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Chiral SU(3) Quack Model and Multiquark State

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Chiral SU(3) Quack Model and Multiquark State

Zhang Zong ye

(Institute of High Energy Physics, Beijing)

- Introduction
- Chiral SU(3) Quark Model
and NN , YN and KN scatterings

- Dibaryon
- Pentaquark state

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 theframework 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 withsquark and try to

see 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 didan 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 the

same parameters we used in the scattering calculations, we got :

A new interesting dibaryon candidate - - - di-Omega .

We also studiedthe structure of the pentaquark state .

- The Model
In the chiral SU(3) quark model, the coupling between chiral field

and quark is introducedto 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 asan extension of the SU(2) - σ model for

studying the system with s quark.

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 form.)

Here we have only one coupling constant,

- Parameters:
(1). Input part: taken to be the usual values.

(2). Chiral field part:

andare adjustable.

( are taken to be experimental values, )

(3). OGE and confinement part:

and are fixed by and .

are determined by the stability condition of

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)

63.775.3 (71.4)

Expt. Theor. Expt. Theor.

N939 939 Δ 1232 1237

Λ 1116 1116 1385 1375

Σ 1193 1194 1530 1515

Ξ 1319 1334 1672 1657

To study the two baryon system, we did a two-cluster dynamical RGM calculation

Phase shifts of N-N scattering

Y-Ncross sections of

Y-N cross sections of

Phase shifts of K-N scattering

S wave

K-N D wave

K-N F wave

- Dibaryon
- Since 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 effect
- Since 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 isvery important to measure the quark exchange effect for various spin-flavor states.

Whenthe 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.

StateB(MeV)

H partical ~ 2 (near 2Λ threshold)

The results are calculated by using chiral SU(3) quark model with the same parameters we used in the NN and YN scattering processes.

StateB(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.

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.

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 thatthe symmetry

property of is really very important to make it bound.

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.

The structure of pentaquark state is studied by chiral SU(3) quark model.

4 configurations of and 4 of are considered. They are:

- Pentaquark state

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:

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: