119889++ 119899

B119889minus

119889minus+ 119899

B119904+

119904++ 119899

B119904minus

119904minus

(13)

where 119899B119902(119899


119899B119902+

(119899B119902minus


minus) For a






119906119889119904

119899119902minus sum

119906119889119904

119899119902)119902


119906119889119904

119899119902+

minus sum

119906119889119904

119899119902minus

)119902+

(14)


|B⟩ equiv

100381610038161003816100381610038161003816100381610038168

1

2

+

⟩ = cos 120579100381610038161003816100381656 0+

⟩119873=0

+ sin 120579100381610038161003816100381670 0

+

⟩119873=2

(15)

with

100381610038161003816100381656 0+

⟩119873=0

=1

radic2(120593

1015840

1205941015840

+ 12059310158401015840

12059410158401015840

) 120595119904

(0+

)

100381610038161003816100381670 0+

⟩119873=2

=1

2[(120593

1015840

12059410158401015840

+ 12059310158401015840

1205941015840

) 1205951015840

(0+

)

+ (1205931015840

1205941015840

minus 12059310158401015840

12059410158401015840

) 12059510158401015840

(0+

)]

(16)





1199032


+minus 119889

+) + sin2

120579 (2119906++ 119889

+)]

1199032


++ 4119889

+) + sin2

120579 (119906++ 2119889

+)]

1199032

Σ+


+) + sin2

120579 (2119906++ 119904

+)]

1199032

Σminus


+) + sin2

120579 (2119889++ 119904

+)]

1199032

Σ0


+minus 119904

+) + sin2

120579 (119906++ 119889

++ 119904

+)]

1199032

Ξ0


+) + sin2

120579 (119906++ 2119904

+)]

1199032

Ξminus


+) + sin2

120579 (119889++ 2119904

+)]

1199032


+) + sin2

120579 (119906++ 119889

++ 119904

+)]

1199032


+minus 119889

+]


Chargeradii NQM

1199032

Δ++

1


+)]

1199032


++ 119889

+)

1199032


++ 2119889

+)

1199032


+)

1199032


++ 119904

+)

1199032


++ 119904

+)

1199032


++ 119889

++ 119904

+)

1199032


++ 2119904

+)

1199032


++ 2119904

+)

1199032

Ωminus




1199032

119901= (A minus 3B) (2119906 + 119889) + 3 (B minus C)


3119906+minus

1

3119889+) + sin2

120579 (2

3119906++

1

3119889+)]

1199032

Σ+

= (A minus 3B) (2119906 + 119904) + 3 (B minus C)


3119906+minus

1

3119904+) + sin2

120579 (2

3119906++

1

3119904+)]

(17)




1003816100381610038161003816Blowast

⟩ equiv

1003816100381610038161003816100381610038161003816100381610

3

2

+

⟩ =100381610038161003816100381656 0

+

⟩119873=0

= 120594119904

120593119904

120595119904

(0+

) (18)




119906119889119904

119899119902minus sum

119906119889119904

119899119902)119902


119906119889119904

119899119902+

minus sum

119906119889119904

119899119902minus

)119902+

(19)


expressed as

1199032

Δ+


+) (20)




119876119901= 3B1015840

(2119906 + 119889 minus 2119906+minus 119889

+)

+ C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119876Σ+ = 3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+)

+ C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

(21)




119876Δ+ = B1015840

(6119906 + 3119889 + 2119906++ 119889

+)

+ C1015840

(minus6119906 minus 3119889 + 10119906++ 5119889

+)


(3119889 + 6119904 + 119889++ 2119904

+)

+ C1015840

(minus3119889 minus 6119904 + 5119889++ 10119904

+)

(22)





be expressed as

119876Δ+

119901= 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889)

119876Σlowastminus


(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)

(23)



rarr





+






+ 1199021015840

∓997888rarr (119902119902

1015840

) + 1199021015840

∓ (24)

where 1199021199021015840



L = 1198928119902Φ

1015840

119902 (25)

with

119902 = (

119906

119889

119904

)

Φ1015840

= (

1205870

radic2

+120573

120578

radic6

+ 120577

1205781015840

radic3

120587+

120572119870+

120587minus

minus

1205870

radic2

+ 120573

120578

radic6

+ 120577

1205781015840

radic3

1205721198700

120572119870minus

120572119870

0

minus120573

2120578

radic6

+ 120577

1205781015840

radic3

)

(26)

where 120577 = 1198921119892

8 119892

1and 119892





2119886 1205732

119886 and 1205772119886




119872119904gt 119872



gt 119872120587and119872

1205781015840 gt 119872

119870120578) [111ndash119]


Φ1015840

= (

120601119906119906

119906119906 + 120601119906119889

119889119889 + 120601119906119904119904119904 120593

119906119889119906119889 120593

119906119904119906119904

120593119889119906

119889119906 120601119889119906

119906119906 + 120601119889119889

119889119889 + 120601119889119904119904119904 120593

119889119904119889119904

120593119904119906119904119906 120593

119904119889119904119889 120601

119904119906119906119906 + 120601

119904119889119889119889 + 120601

119904119904119904119904) (27)

where

120601119906119906

= 120601119889119889

=1

2+

120573

6+

120577

3 120601

119904119904=

2120573

3+

120577

3

120601119906119904

= 120601119889119904

= 120601119904119906

= 120601119904119889

= minus120573

3+

120577

3

120601119889119906

= 120601119906119889

= minus1

2+

120573

6+

120577

3 120593

119906119889= 120593

119889119906= 1

120593119906119904

= 120593119889119904

= 120593119904119906

= 120593119904119889

= 120572

(28)



119902 997888rarr 119875119902119902 +

1003816100381610038161003816120595 (119902)10038161003816100381610038162

119902plusmn997888rarr 119875

119902119902plusmn+1003816100381610038161003816120595 (119902

plusmn)10038161003816100381610038162

(29)

Here119875119902= 1minussum119875



sum119875119906= 119886 (120601

2

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904)

sum119875119889= 119886 (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904)


sum119875119904= 119886 (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889)

(30)

and |120595(119902)|2 (|120595(119902



1003816100381610038161003816120595 (119906)10038161003816100381610038162

= 119886 [(21206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904) 119906 + 120601

2

119906119906119906

+ (1206012

119906119889+ 120593

2

119906119889) (119889 + 119889) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119889)10038161003816100381610038162

= 119886 [(1206012

119889119906+ 2120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904) 119889 + 120601

2

119889119889119889

+ (1206012

119889119906+ 120593

2

119889119906) (119906 + 119906) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119904)10038161003816100381610038162

= 119886 [(1206012

119904119906+ 120601

2

119904119889+ 2120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889) 119904 + 120601

2

119904119904119904

+ (1206012

119904119906+ 120593

2

119904119906) (119906 + 119906) + (120601

2

119904119889+ 120593

2

119904119889) (119889 + 119889)]

1003816100381610038161003816120595 (119906plusmn)10038161003816100381610038162

= 119886 [(1206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904) 119906

∓+ 120593

2

119906119889119889∓+ 120593

2

119906119904119904∓]

1003816100381610038161003816120595 (119889plusmn)10038161003816100381610038162

= 119886 [1205932

119889119906119906∓+ (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904) 119889

∓+ 120593

2

119889119904119904∓]

1003816100381610038161003816120595 (119904plusmn)10038161003816100381610038162

= 119886 [1205932

119904119906119906∓+ 120593

2

119904119889119889∓+ (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904) 119904

∓]

(31)



+


1199032

119901= (A minus 3B) (2119875

119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

minus1

3119875119889119889+minus

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119889119889++

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)]

1199032

Σ+

= (A minus 3B) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119904119904 +

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906)10038161003816100381610038162

minus1

3119875119904119904+minus

1

3

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119904119904++

1

3

1003816100381610038161003816120595 (119904+)10038161003816100381610038162

)]

(32)







1199032

Δ+

= (A minus 3B + 6C) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 5 (B minus C) (2119875119906119906++ 2

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+ 119875119889119889++1003816100381610038161003816120595 (119889

+)10038161003816100381610038162

)

(33)






119876Δ+

= 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

) 119886(2 +1205732

3+

21205772

3)

119876Ξlowastminus

= minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

) 119886(4120572

2

3+ 120573

2

+2120577

2

3)

(34)


lowastminusΣminus


119876Δ+

119901

= 2radic2[B1015840

(1 minus 119886(1 + 1205722

+1205732

3+

21205772

3)) minus C1015840

]

119876Σlowastminus

Σminus

= 2radic2B1015840

119886(1205722

3minus

1205732

3)

(35)


+







119886 = 012 120572 = 07 120573 = 04 120577 = minus015 (36)



119902119902 + |120595(119902)|

2 and 119902plusmn

rarr 119875119902119902plusmn+ |120595(119902




1199032


+ 1205732

+ 21205772

)) + sin2

120579 (1 minus119886

3(6 + 120573

2

+ 21205772

))]

1199032


3(3 + 9120572

2

+ 21205732

+ 41205772

)) + sin2

120579 (119886 (minus1 + 1205722

))]

1199032


119886

3(12 + 5120572

2

+ 41205732

+ 61205772

)) + sin2

120579 (1 minus119886

3(6 + 120572

2

+ 21205772

))]

1199032


119886

3(7120572

2

+ 21205772

)) + sin2

120579 (minus1 +119886

3(5120572

2

+ 21205732

+ 21205772

))]

1199032


119886

3(6 minus 120572

2

+ 21205732

+ 21205772

)) + sin2

120579 (119886

3(minus3 + 2120572

2

+ 1205732

))]

1199032


119886

3(3 + 5120572

2

+ 61205732

+ 41205772

)) + sin2

120579 (119886

3(minus3 + 120572

2

+ 21205732

))]

1199032


119886

3(2120572

2

+ 51205732

+ 21205772

)) + sin2

120579 (minus1 +119886

3(4120572

2

+ 31205732

+ 21205772

))]

1199032


3(3120572

2

+ 41205732

+ 21205772

)) + sin2

120579 (119886

9(minus9 + 6120572

2

+ 71205732

+ 21205772

))]

1199032


radic3(3 + 3120572

2

+ 1205732

+ 21205772

)]


119902119902 + |120595(119902)|

2 and 119902plusmn

rarr

119875119902119902plusmn+ |120595(119902



1199032

Δ++

A + 2B + C minus5119886

6(B minus C)(9 + 3120572

2

+ 21205732

+ 41205772

)

1199032

Δ+

A + 2B + C minus5119886

3(B minus C)(6 + 120573

2

+ 21205772

)

1199032

Δ0 5119886(B minus C)(minus1 + 120572

2

)

1199032

Δminus

A + 2B + C minus5119886

3(B minus C)(6120572

2

+ 1205732

+ 21205772

)

1199032

Σlowast+

A + 2B + C minus5119886

3(B minus C)(6 + 120572

2

+ 21205772

)

1199032

Σlowastminus

A + 2B + C minus5119886

3(B minus C)(5120572

2

+ 21205732

+ 21205772

)

1199032

Σlowast0

5119886


2

+ 1205732

)

1199032

Ξlowast0

5119886


2

+ 21205732

)

1199032


5119886

3(B minus C)(4120572

2

+ 31205732

+ 21205772

)

1199032

Ωminus

A + 2B + C minus5119886

3(B minus C)(3120572

2

+ 41205732

+ 21205772

)




119901=

0877 plusmn 0007 fm [12] 1199032

119899= minus01161 plusmn 00022 fm2 [12]

and 119876Δ+



A = 0879 B = 0094 C = 0016 (37)


B1015840

= minus0047 C1015840

= minus0008 (38)







HB120594PT[60]

120594PT [61 62] CCQM[52]

P120594QM [59] 1119873119888

[57 58]Lattice[63]

120594CQMconfig

With SU(3)


A = 0879

B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

1199010813 mdash 0735 0717 082 072 plusmn 009 0779 0685 0732 0801 0766

119903119901=

0877 plusmn 0007

1199032


minus01161plusmn 000221199032

Σ+

0813 079 1366 060 plusmn 002 113 081 plusmn 010 0928 0749 0732 0802 07671199032

Σminus


Σ0


Ξ0


Ξminus

0675 047 0997 049 plusmn 005 054 062 plusmn 007 0520 0502 0646 0683 06691199032


1199032




120594CQMWith SU(3)


B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

Δ++

1084 118 043 1011 mdash 0938 0961 09961199032

Δ+

1084 082 043 1011 0410 (57) 0938 0946 09831199032

Δ0


Δminus

1084 084 043 1011 minus0410 (57) 0938 1006 10331199032

Σlowast+

1084 097 042 1086 0399 (45) 0938 0940 09781199032

Σlowastminus

1084 084 037 0845 minus0360 (32) 0938 1013 10381199032

Σlowast0

00 034 003 0127 0020 (7) 00 minus0036 minus00301199032

Ξlowast0

00 049 006 0244 0043 (10) 00 minus0043 minus00351199032

Ξlowastminus

1084 082 033 0692 minus0330 (20) 0938 1019 10431199032

Ωminus

0390 078 029 0553 mdash 0245 0429 0355





1199032

Σ+

= 1199032

119901 119903

2

Ξminus

= 1199032

Σminus

= 1199032

119901+ 119903

2

119899 (39)




(2119906 + 119889 minus 2119906+minus 119889

+) + C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119899 3B1015840

(119906 + 2119889 minus 119906+minus 2119889

+) + C1015840

(119906 minus 4119889 minus 119906++ 4119889

+)

Σ+

3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+) + C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

Σminus

3B1015840

(2119889 + 119904 minus 2119889+minus 119904

+) + C1015840

(minus4119889 + 119904 + 4119889+minus 119904

+)

Σ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+)

+C1015840

(minus2119906 minus 2119889 + 119904 + 2119906++ 2119889

+minus 119904

+)

Ξ0

3B1015840

(119906 + 2119904 minus 119906+minus 2119904

+) + C1015840

(119906 minus 4119904 minus 119906++ 4119904

+)

Ξminus

3B1015840

(119889 + 2119904 minus 119889+minus 2119904

+) + C1015840

(119889 minus 4119904 minus 119889++ 4119904

+)

Λ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+) + 3C1015840

(minus119904 + 119904+)


1199032

Σ+

gt 1199032

119901 119903

2

Ξminus

gt 1199032

Σminus

gt 1199032

119901+ 119903

2

119899 (40)

Also we have

21199032

Λ= minus2119903

2

Σ0

= 1199032

Ξ0

= 1199032

119899 (41)


1199032

Λgt minus119903

2

Σ0

1199032

Ξ0

gt 1199032

119899 (42)


1199032

Σ+

minus 21199032

Σ0

minus 1199032

Σminus

= 0 (43)



Σminus

=












1199032

Δ++

= 1199032

Δ+

= 1199032

Δminus

= 1199032

Σlowast+

= 1199032

Σlowastminus

= 1199032

Ξlowastminus

(44)


1199032

Ξlowastminus

gt 1199032

Σlowastminus

gt 1199032

Δminus

gt 1199032

Δ++

gt 1199032

Δ+

gt 1199032

Σlowast+

(45)



21199032

Δ++

minus 1199032

Δ+

minus 1199032

Δ0

minus 1199032

Δminus

= 0

21199032

Δ++

minus 31199032

Δ+

+ 31199032

Δ0

+ 1199032

Δminus

= 0

1199032

Σlowast+

minus 21199032

Σlowast0

minus 1199032

Σlowastminus

= 0

(46)










Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)


(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)


(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)




+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840


(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772


Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772




1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)


1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)



+








Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






1199032


+minus 119889

+) + sin2

120579 (2119906++ 119889

+)]

1199032


++ 4119889

+) + sin2

120579 (119906++ 2119889

+)]

1199032

Σ+


+) + sin2

120579 (2119906++ 119904

+)]

1199032

Σminus


+) + sin2

120579 (2119889++ 119904

+)]

1199032

Σ0


+minus 119904

+) + sin2

120579 (119906++ 119889

++ 119904

+)]

1199032

Ξ0


+) + sin2

120579 (119906++ 2119904

+)]

1199032

Ξminus


+) + sin2

120579 (119889++ 2119904

+)]

1199032


+) + sin2

120579 (119906++ 119889

++ 119904

+)]

1199032


+minus 119889

+]


Chargeradii NQM

1199032

Δ++

1


+)]

1199032


++ 119889

+)

1199032


++ 2119889

+)

1199032


+)

1199032


++ 119904

+)

1199032


++ 119904

+)

1199032


++ 119889

++ 119904

+)

1199032


++ 2119904

+)

1199032


++ 2119904

+)

1199032

Ωminus




1199032

119901= (A minus 3B) (2119906 + 119889) + 3 (B minus C)


3119906+minus

1

3119889+) + sin2

120579 (2

3119906++

1

3119889+)]

1199032

Σ+

= (A minus 3B) (2119906 + 119904) + 3 (B minus C)


3119906+minus

1

3119904+) + sin2

120579 (2

3119906++

1

3119904+)]

(17)




1003816100381610038161003816Blowast

⟩ equiv

1003816100381610038161003816100381610038161003816100381610

3

2

+

⟩ =100381610038161003816100381656 0

+

⟩119873=0

= 120594119904

120593119904

120595119904

(0+

) (18)




119906119889119904

119899119902minus sum

119906119889119904

119899119902)119902


119906119889119904

119899119902+

minus sum

119906119889119904

119899119902minus

)119902+

(19)


expressed as

1199032

Δ+


+) (20)




119876119901= 3B1015840

(2119906 + 119889 minus 2119906+minus 119889

+)

+ C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119876Σ+ = 3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+)

+ C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

(21)




119876Δ+ = B1015840

(6119906 + 3119889 + 2119906++ 119889

+)

+ C1015840

(minus6119906 minus 3119889 + 10119906++ 5119889

+)


(3119889 + 6119904 + 119889++ 2119904

+)

+ C1015840

(minus3119889 minus 6119904 + 5119889++ 10119904

+)

(22)





be expressed as

119876Δ+

119901= 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889)

119876Σlowastminus


(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)

