the structure of nuclear force in a chiral quark-diquark model
DESCRIPTION
The Structure of Nuclear force in a chiral quark-diquark model. K. Nagata and A. Hosaka RCNP, Osaka University. K. Nagata and A. Hosaka, hep-ph/0312161. ’03 3/23 @ RCNP. Contents. Introduction Motivation, outline 2. Lagrangian quark-diquark lagrangian - PowerPoint PPT PresentationTRANSCRIPT
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K. Nagata and A. Hosaka RCNP, Osaka University
The Structure of Nuclear force in a chiral quark-diquark model
K. Nagata and A. Hosaka, hep-ph/0312161
’03 3/23 @ RCNP
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1. Introduction Motivation, outline2. Lagrangian quark-diquark lagrangian meson baryon lagrangian3. Structure of NN force Long range part Short range part4. Summary
Contents
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1. Introduction・ Motivation: Understanding of hadron physics from the quark level
Hadronization of chiral quark-diquark model
Nuclear force
1.long and medium range ; OBEP
2.short range ; internal structure (repulsive core)
To describe the nuclear force in a unified way,
we need to include
1. chiral symmetry
2. hadrons as composites
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NJL model and Auxiliary field method (Bosonization)
NJL model : chiral sym.
q
q
Auxiliary field method :
NJL(quark) model → meson Lagrangian
(Eguchi, Sugawara(1974), Kikkawa (1976))
q
M
Path-integral identity q
Basic idea of hadronization
5
◇ Bosonization was extended to baryon by including diquark.
B
D
q
・ Ebert, Jurke (1998)
・ Abu-Raddad, Hosaka, Ebert, Toki (2002)
1. chiral symmety → O.K
2. hadrons as composites → O.K
B = q + D
◇ GT relation, WT identity is satisfied.
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(Abu-Raddad et al, PRC, 66, 025206 (2002))
I. Quark-meson
2. Lagrangian
M
q
q
chiral sym. breaking
25
20 )()(
2)( qiqqq
GqmiqLNJL
qqiqq 5,
)(2
1)( 22
50 G
qimiqLNJL
2/1
555 ,rep.linear-Non
f
iq
)()(2
1)()( 0
25 mOm
GamviiL qqNJL
55555555 2
1,
2
1
ia
iv
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(0, 0) ‥‥ scalar diquark
(1, 1) ‥‥ axial-vector diquark
・ Pauli principle
for quark
・ Color singlet for baryon
(Spin, Isospin)
◇As a first step, we take into account only scalar diquark
III. Quark-diquark interaction
→ local interaction D
q
~
◇ Microscopic(q, D, M) lagrangian
II. Introduction of diquark
DDGDMD
mOmG
amviiL
S
~)(
)()(2
1)()(
22
02
5
8
BBG
BDχBDχGDDχSχL ~1
)(~
Δ 11
AiAxdiD logtrexpexp 4
221
51 γ,)(
S
q
MΔ
vσMMmiS
II. q and D are integrated out by
◇ Meson baryon lagrangian
I. Baryons are introduced as auxiliary fields B=D
)1(logtr)1(logtr T SBBΔiSMiL
meson baryon
quark diquark
Hadronization
n
pB
9
)1(logtr T SBBΔiL
)()z()()(tr
trtr
zBySyxΔxB
ΔSBBA
ΔSBBΔSBBA trtr 2
2tr)1log( tr:Expansion
2AAA
M
000
1
MSSSS
MmiS q
q-M interaction
BD
q
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・ Two types of NN force
OBEP with form factor
→ long and medium range
q-D loop
→ short range
・ Magnetic moment, radius, gA was calculated.
・ GT relation, WT identity is satisfied.
Nucleon properties (one N term)
Nuclear force (two N term)
Abu-Raddad et al (2002)
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3. Structure of NN force
chiral σ and π exchange
loop diagram in terms of
quark and diquark
long and medium
short range
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OPEP potential
range ~ mπ
= +
NN axial- coupling
・ gA =0.87
・ GT relation is satisfied
‥‥ exchange potentiallong range part
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We evaluate for various B.E.
1.the range, mass and strength of q-D loop
2. relation between these values and nulceon size
and compare our results to OBEP
m q =390, Ms=600 MeV, =630 MeV
・ Fixed parameters
・ Free parameter
constantcouplingdiquarkquark;~
G
)E. B.(
mass.nucleon size,nulceon energy, binding - controls~
NSq MMm
DqG
Short range part
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qDloop
2212
222
22221
22
4
42
)()()(
)())(()())((
2
tr
qSqS
c
NN
mkppMkpmkMkp
pBmkpppBpBmkpB
kdNZi
ΔSBBΔSBBiL
),(1 pEp p
),(2 pEp p
),(2 pEp p
),(1 pEp p
pp
systemCoMtheincaseelastic
15)0,()( 2,
2, qFqF VSVS
222222
2212
222
22221
22
4
42
),(),(
)()()(
)())(()())((
2
BBPqFBBPqF
mkppMkpmkMkp
pBmkpppBpBmkpB
kdNZiL
VS
qSqS
cNN
ppP
ppq
p
p
p
p
attractive repulsive
0casetheineinvestigatWe P
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・ B.E. becomes larger (nulceon becomes smaller), interaction ranges becomes shorter.
scalar Fs(q) vector FV(q)
Form factors for various B.E
)(GeV22q
)(GeV22q
B.E.290
140
10
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Interaction range, mass and strength
Range vs size
(fm)1/22r
Rs
VR
B.E. weak
0
2
2,
2,
2,
)(
)(
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q
VS
VSVS q
qF
qFR
2,
2
2,2
, )(VS
VSVS mq
gqF
Range
Mass and Strength
2/126.1 rRS
2/120.1 rRV
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strength vs size
gS = 23 (10) (attractive)
gV = 4 (13) (repusive)
Vm
SmSg
Mass vs size
(fm)1/22r (fm)
1/22r
mS = 610 MeV ~ mσ
mV = 790 MeV ~ mω
Vg
0.8fm
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・ Nuclear force is composed of two part short range part → qD loop long and medium range part → chiral meson exchange
・ qD loop is composed of scalar type (attraction) and vector type (repulsion).
4. Summary・ Hadronization of q-D model gives the
composite meson- baryon Lagrangian.
・ We need to include P-dependence, exchange term, a.v.diquark
and calculate phase shifts, cross section…
・ Interaction range and mass → good strength → scalar type is stronger than vector type.