chiral su(3) quack model and multiquark state
DESCRIPTION
Chiral SU(3) Quack Model and Multiquark State. Zhang Zong ye (Institute of High Energy Physics, Beijing). Outline. Introduction Chiral SU(3) Quark Model and NN , YN and KN scatterings Dibaryon Pentaquark state. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
Chiral SU(3) Quack Model and
Multiquark State
Zhang Zong ye(Institute of High Energy Physics, Beijing)
Outline
• Introduction
• Chiral SU(3) Quark Model
and NN , YN and KN scatterings
• Dibaryon
• Pentaquark state
Introduction The NPQCD effect is very important for the light quark system. But up to now, there is no effective approach to solve the NPQCD problem seriously. We still need QCD inspired model to help.
In the framework of the constituent quark model, to understand the source of the constituent quark mass, the spontaneous vacuum breaking has to be considered, and as a consequence, the coupling between quark field and goldstone boson is introduced to restore the chiral symmetry. The chiral quark model can be regarded as a quite reasonable and useful model to describe the medium range NPQCD effect.
First we generalized the chiral SU(2) quark model to chiral SU(3) quark model for studying the system with s quark and try tosee if we can get a unified explanation of N-N and Y-N data on quark level. Then we extend the study to the multiquark system.. Since for the multiquark states, quarks should stay in a small area, the quark exchange effect must be important. We did an analysis to see the quark exchange effect in two baryon systems. We found that: the quark exchange effect of some cases is not important; some cases have very strong Pauli Block Effect, and for some cases it makes these two baryon cluster close together--- it is favorable to make two baryon to be bound. According to the analysis, using chiral SU(3) quark model with thesame parameters we used in the scattering calculations, we got : A new interesting dibaryon candidate - - - di-Omega .
We also studied the structure of the pentaquark state .
+0(ΩΩ)
+Θ
• The ModelIn the chiral SU(3) quark model, the coupling between chiral field
and quark is introduced to describe low momentum medium range
NPQCD effect. The interacting Lagrangian can be written as:
.
scalar nonet fields pseudo-scalar nonet fields
It is easy to prove that is invariant under the infinitesimal chiral
transformation. This can be regarded as an extension of the SU(2) - σ model for
studying the system with s quark.
8 8
I ch a a a a 5a=0 a=0
L = -g ψ( σ λ + i π λ γ )ψ
σ,σ', χ,ε π,K, η, η'
IL L RSU(3) SU(3)
IL
In chiral SU(3) quark model, we still employ an effective OGE
interaction to govern the short range behavior, and a confinement
potential to provide the NPQCD effect in the long distance.
Hamiltonian of the system:
( is taken as quadratic for
m.)
i G iji i<j
H = t - T + V ,
,conf ogeij ij i ij
chjV = V + V V+
ch s(a) ps(a)ij ij ij
a
V = (V + V ) .
confijV
The expressions of and :
2( )
, ( ), 2 ( ),( ) ( , )12
( ) ( ) ( ) + tensor term
ps ach ps a ps a ij
qi qj
i j a a
mC g m X m r
m m
i j
, ( ), 1 ( ),( ) ( , ) ( ) ( )
term,
ch ps a s a ij a aC g m X m r i j
l s
2
, 2 2( , ) .chC g m m
m
1( , , ) ( ) ( ),X m r Y mr Y rm
32( , , ) ( ) ( ) ( ),X m r Y mr Y r
m
1( ) ,xY x e
x
psijVs
ijV
Here we have only one coupling constant ,chg
s(a)ijV
2chg
4π
ps(a)ijV
2chg
4π
2 2 2ch u NNπ
2N
g m g9= .
4π 25 4πM
• Parameters:(1). Input part: taken to be the usual values.
(2). Chiral field part: and are adjustable.
( are taken to be experimental values, )
(3). OGE and confinement part: and are fixed by and .
are determined by the stability condition of
ub = 0.5fm, um = 313MeV, sm = 470MeV.
2 2 2ch u NNπ
2N
g m g9= ,
4π 25 M 4π
', , , Km m m m
ug
σm s
' 980 .m m m MeV
sg Δ NM - M Σ ΛM - M
cuu,a ... N, Λ,Ξ.
N-N,Y-N K-N
0.5
313
470
2.63
595 675
0 35.3 (-18)
0.886
0.755
48.1 52.4 (55.2)
63.7 75.3 (71.4)
ub (fm)
um (MeV)
sm (MeV)
chg
σm (MeV)
s (degree)
ug
sg2
cuua (MeV/fm )2
cusa (MeV/fm )
Baryon Mass
Expt. Theor. Expt. Theor.
N 939 939 Δ 1232 1237
Λ 1116 1116 1385 1375
Σ 1193 1194 1530 1515
Ξ 1319 1334 1672 1657
*Σ*Ξ
Ω
To study the two baryon system, we did a two-cluster dynamical RGM calculation
Phase shifts of N-N scattering
10S 3
1S
N-N P wave
N-N D wave
Y-N cross sections of ± ±Λp Λp, Σ p Σ p
Y-N cross sections of - 0 -Σ p Σ n, Σ p Λn
Phase shifts of K-N scattering
S wave
0 200 400 600 800 1000
-100
-80
-60
-40
-20
0
20
40 S11
(de
g)
Plab
(MeV)
0 200 400 600 800 1000-40
-30
-20
-10
0
10 S01
(de
g)
Plab
(MeV)
K-N P wave
K-N D wave
K-N F wave
•DibaryonSince our model can explain the scattering data quite well, using the same groups of parameters to study some two baryon states and multi-quark states is significant.
An analysis of quark exchange effectSince quarks are fermions, when the distance between two baryon clusters
is short enough, the quark exchange effect must be important.
The antisymmetrization operator:
is the permutation operator of quark i and j, and of
baryon A and B. When two cluster is closed together and L=0,
Thus is very important to measure the quark exchange effect for various spin-flavor states.
r σfcij ij ijP = P P ABP
.rij< P > 1
σfcij< P >
)P)(1P(1A ABBjA,i
ij
When the quark exchange effect is not important,
the Pauli Block Effect is very serious,
the quark exchange effect makes two baryon cluster closer. It has so-called quantum coherent effect.
In all of two baryon systems, only 6 of them belong to this interesting case, they are:
Only has enough long lifetime, because it can’t decay through strong interactions.
ST=03(ΔΔ) , ST=30(ΔΔ) , ST=00(ΩΩ)*1
ST=0 ,2
(Ξ Ω)*5
ST=0 ,2
(Σ Δ) *1
ST=3 ,2
(Σ Δ)
σfcij
i A,j B
(1- < P >) 1,
σfcij
i A,j B
(1- < P >) 0,
σfcij
i A,j B
(1- < P >) 2,
ST=00(ΩΩ)
H partical ~ 2 (near 2Λ threshold)
State B(MeV)
1ST=0
2
1ST=1
2
3ST=0
2
(NΛ) 1 unbound
(NΛ) 1 unbound
10(NΣ
10Deuteron
)
9
2.139
1ST=1
2
ST=00
unbound
(NΣ) 1 unbound
(ΛΛ) 1 unbound
σfcij
ij
(1- <P >)
( )N The results are calculated by using chiral SU(3) quark model with the same parameters we used in the NN and YN scattering processes.
State B(MeV)
2 137 2 92 2 25 2 26 2 16 2 37 is the most interesting one, because it
can’t decay through strong interactions , and thus it has enough long lifetime.
ST=00(ΩΩ)*
1ST=0
2
(Ξ Ω)*
5ST=0
2
(Σ Δ)*
1ST=3
2
(Σ Δ)
ST=03(ΔΔ)
ST=30(ΔΔ)
σfcij
ij
(1- <P >)
ST=00(ΩΩ)
Main properties of :1). Binding energy several tens to hundred MeV,2). Distance between two , 0.8fm,3). It carries –2 charges,4). Mean lifetime sec. Decay modes:
All of them are weak decays.
+
- - 0
0(ΩΩ) Ω + Ξ + π ,
+
- 0 -
0(ΩΩ) Ω + Ξ + π ,
+
- -
0(ΩΩ) Ω + Ξ .
-1010
+0(ΩΩ)
Ω Ω-Ωd
ΩΩτ
+0
(ΩΩ)B
+
- - 0
0(ΩΩ) Ω + Ξ + π ,
How the result dependent on the parameters is.
Fit NN Fit KN
I II
137.4 61.2 134.4
Even the mixing of and is taken to be ideally mixing, i.e. there is no
meson exchange between two s quarks, the binding energy of is
still quite large , around 60 MeV. This result tells us again that the symmetry
property of is really very important to make it bound.
+0(ΩΩ)B (MeV)
0( 0 )s 0( 35.3 )s 0( 18.0 )s
0 8 00
( )
0( )
is a very interesting new dibaryon candidate,
but how to search it seems not so easy, because its
production rate is rare.
Some authors estimated its production rate in the relativistic heavy ion
collision processes at RHIC energy by using different models.
Their results show: the ratio of the production rate of
and single ,
Though the searching work is hard, RHIC-STAR group still plans to try to
search it in the heavy ion collision processes and has listed this work in
their research proposal.
+0(ΩΩ)
+0(ΩΩ) /Ω
+0(ΩΩ)
Ω
• Pentaquark state
4(0 ) (0 ), 0, S S L -
π 1J =
23(0 ) (0 )(0 ), 1, S P S L
+π 1
J =2
1[4] [31] 01, 0
21
10, 121
11, 121
21, 22
forb ts TS
ts TS
ts TS
ts TS
1[31] [4] 00, 0
21
11, 123
11, 123
22, 22
forb ts TS
ts TS
ts TS
ts TS
The structure of pentaquark state is studied by chiral SU(3) quark model.
4 configurations of and 4 of are considered. They are:
-π 1
J =2
+π 1
J =2
The trail wave function is taken as an expansion of the
5q states with different size b :
and solve to get
Results tell us that:
5q i 5q ii
Ψ = α Φ (b ),
5q 5q 5qHΨ = E Ψ 5qE .
+Θ
-π 1
J = and T = 0 state is always the lowest one 2
for 3 groups of parameter but its energy is about
250 - 350 MeV higher than the experimental
M
s,
.
Fit NN Fit KN
I II-
π 1J = T = 0 1799 1901 1897
2+
π
1J = T = 0 2153 2221 2
2
206
ΘM (MeV) (calculated)
It seems that in the framework of the chiral SU(3) quark model, when the parameters are taken in the reasonable region, it is difficult to get the mass of Θ to be closed to the experimental value (1540 MeV).
Summary:
Taking the same
Chiral SU(3) qu
parameters we
ark model is quite successful
used in the scattering calcula
in explaining
the N
tion,
a new interes
N, YN and K
ting dibary
N
o
s
n
cattering data
candida
,
te (ΩΩ) +0
-10
is predicted, it is
deeply bound with quite small size, its mean lifetime is about
10 sec and c
The calculated mass of the pentaquark state Θ in the chiral
SU(
arries - 2 char
3) quark model
ges
.
is about 250 - 350 MeV higher than the
experimental value.