Quark-Pauli effects in three octet-baryons PRC94,035803 (2016) - - PowerPoint PPT Presentation

Quark-Pauli effects in three octet-baryons

Choki NAKAMOTO(Suzuka-NCT) Yasuyuki SUZUKI(Niigata Univ. & RIKEN)

2016/11/22 1 NSMAT2016

１．Introduction ２．Formulation ３．Results ４．Summary

PRC94,035803 (2016)

１．Introduction

Three-body force in the 3 baryon system

⇒ It is needed many physics category

• Few-body system physics
• Nuclear matter physics
• Neutron star physics
• ……

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Its origin is unclear

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

Theoretical approach

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q q q q q q q q q

9-quark 3-baryon system（3-cluster 9-body system） ⇒ Three-body force may be appearance

• f the constituent effects ?
• Kinematical ： quark-Pauli effect
• Dynamical ： quark-quark interaction through quark-exchange

Approach by a quark model

Advantage of quark-model

• Systematical research in the unified model-framework

from 1-baryon to few-baryons

• Separate estimation of the Pauli effect, each interaction…

Our final aim

• Understanding of 3-body baryon forces

in the quark-model

Toki, Suzuki, Hecht ： PRC26 (1982) 736 Suzuki, Hecht ： PRC29 (1984) 1586 Maltman ： NPA439 (1985) 648 Takeuchi, Shimizu ： PLB179 (1986) 197

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Quark Hamiltonian Norm kernel Kinetic-energy Confinement & Color-Coulombic Color-magnetic π - exchange effect Nuclei Hyper- nuclei Exotic hadron Decouplet baryon charm & bottom strange up & down

∆ - resonance

Quark-Pauli effect (kinematics) Heavy-quark symmetry Short-range repulsion Fujita-Miyazawa three-body force In this talk

Dynamics Kinematics

Model space PRC94,035803 (2016)

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Present talk

Estimation of the quark-Pauli effect in the B8B8B8 systems through the eigen-value of the RGM norm-kernel (no parameter) Three-body baryonic repulsion

• riginated from quark-kinematics

Does the quark-Pauli blocking effect play a prominent role to support the neutron star with 2-times solar-mass ?

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2．Formulation

9-quark 3-baryon wave-function

We assume the color-singlet for 3q-cluster

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Eigen-value equation µSa = 0 ： Pauli forbidden state µSa ~ 0 ： almost Pauli forbidden state so much repulsive that µSa is smaller

Antisymmetrizer

The degree to which 3-baryons are reluctant to overlap each other

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762 terms ① ② ③ 2B-term D-term

3-baryon system

Antisymmetrizer baryon-exchange operator 1 3 6 5 2 4 quark -exchange operator 20 terms

2-baryon system

Antisymmetrizer

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3．Results

Review of the B8B8 case

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Origin of repulsive Σ nuclear potential

ΣN(I=3/2) 3S-state ΞΞ (I=0) 3S-state

µSa = 2/9 µSa = 2/9

Almost Pauli forbidden state only in the 2-channel

They have the same flavor-SU(3) irreducible representation

B8B8B8 system

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① ② ③ ( color )×( spin-flavor )

Eigen-value components :

We do not need to calculate ③-type Color-singlet condition in each 3q-cluster

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Total Spin ½ case

Λnn Σ-nn Ξ-nn

Σ-Σ-n Ξ-Ξ-n

ΛΛn

PRC94,035803 (2016)

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Total Spin ½ case Strong Pauli-repulsion

Λnn Σ-nn ΛΛn Ξ-nn

Σ-Σ-n Ξ-Ξ-n

PRC94,035803 (2016)

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Total Spin 3/2 case

Σ-Λn

Ξ-Σ-n Ξ-Σ-Λ PRC94,035803 (2016)

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Strong Pauli-repulsion Total Spin 3/2 case

Σ-Λn

Ξ-Σ-n Ξ-Σ-Λ PRC94,035803 (2016)

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① ② ③

Contribution from exchange-diagram among 3-baryons

3-body terms : Replusive tendency Λnn Σ−nn Ξ−nn breakdown

µSa

3-body terms: Replusive tendency 3-body terms: Replusive tendency

４．Summary

• We investigated the quark-Pauli effects in the B8B8B8 systems by estimating the

eigenvalue of the RGM normalization kernel. ( no parameter )

• Almost Pauli-forbidden state

Total spin 1/2 ΣNN(I=2)=Σ−nn, ΣΣN(5/2) =Σ−Σ−n, ΞΞΛ−ΞΞΣ(0), ΞΞΞ(1/2) Total spin 3/2 ΣNN(1), ΣΣΝ−ΣΛΝ(3/2) =Σ−Λn, ΞΣN(2) =Ξ−Σ−n, ΞΞΛ(0), ΞΞΣ(1)

• The Pauli blocking effect is weak in the Λnn system
• The Pauli blocking effect is strong in the Σ−nn system

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Future

・ Estimation of the kinetic-energy term ・ Estimation of the interaction term ・ including decouplet baryon …

The appearance of Σ− is suppressed in the neutron star interior

PRC94,035803 (2016)

No quark-Pauli repulsion effectively works for Λ

No additional repulsion for Λ