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 discussion Ⅳ : 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 for studying the system with s quark. 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.)

1: long range => confinement 2: short range =>OGE –color dependent

The expressions of and : Here we have only one coupling constant, 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 presented by 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, cutoff mass: Λ=1100 Mev, chiral symmetry breaking scale

(3). OGE and confinement part: and are fixed by and. is determined by the stability condition of Model parameters and the corresponding binding nergies of deuter on

To study two baryon system, we did a two-cluster dynamical RGM calculation Phase shifts of N-N scattering S wave single channel 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 1 S 0 scattering red line : with NΔ coupling black line : without NΔ coupling Extended Model with set I (fchv/gchv =0) Discuss:

To get reasonable 1 S 0 phase shifts

1: for different models almost the same good agreement with exp. 2 : b u from 0.5 (not extended) to 0.45fm (extended model) Means the bare radius of baryon becomes smaller when more meson clouds are included. * 3 S 1 -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 Model 1: OGE is weak 2: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 exchange offers 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: f chv /g chv =0, g chv =2.35 f chv =0 set II: f chv /g chv =2/3, g chv =1.97 f chv =1.32 on nucleon level g ωNN ≈ for ω meson, g ρNN ≈ 2-3 for ρ meson Nijmegen model D g ρNN ≈ 2.09 and f ρNN = * the coupling constants of the vector meson exchange g chv and f chv The coupling constant is much weaker on quark level than on baryon level. because on quark level ① the size effect b ② the 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 1 S 0 and 3 S 1 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 b u.