the structure of nuclear force in a chiral quark-diquark model

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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

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◇ 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

qq

~)(

)()(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

qq

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

qq

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.