Nucleon-nucleon interaction
in the extended chiral SU(3)
quark model
L. R. Dai
(Department of Physics, Liaoning Normal University)
Z.Y. Zhang, Y.W. Yu
(Institute of High Energy Physics, Beijing, China)
Outline
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
Ⅰ:Motivations
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 L I can be written as:
8
8
a=0
a=0
L I = -g ch ψ(  σ a λ a + i  πa λ a γ 5 )ψ.
σ,σ', χ,ε
scalar nonet fields
π, K, η, η'
pseudo-scalar nonet fields
It is easy to prove that L I is invariant under the infinitesimal chiral SU(3)L  SU(3)R
transformation. This can be regarded as an 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:
H =  t i - TG +  Vij ,
i
i< j
conf
ij
Vij = V
oge
ij
+V
ch
ij
+V ,
Vijch =  (Vijs(a) + Vijps(a) ) .
a
( V conf
ij
is taken as quadratic form.)
1: long range => confinement
2: short range =>OGE –color dependent
spin-flavor dependent
s(a)
ij
V
s
ij
V
ps
ij
The expressions of
and V :
2
g ch
C ( gch, m ps ( a ), ) X 1 (ms ( a ), , rij )a (i)a ( j )

4π
 l  s term,
ps(a)
ij
V
m 2ps ( a )
2
ch
g C ( g m )
X 2 (m ps ( a ), , rij )
ch , ps ( a ),

12mqi mqj
4π
( i   j )a (i )a ( j ) + tensor term

X 1 ( m, , r )  Y ( mr )  Y ( r ),
m
Y ( x) 
1 x
e ,
x

X 2 ( m, , r )  Y ( mr )  ( )3Y ( r ),
m
2

C ( g ch, m, )  2
m.
2
 m
2
g ch
9 m u2 g 2NNπ
=
.
Here we have only one coupling constant g ch ,
2
4π 25 M N 4π
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
Based on the chiral SU(3) quark model,
we further add vector effective Lagrangian
gchv :Vector coupling constant
fchv: Tensor coupling constant
The Hamiltonian of the system
new =>
“extend”
1: quarkvector fileld
coupling
2:spin-flavor
dependent
color – independent
Parameters:
(1). Input part: taken to be the usual values.
bu  0.5 fm
ms = 470MeV.
mu = 313MeV,
bu  0.45 fm
(2). Chiral field part:
2
g ch
9 mu2 g 2NNπ
=
,
2
4π 25 M N 4π
m ,m ,m' ,mK
and
m  , m , m K * , m
mσ
is adjustable.
are taken to be experimental values,
m '  m  m  980 MeV .
cutoff mass: Λ=1100 Mev, chiral symmetry breaking scale
(3). OGE and confinement part:
gu
and
gs
are fixed by MΔ
- MN and M Σ - M.Λ
auu ... is determined by the stability condition of N, Λ,Ξ.
Model parameters and the corresponding binding nergies of deuteron
Model parameters and the corresponding binding nergies of deuteron
Ⅲ: RESULTS
with 3 sets of
parameters
To study two baryon system, we did a
two-cluster dynamical RGM calculation
Phase shifts of N-N scattering
S wave
single
channel
N-N P-wave scattering
N-N D-wave scattering
N-N F-wave scattering
Discuss:
*About NΔeffect
NN
1S
0
scattering
Extended Model
with set I
(fchv/gchv =0)
.
Extended Model
with set II
(fchv/gchv =2/3)
red line : with NΔ coupling
black line : without NΔ coupling
To get reasonable 1S0 phase shifts
*
3S -wave
1
scattering
1: for different models
almost 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.
*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
chira su(3) quark model
in Extended Model
1: OGE is weak
2:The vector meson exchange is dominate!
Extended su(3)
quark model with
set II
*
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.
* the coupling constants of the vector meson
exchange gchv and fchv
on quark level:
set I: fchv/gchv=0 ,
set II: fchv/gchv=2/3 ,
gchv =2.35
gchv =1.97
fchv =0
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 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 NN 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.