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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 ) .
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
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
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
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
.
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:
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.