1Lianrong Dai,Beijing MENU 2004, Aug.29-Sep.4,2004 2-Sep-2004

L. R. Dai

(Department of Physics, Liaoning Normal University)

Z.Y. Zhang, Y.W. Yu

(Institute of High Energy Physics, Beijing, China)

Nucleon-nucleon interaction in the extended chiral SU(3)

quark model

Ⅰ:Motivations The chiral SU(3) quark model ‘s success baryon structure’s study on quark level the successful study on nucleon level

Ⅱ:The Model The extended chiral SU(3) quark model Determination of parameters

Ⅲ: Result and discussionⅣ: Summary

Outline

The chiral SU(3) quark model (Nucl.Phys. 625(1997)59)

In this 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 forstudying 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

Ⅰ:Motivations

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.)

i G iji i<j

H = t - T + V ,

,conf ogeij ij i ij

chjV = V + V V+ conf

ijV

ch s(a) ps(a)ij ij ij

a

V = (V + V ) .

1: long range => confinement2: short range =>OGE –color dependent

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

spin-flavor dependent

In this chiral SU(3) quark model, in which

short range repulsion is described by OGE

Using the same set of parameters

• Energies of the baryon ground state• NN scattering phase shifts • Hyperon-nucleon (YN) cross sections

can be reproduced reasonably.

* The detailed results have been presentedby Prof.Zhang’s talk today morning!

since last few years, shen et al, Riska and Glozman applied

the quark-chiral field coupling model to study the baryon structure.

Phys. Rev. C55(1997) Phys.Rep.268(1996)263; Nucl.Phys.A663(2000) They have found :

The chiral field coupling is important in explaining the structures of baryons.

As is well known, on baryon level, the

short range repulsion is described successfully by vector meson (ρ,ω, K* and φ) exchanges.

Naturally, we would like to ask which is the

right mechanism for describing the short range interactions ?

1: OGE 2: vector meson exchange 3: or both of them are important

with vector meson

exchange on quark level

no dynamical calculations

before !!

Ⅱ:The Model The Extended chiral su(3) quark Model

gchv :Vector coupling constant fchv: Tensor coupling constant

The Hamiltonian of the system

Based on the chiral SU(3) quark model,

we further add vector effective Lagrangian

new => “extend

”

1: quark-vector fileld

coupling

2:spin-flavor dependent

color – independent

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

(2). Chiral field part:

is adjustable.

and are taken to be experimental values,

um = 313MeV, sm = 470MeV.

2 2 2ch u NNπ

2N

g m g9= ,

4π 25 M 4π

', , , Km m m m

σm

' 980 .m m m MeV

fmbu

fmbu45.0

5.0

cutoff mass: Λ=1100 Mev, chiral symmetry breaking scale

mmmm K ,,, *

(3). OGE and confinement part:

and are fixed by and .

is determined by the stability condition of ...uua

ug sgΔ NM - M Σ ΛM - M

N, Λ,Ξ.

Model parameters and the corresponding binding nergies of deuteron

Model parameters and the corresponding binding nergies of deuteron

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

Phase shifts of N-N scatteringS wave

single chann

el

Ⅲ: RESULTS

with 3 sets of parameters

N-N P-wave scattering

N-N D-wave scattering

N-N F-wave scattering

.

Extended Model with set

II (fchv/gchv

=2/3)

*About NΔeffect

NN 1S0 scattering

red line : with NΔ coupling black line : without NΔ coupling

Extended Model with set

I (fchv/gchv =0)

Discuss:

To get reasonable 1S0 phase shifts

1: for different modelsalmost the same

good agreement with exp.

2: bu from 0.5 (not extended)

to 0.45fm (extended model) Means the bare radius of baryon becomes smaller when more meson clouds

are included.

* 3S1-wave scattering

*Mechanisms for short range interaction are totally different

1: When the vector meson field coupling is considered, the coupling constant of OGE is largely reduced by

fitting the mass difference between Δ and N.

2: in the extended chiral SU(3) quark model, instead of the OGE, the vector meson exchanges play an

important role for the short range interaction between two quarks

GCM ( generator coordinating method ) potential

in Extended Model1: OGE is weak2:The vector meson exchange is dominate!

Extended su(3) quark model

with set II

chira su(3) quark model

* Diagonal matrix elements of generator coordinating method (GCM) for π, ρ and ω mesons

One can see that the ω meson exchangeoffers repulsion not only in the short range

region, but also in medium range part. This property is different from that of π meson, which only contributes repulsive

core.

on quark level: set I: fchv/gchv=0 , gchv =2.35 fchv =0

set II: fchv/gchv=2/3 , gchv =1.97 fchv =1.32

on nucleon level gωNN ≈ 10-15 for ω meson ,

　　　　　　　　 gρNN ≈ 2-3 for ρ meson

Nijmegen model D gρNN ≈ 2.09 and fρNN =17.122

* the coupling constants of the vector meson exchange gchv and fchv

The coupling constant is much weaker on quark level than on baryon level.

because on quark level ① the size effect b ②the quark exchanges between two nucleon clusters both contribute short range repulsion

Ⅳ:summary 1: The vector meson (ρ,ω) exchange effect in N-

N scattering processes on quark level is studied in the extended chiral SU(3) quark model.

2: The phase shifts of 1S0 and 3S1 waves can be

fitted rather well. 3: the strength of OGE interaction is greatly

reduced and the short range NN repulsion is due to vector meson exchanges (instead of OGE), which also results in smaller size parameter bu.