(23)



rarr





+






+ 1199021015840

∓997888rarr (119902119902

1015840

) + 1199021015840

∓ (24)

where 1199021199021015840



L = 1198928119902Φ

1015840

119902 (25)

with

119902 = (

119906

119889

119904

)

Φ1015840

= (

1205870

radic2

+120573

120578

radic6

+ 120577

1205781015840

radic3

120587+

120572119870+

120587minus

minus

1205870

radic2

+ 120573

120578

radic6

+ 120577

1205781015840

radic3

1205721198700

120572119870minus

120572119870

0

minus120573

2120578

radic6

+ 120577

1205781015840

radic3

)

(26)

where 120577 = 1198921119892

8 119892

1and 119892





2119886 1205732

119886 and 1205772119886




119872119904gt 119872



gt 119872120587and119872

1205781015840 gt 119872

119870120578) [111ndash119]


Φ1015840

= (

120601119906119906

119906119906 + 120601119906119889

119889119889 + 120601119906119904119904119904 120593

119906119889119906119889 120593

119906119904119906119904

120593119889119906

119889119906 120601119889119906

119906119906 + 120601119889119889

119889119889 + 120601119889119904119904119904 120593

119889119904119889119904

120593119904119906119904119906 120593

119904119889119904119889 120601

119904119906119906119906 + 120601

119904119889119889119889 + 120601

119904119904119904119904) (27)

where

120601119906119906

= 120601119889119889

=1

2+

120573

6+

120577

3 120601

119904119904=

2120573

3+

120577

3

120601119906119904

= 120601119889119904

= 120601119904119906

= 120601119904119889

= minus120573

3+

120577

3

120601119889119906

= 120601119906119889

= minus1

2+

120573

6+

120577

3 120593

119906119889= 120593

119889119906= 1

120593119906119904

= 120593119889119904

= 120593119904119906

= 120593119904119889

= 120572

(28)



119902 997888rarr 119875119902119902 +

1003816100381610038161003816120595 (119902)10038161003816100381610038162

119902plusmn997888rarr 119875

119902119902plusmn+1003816100381610038161003816120595 (119902

plusmn)10038161003816100381610038162

(29)

Here119875119902= 1minussum119875



sum119875119906= 119886 (120601

2

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904)

sum119875119889= 119886 (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904)


sum119875119904= 119886 (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889)

(30)

and |120595(119902)|2 (|120595(119902



1003816100381610038161003816120595 (119906)10038161003816100381610038162

= 119886 [(21206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904) 119906 + 120601

2

119906119906119906

+ (1206012

119906119889+ 120593

2

119906119889) (119889 + 119889) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119889)10038161003816100381610038162

= 119886 [(1206012

119889119906+ 2120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904) 119889 + 120601

2

119889119889119889

+ (1206012

119889119906+ 120593

2

119889119906) (119906 + 119906) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119904)10038161003816100381610038162

= 119886 [(1206012

119904119906+ 120601

2

119904119889+ 2120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889) 119904 + 120601

2

119904119904119904

+ (1206012

119904119906+ 120593

2

119904119906) (119906 + 119906) + (120601

2

119904119889+ 120593

2

119904119889) (119889 + 119889)]

1003816100381610038161003816120595 (119906plusmn)10038161003816100381610038162

= 119886 [(1206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904) 119906

∓+ 120593

2

119906119889119889∓+ 120593

2

119906119904119904∓]

1003816100381610038161003816120595 (119889plusmn)10038161003816100381610038162

= 119886 [1205932

119889119906119906∓+ (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904) 119889

∓+ 120593

2

119889119904119904∓]

1003816100381610038161003816120595 (119904plusmn)10038161003816100381610038162

= 119886 [1205932

119904119906119906∓+ 120593

2

119904119889119889∓+ (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904) 119904

∓]

(31)



+


1199032

119901= (A minus 3B) (2119875

119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

minus1

3119875119889119889+minus

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119889119889++

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)]

1199032

Σ+

= (A minus 3B) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119904119904 +

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906)10038161003816100381610038162

minus1

3119875119904119904+minus

1

3

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119904119904++

1

3

1003816100381610038161003816120595 (119904+)10038161003816100381610038162

)]

(32)







1199032

Δ+

= (A minus 3B + 6C) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 5 (B minus C) (2119875119906119906++ 2

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+ 119875119889119889++1003816100381610038161003816120595 (119889

+)10038161003816100381610038162

)

(33)






119876Δ+

= 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

) 119886(2 +1205732

3+

21205772

3)

119876Ξlowastminus

= minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

) 119886(4120572

2

3+ 120573

2

+2120577

2

3)

(34)


lowastminusΣminus


119876Δ+

119901

= 2radic2[B1015840

(1 minus 119886(1 + 1205722

+1205732

3+

21205772

3)) minus C1015840

]

119876Σlowastminus

Σminus

= 2radic2B1015840

119886(1205722

3minus

1205732

3)

(35)


+







119886 = 012 120572 = 07 120573 = 04 120577 = minus015 (36)



119902119902 + |120595(119902)|

2 and 119902plusmn

rarr 119875119902119902plusmn+ |120595(119902




1199032


+ 1205732

+ 21205772

)) + sin2

120579 (1 minus119886

3(6 + 120573

2

+ 21205772

))]

1199032


3(3 + 9120572

2

+ 21205732

+ 41205772

)) + sin2

120579 (119886 (minus1 + 1205722

))]

1199032


119886

3(12 + 5120572

2

+ 41205732

+ 61205772

)) + sin2

120579 (1 minus119886

3(6 + 120572

2

+ 21205772

))]

1199032


119886

3(7120572

2

+ 21205772

)) + sin2

120579 (minus1 +119886

3(5120572

2

+ 21205732

+ 21205772

))]

1199032


119886

3(6 minus 120572

2

+ 21205732

+ 21205772

)) + sin2

120579 (119886

3(minus3 + 2120572

2

+ 1205732

))]

1199032


119886

3(3 + 5120572

2

+ 61205732

+ 41205772

)) + sin2

120579 (119886

3(minus3 + 120572

2

+ 21205732

))]

1199032


119886

3(2120572

2

+ 51205732

+ 21205772

)) + sin2

120579 (minus1 +119886

3(4120572

2

+ 31205732

+ 21205772

))]

1199032


3(3120572

2

+ 41205732

+ 21205772

)) + sin2

120579 (119886

9(minus9 + 6120572

2

+ 71205732

+ 21205772

))]

1199032


radic3(3 + 3120572

2

+ 1205732

+ 21205772

)]


119902119902 + |120595(119902)|

2 and 119902plusmn

rarr

119875119902119902plusmn+ |120595(119902



1199032

Δ++

A + 2B + C minus5119886

6(B minus C)(9 + 3120572

2

+ 21205732

+ 41205772

)

1199032

Δ+

A + 2B + C minus5119886

3(B minus C)(6 + 120573

2

+ 21205772

)

1199032

Δ0 5119886(B minus C)(minus1 + 120572

2

)

1199032

Δminus

A + 2B + C minus5119886

3(B minus C)(6120572

2

+ 1205732

+ 21205772

)

1199032

Σlowast+

A + 2B + C minus5119886

3(B minus C)(6 + 120572

2

+ 21205772

)

1199032

Σlowastminus

A + 2B + C minus5119886

3(B minus C)(5120572

2

+ 21205732

+ 21205772

)

1199032

Σlowast0

5119886


2

+ 1205732

)

1199032

Ξlowast0

5119886


2

+ 21205732

)

1199032


5119886

3(B minus C)(4120572

2

+ 31205732

+ 21205772

)

1199032

Ωminus

A + 2B + C minus5119886

3(B minus C)(3120572

2

+ 41205732

+ 21205772

)




119901=

0877 plusmn 0007 fm [12] 1199032

119899= minus01161 plusmn 00022 fm2 [12]

and 119876Δ+



A = 0879 B = 0094 C = 0016 (37)


B1015840

= minus0047 C1015840

= minus0008 (38)







HB120594PT[60]

120594PT [61 62] CCQM[52]

P120594QM [59] 1119873119888

[57 58]Lattice[63]

120594CQMconfig

With SU(3)


A = 0879

B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

1199010813 mdash 0735 0717 082 072 plusmn 009 0779 0685 0732 0801 0766

119903119901=

0877 plusmn 0007

1199032


minus01161plusmn 000221199032

Σ+

0813 079 1366 060 plusmn 002 113 081 plusmn 010 0928 0749 0732 0802 07671199032

Σminus


Σ0


Ξ0


Ξminus

0675 047 0997 049 plusmn 005 054 062 plusmn 007 0520 0502 0646 0683 06691199032


1199032




120594CQMWith SU(3)


B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

Δ++

1084 118 043 1011 mdash 0938 0961 09961199032

Δ+

1084 082 043 1011 0410 (57) 0938 0946 09831199032

Δ0


Δminus

1084 084 043 1011 minus0410 (57) 0938 1006 10331199032

Σlowast+

1084 097 042 1086 0399 (45) 0938 0940 09781199032

Σlowastminus

1084 084 037 0845 minus0360 (32) 0938 1013 10381199032

Σlowast0

00 034 003 0127 0020 (7) 00 minus0036 minus00301199032

Ξlowast0

00 049 006 0244 0043 (10) 00 minus0043 minus00351199032

Ξlowastminus

1084 082 033 0692 minus0330 (20) 0938 1019 10431199032

Ωminus

0390 078 029 0553 mdash 0245 0429 0355





1199032

Σ+

= 1199032

119901 119903

2

Ξminus

= 1199032

Σminus

= 1199032

119901+ 119903

2

119899 (39)




(2119906 + 119889 minus 2119906+minus 119889

+) + C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119899 3B1015840

(119906 + 2119889 minus 119906+minus 2119889

+) + C1015840

(119906 minus 4119889 minus 119906++ 4119889

+)

Σ+

3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+) + C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

Σminus

3B1015840

(2119889 + 119904 minus 2119889+minus 119904

+) + C1015840

(minus4119889 + 119904 + 4119889+minus 119904

+)

Σ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+)

+C1015840

(minus2119906 minus 2119889 + 119904 + 2119906++ 2119889

+minus 119904

+)

Ξ0

3B1015840

(119906 + 2119904 minus 119906+minus 2119904

+) + C1015840

(119906 minus 4119904 minus 119906++ 4119904

+)

Ξminus

3B1015840

(119889 + 2119904 minus 119889+minus 2119904

+) + C1015840

(119889 minus 4119904 minus 119889++ 4119904

+)

Λ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+) + 3C1015840

(minus119904 + 119904+)


1199032

Σ+

gt 1199032

119901 119903

2

Ξminus

gt 1199032

Σminus

gt 1199032

119901+ 119903

2

119899 (40)

Also we have

21199032

Λ= minus2119903

2

Σ0

= 1199032

Ξ0

= 1199032

119899 (41)


1199032

Λgt minus119903

2

Σ0

1199032

Ξ0

gt 1199032

119899 (42)


1199032

Σ+

minus 21199032

Σ0

minus 1199032

Σminus

= 0 (43)



Σminus

=












1199032

Δ++

= 1199032

Δ+

= 1199032

Δminus

= 1199032

Σlowast+

= 1199032

Σlowastminus

= 1199032

Ξlowastminus

(44)


1199032

Ξlowastminus

gt 1199032

Σlowastminus

gt 1199032

Δminus

gt 1199032

Δ++

gt 1199032

Δ+

gt 1199032

Σlowast+

(45)



21199032

Δ++

minus 1199032

Δ+

minus 1199032

Δ0

minus 1199032

Δminus

= 0

21199032

Δ++

minus 31199032

Δ+

+ 31199032

Δ0

+ 1199032

Δminus

= 0

1199032

Σlowast+

minus 21199032

Σlowast0

minus 1199032

Σlowastminus

= 0

(46)










Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)


(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)


(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)




+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840


(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772


Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772




1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)


1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)



+








Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






119876Δ+ = B1015840

(6119906 + 3119889 + 2119906++ 119889

+)

+ C1015840

(minus6119906 minus 3119889 + 10119906++ 5119889

+)


(3119889 + 6119904 + 119889++ 2119904

+)

+ C1015840

(minus3119889 minus 6119904 + 5119889++ 10119904

+)

(22)





be expressed as

119876Δ+

119901= 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889)

119876Σlowastminus


(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)

(23)



rarr





+






+ 1199021015840

∓997888rarr (119902119902

1015840

) + 1199021015840

∓ (24)

where 1199021199021015840



L = 1198928119902Φ

1015840

119902 (25)

with

119902 = (

119906

119889

119904

)

Φ1015840

= (

1205870

radic2

+120573

120578

radic6

+ 120577

1205781015840

radic3

120587+

120572119870+

120587minus

minus

1205870

radic2

+ 120573

120578

radic6

+ 120577

1205781015840

radic3

1205721198700

120572119870minus

120572119870

0

minus120573

2120578

radic6

+ 120577

1205781015840

radic3

)

(26)

where 120577 = 1198921119892

8 119892

1and 119892





2119886 1205732

119886 and 1205772119886




119872119904gt 119872



gt 119872120587and119872

1205781015840 gt 119872

119870120578) [111ndash119]


Φ1015840

= (

120601119906119906

119906119906 + 120601119906119889

119889119889 + 120601119906119904119904119904 120593

119906119889119906119889 120593

119906119904119906119904

120593119889119906

119889119906 120601119889119906

119906119906 + 120601119889119889

119889119889 + 120601119889119904119904119904 120593

119889119904119889119904

120593119904119906119904119906 120593

119904119889119904119889 120601

119904119906119906119906 + 120601

119904119889119889119889 + 120601

119904119904119904119904) (27)

where

120601119906119906

= 120601119889119889

=1

2+

120573

6+

120577

3 120601

119904119904=

2120573

3+

120577

3

120601119906119904

= 120601119889119904

= 120601119904119906

= 120601119904119889

= minus120573

3+

120577

3

120601119889119906

= 120601119906119889

= minus1

2+

120573

6+

120577

3 120593

119906119889= 120593

119889119906= 1

120593119906119904

= 120593119889119904

= 120593119904119906

= 120593119904119889

= 120572

(28)



119902 997888rarr 119875119902119902 +

1003816100381610038161003816120595 (119902)10038161003816100381610038162

119902plusmn997888rarr 119875

119902119902plusmn+1003816100381610038161003816120595 (119902

plusmn)10038161003816100381610038162

(29)

Here119875119902= 1minussum119875



sum119875119906= 119886 (120601

2

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904)

sum119875119889= 119886 (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904)


sum119875119904= 119886 (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889)

(30)

and |120595(119902)|2 (|120595(119902



1003816100381610038161003816120595 (119906)10038161003816100381610038162

= 119886 [(21206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904) 119906 + 120601

2

119906119906119906

+ (1206012

119906119889+ 120593

2

119906119889) (119889 + 119889) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119889)10038161003816100381610038162

= 119886 [(1206012

119889119906+ 2120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904) 119889 + 120601

2

119889119889119889

+ (1206012

119889119906+ 120593

2

119889119906) (119906 + 119906) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119904)10038161003816100381610038162

= 119886 [(1206012

119904119906+ 120601

2

119904119889+ 2120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889) 119904 + 120601

2

119904119904119904

+ (1206012

119904119906+ 120593

2

119904119906) (119906 + 119906) + (120601

2

119904119889+ 120593

2

119904119889) (119889 + 119889)]

1003816100381610038161003816120595 (119906plusmn)10038161003816100381610038162

= 119886 [(1206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904) 119906

∓+ 120593

2

119906119889119889∓+ 120593

2

119906119904119904∓]

1003816100381610038161003816120595 (119889plusmn)10038161003816100381610038162

= 119886 [1205932

119889119906119906∓+ (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904) 119889

∓+ 120593

2

119889119904119904∓]

1003816100381610038161003816120595 (119904plusmn)10038161003816100381610038162

= 119886 [1205932

119904119906119906∓+ 120593

2

119904119889119889∓+ (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904) 119904

∓]

(31)



+


1199032

119901= (A minus 3B) (2119875

119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

minus1

3119875119889119889+minus

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119889119889++

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)]

1199032

Σ+

= (A minus 3B) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119904119904 +

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906)10038161003816100381610038162

minus1

3119875119904119904+minus

1

3

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119904119904++

1

3

1003816100381610038161003816120595 (119904+)10038161003816100381610038162

)]

(32)







1199032

Δ+

= (A minus 3B + 6C) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 5 (B minus C) (2119875119906119906++ 2

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+ 119875119889119889++1003816100381610038161003816120595 (119889

+)10038161003816100381610038162

)

(33)






119876Δ+

= 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

) 119886(2 +1205732

3+

21205772

3)

119876Ξlowastminus

= minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

) 119886(4120572

2

3+ 120573

2

+2120577

2

3)

(34)


lowastminusΣminus


119876Δ+

119901

= 2radic2[B1015840

(1 minus 119886(1 + 1205722

+1205732

3+

21205772

3)) minus C1015840

]

119876Σlowastminus

Σminus

= 2radic2B1015840

119886(1205722

3minus

1205732

3)

(35)


+







119886 = 012 120572 = 07 120573 = 04 120577 = minus015 (36)



119902119902 + |120595(119902)|

2 and 119902plusmn

rarr 119875119902119902plusmn+ |120595(119902




1199032


+ 1205732

+ 21205772

)) + sin2

120579 (1 minus119886

3(6 + 120573

2

+ 21205772

))]

1199032


3(3 + 9120572

2

+ 21205732

+ 41205772

)) + sin2

120579 (119886 (minus1 + 1205722

))]

1199032


119886

3(12 + 5120572

2

+ 41205732

+ 61205772

)) + sin2

120579 (1 minus119886

3(6 + 120572

2

+ 21205772

))]

1199032


119886

3(7120572

2

+ 21205772

)) + sin2

120579 (minus1 +119886

3(5120572

2

+ 21205732

+ 21205772

))]

1199032


119886

3(6 minus 120572

2

+ 21205732

+ 21205772

)) + sin2

120579 (119886

3(minus3 + 2120572

2

+ 1205732

))]

1199032


119886

3(3 + 5120572

2

+ 61205732

+ 41205772

)) + sin2

120579 (119886

3(minus3 + 120572

2

+ 21205732

))]

1199032


119886

3(2120572

2

+ 51205732

+ 21205772

)) + sin2

120579 (minus1 +119886

3(4120572

2

+ 31205732

+ 21205772

))]

1199032


3(3120572

2

+ 41205732

+ 21205772

)) + sin2

120579 (119886

9(minus9 + 6120572

2

+ 71205732

+ 21205772

))]

1199032


radic3(3 + 3120572

2

+ 1205732

+ 21205772

)]


119902119902 + |120595(119902)|

2 and 119902plusmn

rarr

119875119902119902plusmn+ |120595(119902



1199032

Δ++

A + 2B + C minus5119886

6(B minus C)(9 + 3120572

2

+ 21205732

+ 41205772

)

1199032

Δ+

A + 2B + C minus5119886

3(B minus C)(6 + 120573

2

+ 21205772

)

1199032

Δ0 5119886(B minus C)(minus1 + 120572

2

)

1199032

Δminus

A + 2B + C minus5119886

3(B minus C)(6120572

2

+ 1205732

+ 21205772

)

1199032

Σlowast+

A + 2B + C minus5119886

3(B minus C)(6 + 120572

2

+ 21205772

)

1199032

Σlowastminus

A + 2B + C minus5119886

3(B minus C)(5120572

2

+ 21205732

+ 21205772

)

1199032

Σlowast0

5119886


2

+ 1205732

)

1199032

Ξlowast0

5119886


2

+ 21205732

)

1199032


5119886

3(B minus C)(4120572

2

+ 31205732

+ 21205772

)

1199032

Ωminus

A + 2B + C minus5119886

3(B minus C)(3120572

2

+ 41205732

+ 21205772

)




119901=

0877 plusmn 0007 fm [12] 1199032

119899= minus01161 plusmn 00022 fm2 [12]

and 119876Δ+



A = 0879 B = 0094 C = 0016 (37)


B1015840

= minus0047 C1015840

= minus0008 (38)







HB120594PT[60]

120594PT [61 62] CCQM[52]

P120594QM [59] 1119873119888

[57 58]Lattice[63]

120594CQMconfig

With SU(3)


A = 0879

B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

1199010813 mdash 0735 0717 082 072 plusmn 009 0779 0685 0732 0801 0766

119903119901=

0877 plusmn 0007

1199032


minus01161plusmn 000221199032

Σ+

0813 079 1366 060 plusmn 002 113 081 plusmn 010 0928 0749 0732 0802 07671199032

Σminus


Σ0


Ξ0


Ξminus

0675 047 0997 049 plusmn 005 054 062 plusmn 007 0520 0502 0646 0683 06691199032


1199032




120594CQMWith SU(3)


B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

Δ++

1084 118 043 1011 mdash 0938 0961 09961199032

Δ+

1084 082 043 1011 0410 (57) 0938 0946 09831199032

Δ0


Δminus

1084 084 043 1011 minus0410 (57) 0938 1006 10331199032

Σlowast+

1084 097 042 1086 0399 (45) 0938 0940 09781199032

Σlowastminus

1084 084 037 0845 minus0360 (32) 0938 1013 10381199032

Σlowast0

00 034 003 0127 0020 (7) 00 minus0036 minus00301199032

Ξlowast0

00 049 006 0244 0043 (10) 00 minus0043 minus00351199032

Ξlowastminus

1084 082 033 0692 minus0330 (20) 0938 1019 10431199032

Ωminus

0390 078 029 0553 mdash 0245 0429 0355





1199032

Σ+

= 1199032

119901 119903

2

Ξminus

= 1199032

Σminus

= 1199032

119901+ 119903

2

119899 (39)




(2119906 + 119889 minus 2119906+minus 119889

+) + C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119899 3B1015840

(119906 + 2119889 minus 119906+minus 2119889

+) + C1015840

(119906 minus 4119889 minus 119906++ 4119889

+)

Σ+

3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+) + C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

Σminus

3B1015840

(2119889 + 119904 minus 2119889+minus 119904

+) + C1015840

(minus4119889 + 119904 + 4119889+minus 119904

+)

Σ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+)

+C1015840

(minus2119906 minus 2119889 + 119904 + 2119906++ 2119889

+minus 119904

+)

Ξ0

3B1015840

(119906 + 2119904 minus 119906+minus 2119904

+) + C1015840

(119906 minus 4119904 minus 119906++ 4119904

+)

Ξminus

3B1015840

(119889 + 2119904 minus 119889+minus 2119904

+) + C1015840

(119889 minus 4119904 minus 119889++ 4119904

+)

Λ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+) + 3C1015840

(minus119904 + 119904+)


1199032

Σ+

gt 1199032

119901 119903

2

Ξminus

gt 1199032

Σminus

gt 1199032

119901+ 119903

2

119899 (40)

Also we have

21199032

Λ= minus2119903

2

Σ0

= 1199032

Ξ0

= 1199032

119899 (41)


1199032

Λgt minus119903

2

Σ0

1199032

Ξ0

gt 1199032

119899 (42)


1199032

Σ+

minus 21199032

Σ0

minus 1199032

Σminus

= 0 (43)



Σminus

=












1199032

Δ++

= 1199032

Δ+

= 1199032

Δminus

= 1199032

Σlowast+

= 1199032

Σlowastminus

= 1199032

Ξlowastminus

(44)


1199032

Ξlowastminus

gt 1199032

Σlowastminus

gt 1199032

Δminus

gt 1199032

Δ++

gt 1199032

Δ+

gt 1199032

Σlowast+

(45)



21199032

Δ++

minus 1199032

Δ+

minus 1199032

Δ0

minus 1199032

Δminus

= 0

21199032

Δ++

minus 31199032

Δ+

+ 31199032

Δ0

+ 1199032

Δminus

= 0

1199032

Σlowast+

minus 21199032

Σlowast0

minus 1199032

Σlowastminus

= 0

(46)










Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)


(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)


(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)




+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840


(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772


Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772




1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)


1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)



+








Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




sum119875119904= 119886 (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889)

(30)

and |120595(119902)|2 (|120595(119902



1003816100381610038161003816120595 (119906)10038161003816100381610038162

= 119886 [(21206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904+ 120593

2

119906119889+ 120593

2

119906119904) 119906 + 120601

2

119906119906119906

+ (1206012

119906119889+ 120593

2

119906119889) (119889 + 119889) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119889)10038161003816100381610038162

= 119886 [(1206012

119889119906+ 2120601

2

119889119889+ 120601

2

119889119904+ 120593

2

119889119906+ 120593

2

119889119904) 119889 + 120601

2

119889119889119889

+ (1206012

119889119906+ 120593

2

119889119906) (119906 + 119906) + (120601

2

119906119904+ 120593

2

119906119904) (119904 + 119904)]

1003816100381610038161003816120595 (119904)10038161003816100381610038162

= 119886 [(1206012

119904119906+ 120601

2

119904119889+ 2120601

2

119904119904+ 120593

2

119904119906+ 120593

2

119904119889) 119904 + 120601

2

119904119904119904

+ (1206012

119904119906+ 120593

2

119904119906) (119906 + 119906) + (120601

2

119904119889+ 120593

2

119904119889) (119889 + 119889)]

1003816100381610038161003816120595 (119906plusmn)10038161003816100381610038162

= 119886 [(1206012

119906119906+ 120601

2

119906119889+ 120601

2

119906119904) 119906

∓+ 120593

2

119906119889119889∓+ 120593

2

119906119904119904∓]

1003816100381610038161003816120595 (119889plusmn)10038161003816100381610038162

= 119886 [1205932

119889119906119906∓+ (120601

2

119889119906+ 120601

2

119889119889+ 120601

2

119889119904) 119889

∓+ 120593

2

119889119904119904∓]

1003816100381610038161003816120595 (119904plusmn)10038161003816100381610038162

= 119886 [1205932

119904119906119906∓+ 120593

2

119904119889119889∓+ (120601

2

119904119906+ 120601

2

119904119889+ 120601

2

119904119904) 119904

∓]

(31)



+


1199032

119901= (A minus 3B) (2119875

119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

minus1

3119875119889119889+minus

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119889119889++

1

3

1003816100381610038161003816120595 (119889+)10038161003816100381610038162

)]

1199032

Σ+

= (A minus 3B) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119904119904 +

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ 3 (B minus C) [cos2120579 (4

3119875119906119906++

4

3

1003816100381610038161003816120595 (119906)10038161003816100381610038162

minus1

3119875119904119904+minus

1

3

1003816100381610038161003816120595 (119904)10038161003816100381610038162

)

+ sin2

120579 (2

3119875119906119906++

2

3

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+1

3119875119904119904++

1

3

1003816100381610038161003816120595 (119904+)10038161003816100381610038162

)]

(32)







1199032

Δ+

= (A minus 3B + 6C) (2119875119906119906 + 2

1003816100381610038161003816120595 (119906)10038161003816100381610038162

+ 119875119889119889 +

1003816100381610038161003816120595 (119889)10038161003816100381610038162

)

+ 5 (B minus C) (2119875119906119906++ 2

1003816100381610038161003816120595 (119906+)10038161003816100381610038162

+ 119875119889119889++1003816100381610038161003816120595 (119889

+)10038161003816100381610038162

)

