spin structure of proton in dynamical quark model spin structure of proton in dynamical quark model...
TRANSCRIPT
![Page 1: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/1.jpg)
SPIN STRUCTURE OF PROTON SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK IN DYNAMICAL QUARK
MODEL MODEL G. Musulmanbekov JINR, Dubna, Russiae-mail:[email protected]
Contents
•Introduction•Strongly Correlated Quark Model (SCQM)•Spin in SCQM•Single Spin Asymmetry•Conclusions
SPIN’04
![Page 2: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/2.jpg)
Introduction
)]([)(2
15
3 BExAEixxd
JJJ gq
Where does the Proton Spin come from?
Spin "Crisis“:DIS experiments: ΔΣ=Δu+Δd+Δs 1≪SU(6) 1
QCD sum rule for the nucleon spin:1/2 =(1/2)ΔΣ(Q²)+Lq(Q²)+Δg(Q²)+Lg(Q²)
QCD angular momentum operator (X. Ji, PRL 1997):
SCQM All nucleon spin comes from circulating around each valence quarks gluon and quark-antiquark condensate (term 4)
![Page 3: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/3.jpg)
Strongly Correlated Quark Model
1. Constituent Quarks – Solitons
0),(sin),( txtx
2
21
1/cosh
1/sinhtan4),(
uxu
uuttx ass
x
txtx ass
ass
),(),(
Sine- Gordon equation
Breather – oscillating soliton-antisoliton pair, the periodic solution of SG:
The density profile of the soliton-antisoliton pair (breather)
)(tanh2)( 2 mxMxV
Effective soliton – antisoliton potential
![Page 4: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/4.jpg)
Breather (soliton –antisoliton) solution of SG equation
![Page 5: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/5.jpg)
What is Chiral Symmetry and its Breaking?
• Chiral Symmetry
U(3)L × U(3)R for ψL,R = u, d, s
• The order parameter for symmetry breaking is quark or chiral condensate:
<ψψ> - (250 MeV)³, ψ = ≃ u,d,s.
• As a consequence massless valence quarks (u, d, s) acquire dynamical masses which we call constituent quarks
MC ≈ 350 – 400 MeV
![Page 6: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/6.jpg)
Strongly Correlated Quark Model
(SCQM)
Attractive Force
Attractive Force
Vacuum polarization around single quark
Quark and Gluon Condensate
Vacuum fluctuations(radiation) pressure
Vacuum fluctuations(radiation) pressure
(x)
![Page 7: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/7.jpg)
Interplay Between Current and Constituent Quarks
Chiral Symmetry Breaking and Restoration Dynamical Constituent Mass Generation
2 0 21
0
1
x, fermi
Po
lari
zati
on
Fie
ld
2 0 20
0.5
1
x, fermi
Had
ron
ic M
att
er
Dis
trib
uti
on
d=0.64
t = 0
2 0 21
0
1
x, fermi
Po
lari
zati
on
Fie
ld
2 0 20
0.5
1
x, fermi
Had
ron
ic M
att
er
Dis
trib
uti
on
d=0.05
2 0 21
0
1
x, fermi
Po
lari
zati
on
Fie
ld
2 0 20
0.5
1
x, fermi
Had
ron
ic M
att
er
Dis
trib
uti
on
d=0.05
t = T/4
2 0 21
0
1
x, fermi
Po
lari
zati
on
Fie
ld
2 0 20
0.5
1
x, fermi
Had
ron
ic M
att
er
Dis
trib
uti
on
d=0.64 t = T/2
![Page 8: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/8.jpg)
The Strongly Correlated Quark Model
Hamiltonian of the Quark – AntiQuark System
)2()1()1( 2/122/12 xV
mmH qq
q
q
q
q
, are the current masses of quarks, = (x) – the velocity of the quark (antiquark), is the quark–antiquark potential.
qm qm
qqV
)(
)1()(
)1( 2/122/12 xUm
xUm
Hq
q
q
q
)2(2
1)( xVxU
qq is the potential energy of the
quark.
