Quark-Pauli effectin the three-baryon systems
consisted of baryon-octet
Choki NAKAMOTO(Suzuka-NCT)
Yasuyuki SUZUKI(Niigata Univ. & RIKEN)

１．Introduction
２．Formulation
３．Results
４．Summary
2014/11/30

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1１．Introduction
Three-body force in the 3 baryon system• Few-body system physics• Nuclear matter physics
Its origin is unclear• Neutron star physics• ……

Theoretical approach•••••

2π-exchange potential model（Fujita&Miyazawa）
Phenomenological procedure
Chiral effective-field theory
Lattice QCD（HAL-QCD）……

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Approach by the quark model
9-quark 3-baryon system（3-cluster 9-body system）⇒ appearance of the constituent effects

qq q• Kinematical ： quark-Pauli effect• Dynamical ： quark-quark interaction through quark-exchangeqq qqq q

Quark-model approach to date

• Toki, Suzuki, Hecht ： PRC26 (1982) 736

Investigation of Pauli effect in the 3He density through the NNN norm-kernel• Suzuki, Hecht ： PRC29 (1984) 1586

Estimation of the Fermi-Breit interaction(OGEP) kernel in the NNN system• Maltman ： NPA439 (1985) 648

Contribution to the charge form-factor of the FB-int. in the NNN & NNNN systems• Takeuchi, Shimizu ： PLB179 (1986) 197

Estimation of the norm-kernel & kinetic-energy term in the ΛNN & ΛNNN systems

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Advantage of quark-model••

Systematical research in the unified model-frameworkfrom 1-baryon to few-baryons
Separate estimation of the Pauli effect, each interaction…

Our aim• Understanding of 3-body baryon forcesin the quark-model

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In this talkNucleiHypernuclei

Exotichadron

quark-flavor
up & down strange

Quark Hamiltonian

Norm kernel
Kinetic-energy

Heavy-quark
symmetry
Short-range
repulsion

π - exchange effect

2014/11/30∆ - resonancecharm& bottom

Quark-Pauli effect(kinematics)

Confinement &Color-Coulombic
Color-magnetic

DecoupletbaryonProgress on J-PARC hadron physics in 2014

Fujita-Miyazawa
three-body force
5Advantage of quark-model••

Systematical research in the unified model-frameworkfrom 1-baryon to few-baryons
Separate estimation of the Pauli effect, each interaction…

Our aim• Understanding of 3-body baryon forcesin the quark-model

Present talkEstimation of the quark-Pauli effect through the eigen-valueof the RGM norm-kernel in the B8B8B8 systems⇒ no parameter2014/11/30

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２．Formulation
Resonating-group method (RGM) equation
2-baryon system
RGM norm kernel

3-baryon system

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Relative wave-function
between clusters

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Eigen-value equation
2-baryon system
Eigen-value

3-baryon systemµk = 0 ： Pauli forbidden stateµk ~ 0 ： almost Pauli forbidden state
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Eigen-value
2-baryon system
Harmonic-oscillator function

3-baryon system
We need only this RGM norm kernel
orbital part vanishes through the integral
We need only the factor for the color, spin and flavor parts

No parameter !
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9

RGM normalization kernel
2-baryon system
Internal wave-function in the Baryon 1 & 2（2-baryon system with the spin S and isospin I ）Antisymmetrizer
baryon-exchange operator
quark -exchange operator

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3-baryon system

D-term2B-term①②

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762 terms

113．Results

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2-baryon system
Eigen-value components : ( color )×( spin-flavor )2014/11/30

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8

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827

1010*8s

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1Results

14

8827

1010*8s8a1

Origin ofrepulsiveΣ nuclearpotential

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3-baryon system
Eigen-value components : ( color )×( spin-flavor )①

We do not need to calculate ③-type

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③16

3-baryon system
Eigen-value components : ( color )×( spin-flavor )2014/11/30

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Interesting B8B8B8-systems
TritonΛΛΛΣ-Σ-Σ-

Hyper-triton

Ξ-Ξ-Ξ-nnΛ
nnnnnΣnnΞ2014/11/30

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Eigenvalue for Β8Β8Β8qqq q

Total spin : S = ½q q

Eigenvalue①qq q②(n1l1) = (n2l2) = (00)Internal S-wave only

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Interesting B8B8B8-systems
Triton＝（１４）ΛΛΛΣ-Σ-Σ-

Hyper-triton

Ξ-Ξ-Ξ-nnΛ
nnn

＝（４１）

nnΣnnΞ2014/11/30

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&
Eigen-value components( color )×( spin-flavor )×( orbital )ΝΝΝ system

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&Eigen-value components( color )×( spin-flavor )×( orbital )ΞΞΞ system

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Progress on J-PARC hadron physics in 201422&ΝΝΝ system10*

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ΞΞΞ system

35*

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1035

23&
①

14

4②

③・ ΞΞΞ(SI=½½) state ⇒ strong Pauli-repulsion
・ Quark-exchange contribution has opposite signbetween ΝΝΝ and ΞΞΞ systems

・ Quark-exchange contribution in the 3B8 system is 1/3-1/20
of it in the 2B8 system with opposite sign in this case2014/11/30

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Interesting B8B8B8-systems
TritonΛΛΛHyper-triton

Σ-Σ-Σ-＝（３３）Ξ-Ξ-Ξ-＝（３３）

nnΛ
nnn

＝（３３）

nnΣnnΞ2014/11/30

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Complete Pauli-forbidden statesnnn
Σ-Σ-Σ64Ξ-Ξ-Ξ-

27s

64

8s

27

8
derived from 27 88
derived from 18

１All eigen-value in internal S-wave are 0
Check of calculation : OK!
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Interesting B8B8B8-systems
TritonΛΛΛΣ-Σ-Σ-

Hyper-triton

Ξ-Ξ-Ξ-nnΛ
nnn
nnΣnnΞ2014/11/30Progress on J-PARC hadron physics in 201427

NNY systems
In this case,we consider as Pauli effectthe ratio of the eigen-value to D-term.

N2014/11/30

q Yq qq
N qq

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qq q

28

I must apologize forchanging the eigen-value
in this NNY systems andthereby conclusion also.
＝

NNY systems
cf. :relatively＝moderatennΛ

relatively＝nnΣ-Strongly repulsive
relatively＝repulsivennΞWe have to investigate YN-N configuration also
in order to get more information about the quark-Pauli effect.
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４．Summary• We investigated the quark-Pauli effects by evaluating the RGM
normalization kernel for the B8B8B8 systems. ( no parameter )• Strong ordering of quark-Pauli repulsion :nnΣ− = ΞΞΞ(1/2) > nnΞ− > nnΛ = ΝΝΛ(0) > ΝΝΝ(1/2)• In order to get more information about the quark-Pauli effect ofNNY system, we need to investigate YN-N configuration also.

Future・ About YN-N configuration
・ Total spin 3/2 case・ Contribution to total S-state from internal P-wave between 2-baryon
・ Estimation of the kinetic-energy term
・ Estimation of the interaction term・ including decouplet baryon…
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