(33)






119876Δ+

= 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

) 119886(2 +1205732

3+

21205772

3)

119876Ξlowastminus

= minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

) 119886(4120572

2

3+ 120573

2

+2120577

2

3)

(34)


lowastminusΣminus


119876Δ+

119901

= 2radic2[B1015840

(1 minus 119886(1 + 1205722

+1205732

3+

21205772

3)) minus C1015840

]

119876Σlowastminus

Σminus

= 2radic2B1015840

119886(1205722

3minus

1205732

3)

(35)


+







119886 = 012 120572 = 07 120573 = 04 120577 = minus015 (36)



119902119902 + |120595(119902)|

2 and 119902plusmn

rarr 119875119902119902plusmn+ |120595(119902




1199032


+ 1205732

+ 21205772

)) + sin2

120579 (1 minus119886

3(6 + 120573

2

+ 21205772

))]

1199032


3(3 + 9120572

2

+ 21205732

+ 41205772

)) + sin2

120579 (119886 (minus1 + 1205722

))]

1199032


119886

3(12 + 5120572

2

+ 41205732

+ 61205772

)) + sin2

120579 (1 minus119886

3(6 + 120572

2

+ 21205772

))]

1199032


119886

3(7120572

2

+ 21205772

)) + sin2

120579 (minus1 +119886

3(5120572

2

+ 21205732

+ 21205772

))]

1199032


119886

3(6 minus 120572

2

+ 21205732

+ 21205772

)) + sin2

120579 (119886

3(minus3 + 2120572

2

+ 1205732

))]

1199032


119886

3(3 + 5120572

2

+ 61205732

+ 41205772

)) + sin2

120579 (119886

3(minus3 + 120572

2

+ 21205732

))]

1199032


119886

3(2120572

2

+ 51205732

+ 21205772

)) + sin2

120579 (minus1 +119886

3(4120572

2

+ 31205732

+ 21205772

))]

1199032


3(3120572

2

+ 41205732

+ 21205772

)) + sin2

120579 (119886

9(minus9 + 6120572

2

+ 71205732

+ 21205772

))]

1199032


radic3(3 + 3120572

2

+ 1205732

+ 21205772

)]


119902119902 + |120595(119902)|

2 and 119902plusmn

rarr

119875119902119902plusmn+ |120595(119902



1199032

Δ++

A + 2B + C minus5119886

6(B minus C)(9 + 3120572

2

+ 21205732

+ 41205772

)

1199032

Δ+

A + 2B + C minus5119886

3(B minus C)(6 + 120573

2

+ 21205772

)

1199032

Δ0 5119886(B minus C)(minus1 + 120572

2

)

1199032

Δminus

A + 2B + C minus5119886

3(B minus C)(6120572

2

+ 1205732

+ 21205772

)

1199032

Σlowast+

A + 2B + C minus5119886

3(B minus C)(6 + 120572

2

+ 21205772

)

1199032

Σlowastminus

A + 2B + C minus5119886

3(B minus C)(5120572

2

+ 21205732

+ 21205772

)

1199032

Σlowast0

5119886


2

+ 1205732

)

1199032

Ξlowast0

5119886


2

+ 21205732

)

1199032


5119886

3(B minus C)(4120572

2

+ 31205732

+ 21205772

)

1199032

Ωminus

A + 2B + C minus5119886

3(B minus C)(3120572

2

+ 41205732

+ 21205772

)




119901=

0877 plusmn 0007 fm [12] 1199032

119899= minus01161 plusmn 00022 fm2 [12]

and 119876Δ+



A = 0879 B = 0094 C = 0016 (37)


B1015840

= minus0047 C1015840

= minus0008 (38)







HB120594PT[60]

120594PT [61 62] CCQM[52]

P120594QM [59] 1119873119888

[57 58]Lattice[63]

120594CQMconfig

With SU(3)


A = 0879

B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

1199010813 mdash 0735 0717 082 072 plusmn 009 0779 0685 0732 0801 0766

119903119901=

0877 plusmn 0007

1199032


minus01161plusmn 000221199032

Σ+

0813 079 1366 060 plusmn 002 113 081 plusmn 010 0928 0749 0732 0802 07671199032

Σminus


Σ0


Ξ0


Ξminus

0675 047 0997 049 plusmn 005 054 062 plusmn 007 0520 0502 0646 0683 06691199032


1199032




120594CQMWith SU(3)


B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

Δ++

1084 118 043 1011 mdash 0938 0961 09961199032

Δ+

1084 082 043 1011 0410 (57) 0938 0946 09831199032

Δ0


Δminus

1084 084 043 1011 minus0410 (57) 0938 1006 10331199032

Σlowast+

1084 097 042 1086 0399 (45) 0938 0940 09781199032

Σlowastminus

1084 084 037 0845 minus0360 (32) 0938 1013 10381199032

Σlowast0

00 034 003 0127 0020 (7) 00 minus0036 minus00301199032

Ξlowast0

00 049 006 0244 0043 (10) 00 minus0043 minus00351199032

Ξlowastminus

1084 082 033 0692 minus0330 (20) 0938 1019 10431199032

Ωminus

0390 078 029 0553 mdash 0245 0429 0355





1199032

Σ+

= 1199032

119901 119903

2

Ξminus

= 1199032

Σminus

= 1199032

119901+ 119903

2

119899 (39)




(2119906 + 119889 minus 2119906+minus 119889

+) + C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119899 3B1015840

(119906 + 2119889 minus 119906+minus 2119889

+) + C1015840

(119906 minus 4119889 minus 119906++ 4119889

+)

Σ+

3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+) + C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

Σminus

3B1015840

(2119889 + 119904 minus 2119889+minus 119904

+) + C1015840

(minus4119889 + 119904 + 4119889+minus 119904

+)

Σ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+)

+C1015840

(minus2119906 minus 2119889 + 119904 + 2119906++ 2119889

+minus 119904

+)

Ξ0

3B1015840

(119906 + 2119904 minus 119906+minus 2119904

+) + C1015840

(119906 minus 4119904 minus 119906++ 4119904

+)

Ξminus

3B1015840

(119889 + 2119904 minus 119889+minus 2119904

+) + C1015840

(119889 minus 4119904 minus 119889++ 4119904

+)

Λ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+) + 3C1015840

(minus119904 + 119904+)


1199032

Σ+

gt 1199032

119901 119903

2

Ξminus

gt 1199032

Σminus

gt 1199032

119901+ 119903

2

119899 (40)

Also we have

21199032

Λ= minus2119903

2

Σ0

= 1199032

Ξ0

= 1199032

119899 (41)


1199032

Λgt minus119903

2

Σ0

1199032

Ξ0

gt 1199032

119899 (42)


1199032

Σ+

minus 21199032

Σ0

minus 1199032

Σminus

= 0 (43)



Σminus

=












1199032

Δ++

= 1199032

Δ+

= 1199032

Δminus

= 1199032

Σlowast+

= 1199032

Σlowastminus

= 1199032

Ξlowastminus

(44)


1199032

Ξlowastminus

gt 1199032

Σlowastminus

gt 1199032

Δminus

gt 1199032

Δ++

gt 1199032

Δ+

gt 1199032

Σlowast+

(45)



21199032

Δ++

minus 1199032

Δ+

minus 1199032

Δ0

minus 1199032

Δminus

= 0

21199032

Δ++

minus 31199032

Δ+

+ 31199032

Δ0

+ 1199032

Δminus

= 0

1199032

Σlowast+

minus 21199032

Σlowast0

minus 1199032

Σlowastminus

= 0

(46)










Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)


(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)


(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)




+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840


(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772


Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772




1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)


1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)



+








Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





119902119902 + |120595(119902)|

2 and 119902plusmn

rarr 119875119902119902plusmn+ |120595(119902




1199032


+ 1205732

+ 21205772

)) + sin2

120579 (1 minus119886

3(6 + 120573

2

+ 21205772

))]

1199032


3(3 + 9120572

2

+ 21205732

+ 41205772

)) + sin2

120579 (119886 (minus1 + 1205722

))]

1199032


119886

3(12 + 5120572

2

+ 41205732

+ 61205772

)) + sin2

120579 (1 minus119886

3(6 + 120572

2

+ 21205772

))]

1199032


119886

3(7120572

2

+ 21205772

)) + sin2

120579 (minus1 +119886

3(5120572

2

+ 21205732

+ 21205772

))]

1199032


119886

3(6 minus 120572

2

+ 21205732

+ 21205772

)) + sin2

120579 (119886

3(minus3 + 2120572

2

+ 1205732

))]

1199032


119886

3(3 + 5120572

2

+ 61205732

+ 41205772

)) + sin2

120579 (119886

3(minus3 + 120572

2

+ 21205732

))]

1199032


119886

3(2120572

2

+ 51205732

+ 21205772

)) + sin2

120579 (minus1 +119886

3(4120572

2

+ 31205732

+ 21205772

))]

1199032


3(3120572

2

+ 41205732

+ 21205772

)) + sin2

120579 (119886

9(minus9 + 6120572

2

+ 71205732

+ 21205772

))]