![Page 9: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/9.jpg)
Conjecture:
),(2),()(2 xMrxxdydzdxU Q
where is the dynamical mass of the constituent quark and
)()(
xMQQ
),,(),,(
),(),(
zyxxzyxxC
rxCrx
For simplicity
XAXA
rT
exp)(det
)(2/3
2/1
![Page 10: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/10.jpg)
I
II
U(x) > I – constituent quarksU(x) < II – current(relativistic) quarks
Quark Potential and “Confining Force” inside Light Hadons
![Page 11: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/11.jpg)
Quark Potential inside Light Quark Potential inside Light HadronsHadrons
Uq = 0.36tanh2(m0x) Uq x
![Page 12: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/12.jpg)
Generalization to the 3 – quark system (baryons)
ColorSU )3(
3 RGB,
_ 3 CMY
qq 1 33-
qqq 3 3
3
3
3
31- -
-
_ ( 3)Color
![Page 13: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/13.jpg)
The Proton
![Page 14: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/14.jpg)
Chiral Symmerty Breaking and its Restoration
Consituent Current Quarks Consituent Quarks Asymptotic Freedom Quarks
t = 0x = xmax
t = T/4x = 0
t = T/2x = xmax
During the valence quarks oscillations:
...321132113211 gqqqcqqqqqcqqqcB
![Page 15: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/15.jpg)
SCQM The Local Gauge
Invariance Principle
Destructive Interference of color fields Phase rotation of the quark w.f. in color space:
Colorxig
Color xex )()( )(
Phase rotation in color space dressing (undressing) of the quark the gauge transformation );()()( xxAxA here
)0,0,0,( A
![Page 16: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/16.jpg)
Parameters of SCQM
in pp_
2.Maximal Displacement of Quarks: xmax=0.64 fm,
3.Constituent quark sizes (parameters of gaussian distribution): x,y=0.24 fm, z =0.12 fm
,36023
1)( max)( MeV
mmxM N
Parameters 2 and 3 are derived from the calculations of Inelastic Overlap Function (IOF) and in and pp – collisions.
1.Mass of Consituent Quark
![Page 17: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/17.jpg)
Structure Function of Valence Quarks in Proton
![Page 18: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/18.jpg)
Summary on SCQM
• Quarks and gluons inside hadrons are strongly correlated;
• Constituent quarks are identical to solitons.• Hadronic matter distribution inside hadrons is
fluctuating quantity resulting in interplay between constituent and current quarks.
• Explicit manifestation of these fluctuations is single diffraction.
• There are no strings stretched between quarks inside hadrons;
• Strong interactions between quarks are nonlocal: they emerge as the vacuum response (radiation field) on violation of vacuum homogeneity by embedded quarks.
• Parameters of SCQM:1. Maximal displacement of quarks in hadrons x 0.64f
2. Sizes of the constituent quark: x,y 0.24f, z 0.12f
![Page 19: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/19.jpg)
Inelastic Overlap Function
sxxM 21
+ energy – momentum conservation
Monte-Carlo Simulation of Inelastic Events
![Page 20: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/20.jpg)
Spin in SCQM
a
rd )(3 BErJJ gQ
Our conjecture: spin of consituent quark is entirely analogous to the angular momentum carried by classical circularly polarized wave:
Classical analog of electron spin – F.Belinfante 1939; R. Feynman 1964; H.Ohanian 1986; J. Higbie 1988.
Electron surrounded by proper electric E and B fields creates circulating flow of energy:
S=ɛ₀c²E×B.
Total angular momentum created by this Pointing’s vector
is associated with the entire spin angular momentum of the electron. Here if a = 2/3 r0.entiire mass of electron is contained in its field.
a
rd )((...) 3 BErLs
![Page 21: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/21.jpg)
Spin in SCQM
a
rd )((...) 3chchgQ BErLs
1. Now we accept that
Sch = c²Ech× Bch .
3. Total angular momentum created by this Pointing’s vector
is associated with the entire spin angular momentum of the constituent quark.
A},{ A
and intersecting Ech and Bch create around VQ color
analog of Pointing’s vector
4. Quark oscillations lead to changing of the values of Ech and Bch : at the origin of oscillations they are concentrated
in a small space region around VQ. As a result hadronic current is concentrated on a narrow shell with small
radius.
5. Quark spins are perpendicular to the plane of oscillation.
6. Quark spin module is conserved during oscillation:
2. Circulating flow of energy carrying along with it hadronic matter is associated with hadronic matter current.
![Page 22: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/22.jpg)
7. At small displacements spins of both u – quarks inside the proton are predominantly parallel.
8. At large displacements there is a spin – flip of d
and one of u quarks (according to spin-flavor SU(6)).
9. Velocity field is irrotational:
Analogue from hydrodynamics
((∂ξ)/(∂t))+ ×(ξ×v)=0,∇
ξ= ×v,∇
const.srv d
r/1v This means the suggestion that sea quarks are not polarized
![Page 23: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/23.jpg)
Single Spin Asymmetry in proton – proton collisions
• In the factorized parton model
'' // qqqp Dq
• In our model the second term is dominating in SSA (Szwed mechanism)
![Page 24: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/24.jpg)
Single Spin Asymmetry in proton – proton collisions
![Page 25: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/25.jpg)
Collision of Vorticing Quarks
Anti-parallel Spins Parallel Spins
Single Polarized Quark
![Page 26: SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL SPIN STRUCTURE OF PROTON IN DYNAMICAL QUARK MODEL G. Musulmanbekov JINR, Dubna, Russia e-mail:genis@jinr.ru](https://reader035.vdocuments.net/reader035/viewer/2022062423/5697c00e1a28abf838cc9a94/html5/thumbnails/26.jpg)
Experiments with Polarized Protons