1199032


radic3(3 + 3120572

2

+ 1205732

+ 21205772

)]


119902119902 + |120595(119902)|

2 and 119902plusmn

rarr

119875119902119902plusmn+ |120595(119902



1199032

Δ++

A + 2B + C minus5119886

6(B minus C)(9 + 3120572

2

+ 21205732

+ 41205772

)

1199032

Δ+

A + 2B + C minus5119886

3(B minus C)(6 + 120573

2

+ 21205772

)

1199032

Δ0 5119886(B minus C)(minus1 + 120572

2

)

1199032

Δminus

A + 2B + C minus5119886

3(B minus C)(6120572

2

+ 1205732

+ 21205772

)

1199032

Σlowast+

A + 2B + C minus5119886

3(B minus C)(6 + 120572

2

+ 21205772

)

1199032

Σlowastminus

A + 2B + C minus5119886

3(B minus C)(5120572

2

+ 21205732

+ 21205772

)

1199032

Σlowast0

5119886


2

+ 1205732

)

1199032

Ξlowast0

5119886


2

+ 21205732

)

1199032


5119886

3(B minus C)(4120572

2

+ 31205732

+ 21205772

)

1199032

Ωminus

A + 2B + C minus5119886

3(B minus C)(3120572

2

+ 41205732

+ 21205772

)




119901=

0877 plusmn 0007 fm [12] 1199032

119899= minus01161 plusmn 00022 fm2 [12]

and 119876Δ+



A = 0879 B = 0094 C = 0016 (37)


B1015840

= minus0047 C1015840

= minus0008 (38)







HB120594PT[60]

120594PT [61 62] CCQM[52]

P120594QM [59] 1119873119888

[57 58]Lattice[63]

120594CQMconfig

With SU(3)


A = 0879

B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

1199010813 mdash 0735 0717 082 072 plusmn 009 0779 0685 0732 0801 0766

119903119901=

0877 plusmn 0007

1199032


minus01161plusmn 000221199032

Σ+

0813 079 1366 060 plusmn 002 113 081 plusmn 010 0928 0749 0732 0802 07671199032

Σminus


Σ0


Ξ0


Ξminus

0675 047 0997 049 plusmn 005 054 062 plusmn 007 0520 0502 0646 0683 06691199032


1199032




120594CQMWith SU(3)


B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

Δ++

1084 118 043 1011 mdash 0938 0961 09961199032

Δ+

1084 082 043 1011 0410 (57) 0938 0946 09831199032

Δ0


Δminus

1084 084 043 1011 minus0410 (57) 0938 1006 10331199032

Σlowast+

1084 097 042 1086 0399 (45) 0938 0940 09781199032

Σlowastminus

1084 084 037 0845 minus0360 (32) 0938 1013 10381199032

Σlowast0

00 034 003 0127 0020 (7) 00 minus0036 minus00301199032

Ξlowast0

00 049 006 0244 0043 (10) 00 minus0043 minus00351199032

Ξlowastminus

1084 082 033 0692 minus0330 (20) 0938 1019 10431199032

Ωminus

0390 078 029 0553 mdash 0245 0429 0355





1199032

Σ+

= 1199032

119901 119903

2

Ξminus

= 1199032

Σminus

= 1199032

119901+ 119903

2

119899 (39)




(2119906 + 119889 minus 2119906+minus 119889

+) + C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119899 3B1015840

(119906 + 2119889 minus 119906+minus 2119889

+) + C1015840

(119906 minus 4119889 minus 119906++ 4119889

+)

Σ+

3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+) + C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

Σminus

3B1015840

(2119889 + 119904 minus 2119889+minus 119904

+) + C1015840

(minus4119889 + 119904 + 4119889+minus 119904

+)

Σ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+)

+C1015840

(minus2119906 minus 2119889 + 119904 + 2119906++ 2119889

+minus 119904

+)

Ξ0

3B1015840

(119906 + 2119904 minus 119906+minus 2119904

+) + C1015840

(119906 minus 4119904 minus 119906++ 4119904

+)

Ξminus

3B1015840

(119889 + 2119904 minus 119889+minus 2119904

+) + C1015840

(119889 minus 4119904 minus 119889++ 4119904

+)

Λ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+) + 3C1015840

(minus119904 + 119904+)


1199032

Σ+

gt 1199032

119901 119903

2

Ξminus

gt 1199032

Σminus

gt 1199032

119901+ 119903

2

119899 (40)

Also we have

21199032

Λ= minus2119903

2

Σ0

= 1199032

Ξ0

= 1199032

119899 (41)


1199032

Λgt minus119903

2

Σ0

1199032

Ξ0

gt 1199032

119899 (42)


1199032

Σ+

minus 21199032

Σ0

minus 1199032

Σminus

= 0 (43)



Σminus

=












1199032

Δ++

= 1199032

Δ+

= 1199032

Δminus

= 1199032

Σlowast+

= 1199032

Σlowastminus

= 1199032

Ξlowastminus

(44)


1199032

Ξlowastminus

gt 1199032

Σlowastminus

gt 1199032

Δminus

gt 1199032

Δ++

gt 1199032

Δ+

gt 1199032

Σlowast+

(45)



21199032

Δ++

minus 1199032

Δ+

minus 1199032

Δ0

minus 1199032

Δminus

= 0

21199032

Δ++

minus 31199032

Δ+

+ 31199032

Δ0

+ 1199032

Δminus

= 0

1199032

Σlowast+

minus 21199032

Σlowast0

minus 1199032

Σlowastminus

= 0

(46)










Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)


(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)


(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)




+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840


(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772


Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772




1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)


1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)



+








Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






HB120594PT[60]

120594PT [61 62] CCQM[52]

P120594QM [59] 1119873119888

[57 58]Lattice[63]

120594CQMconfig

With SU(3)


A = 0879

B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

1199010813 mdash 0735 0717 082 072 plusmn 009 0779 0685 0732 0801 0766

119903119901=

0877 plusmn 0007

1199032


minus01161plusmn 000221199032

Σ+

0813 079 1366 060 plusmn 002 113 081 plusmn 010 0928 0749 0732 0802 07671199032

Σminus


Σ0


Ξ0


Ξminus

0675 047 0997 049 plusmn 005 054 062 plusmn 007 0520 0502 0646 0683 06691199032


1199032




120594CQMWith SU(3)


B = 0094

C = 00

A = 0879

B = 0094

C = 0016

1199032

Δ++

1084 118 043 1011 mdash 0938 0961 09961199032

Δ+

1084 082 043 1011 0410 (57) 0938 0946 09831199032

Δ0


Δminus

1084 084 043 1011 minus0410 (57) 0938 1006 10331199032

Σlowast+

1084 097 042 1086 0399 (45) 0938 0940 09781199032

Σlowastminus

1084 084 037 0845 minus0360 (32) 0938 1013 10381199032

Σlowast0

00 034 003 0127 0020 (7) 00 minus0036 minus00301199032

Ξlowast0

00 049 006 0244 0043 (10) 00 minus0043 minus00351199032

Ξlowastminus

1084 082 033 0692 minus0330 (20) 0938 1019 10431199032

Ωminus

0390 078 029 0553 mdash 0245 0429 0355





1199032

Σ+

= 1199032

119901 119903

2

Ξminus

= 1199032

Σminus

= 1199032

119901+ 119903

2

119899 (39)




(2119906 + 119889 minus 2119906+minus 119889

+) + C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119899 3B1015840

(119906 + 2119889 minus 119906+minus 2119889

+) + C1015840

(119906 minus 4119889 minus 119906++ 4119889

+)

Σ+

3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+) + C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

Σminus

3B1015840

(2119889 + 119904 minus 2119889+minus 119904

+) + C1015840

(minus4119889 + 119904 + 4119889+minus 119904

+)

Σ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+)

+C1015840

(minus2119906 minus 2119889 + 119904 + 2119906++ 2119889

+minus 119904

+)

Ξ0

3B1015840

(119906 + 2119904 minus 119906+minus 2119904

+) + C1015840

(119906 minus 4119904 minus 119906++ 4119904

+)

Ξminus

3B1015840

(119889 + 2119904 minus 119889+minus 2119904

+) + C1015840

(119889 minus 4119904 minus 119889++ 4119904

+)

Λ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+) + 3C1015840

(minus119904 + 119904+)


1199032

Σ+

gt 1199032

119901 119903

2

Ξminus

gt 1199032

Σminus

gt 1199032

119901+ 119903

2

119899 (40)

Also we have

21199032

Λ= minus2119903

2

Σ0

= 1199032

Ξ0

= 1199032

119899 (41)


1199032

Λgt minus119903

2

Σ0

1199032

Ξ0

gt 1199032

119899 (42)


1199032

Σ+

minus 21199032

Σ0

minus 1199032

Σminus

= 0 (43)



Σminus

=












1199032

Δ++

= 1199032

Δ+

= 1199032

Δminus

= 1199032

Σlowast+

= 1199032

Σlowastminus

= 1199032

Ξlowastminus

(44)


1199032

Ξlowastminus

gt 1199032

Σlowastminus

gt 1199032

Δminus

gt 1199032

Δ++

gt 1199032

Δ+

gt 1199032

Σlowast+

(45)



21199032

Δ++

minus 1199032

Δ+

minus 1199032

Δ0

minus 1199032

Δminus

= 0

21199032

Δ++

minus 31199032

Δ+

+ 31199032

Δ0

+ 1199032

Δminus

= 0

1199032

Σlowast+

minus 21199032

Σlowast0

minus 1199032

Σlowastminus

= 0

(46)










Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)


(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)


(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)




+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840


(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772


Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772




1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)


1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)



+








Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






(2119906 + 119889 minus 2119906+minus 119889

+) + C1015840

(minus4119906 + 119889 + 4119906+minus 119889

+)

119899 3B1015840

(119906 + 2119889 minus 119906+minus 2119889

+) + C1015840

(119906 minus 4119889 minus 119906++ 4119889

+)

Σ+

3B1015840

(2119906 + 119904 minus 2119906+minus 119904

+) + C1015840

(minus4119906 + 119904 + 4119906+minus 119904

+)

Σminus

3B1015840

(2119889 + 119904 minus 2119889+minus 119904

+) + C1015840

(minus4119889 + 119904 + 4119889+minus 119904

+)

Σ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+)

+C1015840

(minus2119906 minus 2119889 + 119904 + 2119906++ 2119889

+minus 119904

+)

Ξ0

3B1015840

(119906 + 2119904 minus 119906+minus 2119904

+) + C1015840

(119906 minus 4119904 minus 119906++ 4119904

+)

Ξminus

3B1015840

(119889 + 2119904 minus 119889+minus 2119904

+) + C1015840

(119889 minus 4119904 minus 119889++ 4119904

+)

Λ0

3B1015840

(119906 + 119889 + 119904 minus 119906+minus 119889

+minus 119904

+) + 3C1015840

(minus119904 + 119904+)


1199032

Σ+

gt 1199032

119901 119903

2

Ξminus

gt 1199032

Σminus

gt 1199032

119901+ 119903

2

119899 (40)

Also we have

21199032

Λ= minus2119903

2

Σ0

= 1199032

Ξ0

= 1199032

119899 (41)


1199032

Λgt minus119903

2

Σ0

1199032

Ξ0

gt 1199032

119899 (42)


1199032

Σ+

minus 21199032

Σ0

minus 1199032

Σminus

= 0 (43)



Σminus

=












1199032

Δ++

= 1199032

Δ+

= 1199032

Δminus

= 1199032

Σlowast+

= 1199032

Σlowastminus

= 1199032

Ξlowastminus

(44)


1199032

Ξlowastminus

gt 1199032

Σlowastminus

gt 1199032

Δminus

gt 1199032

Δ++

gt 1199032

Δ+

gt 1199032

Σlowast+

(45)



21199032

Δ++

minus 1199032

Δ+

minus 1199032

Δ0

minus 1199032

Δminus

= 0

21199032

Δ++

minus 31199032

Δ+

+ 31199032

Δ0

+ 1199032

Δminus

= 0

1199032

Σlowast+

minus 21199032

Σlowast0

minus 1199032

Σlowastminus

= 0

(46)










Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)


(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)


(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)




+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840


(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772


Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772




1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)


1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)



+








Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






Δ++ B1015840

(9119906 + 3119906+) + C1015840

(minus9119906 + 15119906+) 8B1015840

+ 4C1015840

minus (B1015840

+ 5C1015840

)119886

3(9 + 3120572

2

+ 21205732

+ 41205772

)

Δ+ B1015840

(3(2119906 + 119889) + 2119906++ 119889

+) + C1015840

(minus3(2119906 + 119889) + 5(2119906++ 119889

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120573

2

+ 21205772

)

Δ0 B1015840

(3(119906 + 2119889) + 119906++ 2119889

+) + C1015840

(minus3(119906 + 2119889) + 5(119906++ 2119889

+)) (B1015840

+ 5C1015840

)119886 (minus1 + 1205722

)

Δminus B1015840

(9119889 + 3119889+) + C1015840

(minus9119889 + 15119889+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(6120572

2

+ 1205732

+ 21205772

)

Σlowast+ B1015840

(3(2119906 + 119904) + 2119906++ 119904

+) + C1015840

(minus3(2119906 + 119904) + 5(2119906++ 119904

+)) 4B1015840

+ 2C1015840

minus (B1015840

+ 5C1015840

)119886

3(6 + 120572

2

+ 21205772

)


(3(2119889 + 119904) + 2119889++ 119904

+) + C1015840

(minus3(2119889 + 119904) + 5(2119889++ 119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(5120572

2

+ 21205732

+ 21205772

)

Σlowast0 B1015840

(3(119906 + 119889 + 119904) + 119906++ 119889

++ 119904

+) (B1015840

+ 5C1015840

)119886

3(minus3 + 2120572

2

+ 1205732

)

+C (minus3(119906 + 119889 + 119904) + 5(119906++ 119889

++ 119904

+))

Ξlowast0 B1015840

(3(119906 + 2119904) + 119906++ 2119904

+) + C1015840

(minus3(119906 + 2119904) + 5(119906++ 2119904

+)) (B1015840

+ 5C1015840

)119886

3(minus3 + 120572

2

+ 21205732

)


(3(119889 + 2119904) + 119889++ 2119904

+) + C1015840

(minus3(119889 + 2119904) + 5(119889++ 2119904

+)) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(4120572

2

+ 31205732

+ 21205772

)

Ωminus B1015840

(9119904 + 3119904+) + C1015840

(minus9119904 + 15119904+) minus4B1015840

minus 2C1015840

+ (B1015840

+ 5C1015840

)119886

3(3120572

2

+ 41205732

+ 21205772

)




+

119901 2radic2B1015840

(119906+minus 119889

+) + 2radic2C1015840

(minus119906 + 119889) 2radic2B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772


Σlowast+

Σ+

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Σlowastminus

Σminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Σ0 radic2B1015840

(119906++ 119889

+minus 2119904

+) + radic2C1015840


(1 minus 119886(1 +1205722

3+ 120573

2

+2

31205772


Ξlowast0

Ξ0

2radic2B1015840

(119906+minus 119904

+) + 2radic2C1015840

(minus119906 + 119904) 2radic2B1015840

(1 minus119886

3(3 + 2120572

2

+ 21205732

+ 21205772


Ξlowastminus

Ξminus

2radic2B1015840

(119889+minus 119904

+) + 2radic2C1015840

(minus119889 + 119904)2radic2

3B1015840

119886 (1205722

minus 1205732

)

Σlowast0

Λ radic6B1015840

(119906+minus 119889

+) + radic6C1015840

(minus119906 + 119889) radic6B1015840

(1 minus119886

3(3 + 3120572

2

+ 1205732

+ 21205772




1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= 1199032

Σ+

minus 1199032

Σlowast+

= 1199032

Ξ0

minus 1199032

Ξlowast0

= 1199032

119899 (47)


1199032

119901minus 119903

2

Δ+

= 1199032

Σ+

minus 1199032

Σlowast+

= minus031

1199032

Σminus

minus 1199032

Σlowastminus

= 1199032

Ξminus

minus 1199032

Ξlowastminus

= minus048

1199032

119899minus 119903

2

Δ0

= 1199032

Ξ0

minus 1199032

Ξlowast0

= minus009

(48)



+








Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics







Skyrme[91 92]


10minus2 fm2

10minus1 fm2

10minus1 fm2


Δ++


+


0 00 00 012 plusmn 005 024 29 00 00 00055Δ






Ωminus 0204 28 009 plusmn 005 024 00 0014 01719 01966




119876Δ++

2= 119876

Δ+

= 119876Δminus

= 119876Σlowast+



= 119876Ωminus

119876Δ+

119901

= 119876Σlowast+

Σ+

= 2119876Σlowast0

Σ0

= 119876Ξlowast0

Ξ0

=2

radic3119876

Σlowast0

Λ

(49)


119876Ωminus



gt 119876Δminus

gt119876

Δ++

2gt 119876

Δ+

gt 119876Σlowast+

2119876Σlowast0

Σ0

gt 119876Ξlowast0

Ξ0

= 119876Σlowast+

Σ+

gt 119876Δ+

119901

=2

radic3119876

Σlowast0

Λ

(50)

Also we have

119876Ξlowast0

= 119876Σlowast0

= 119876Δ0

(51)


119876Ξlowast0

gt 119876Σlowast0

gt 119876Δ0

(52)


119876Ξlowastminus

Ξminus


Σminus

= 0 (53)



















rarr (12)+





breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






breaking



Δ+


Σlowast+

Σ+



Σlowast0

Σ0


Ξ0



Σlowast0







Acknowledgments


References



1










119901119866

119864119901119866

119872119901via



119864119901119866

119872119901in 119890

rarr

119901 rarr 119890119901rarr to 119876




119867rarr (119890rarr 119890

1015840











120587) and119901(120574

rarr




rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





rarr




rarr

120574)119901(120574rarr

120587119900

) and119901(120574rarr

120587+





















119899

2119865

119901




















































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics
































119888

















































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics

































































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



review article charge radii and quadrupole moments of the low … · 2019. 7. 31. · eld theories,...

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