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

Quark-Pauli effects in three octet-baryons PRC94,035803 (2016) Choki NAKAMOTO(Suzuka-NCT) Yasuyuki SUZUKI(Niigata Univ. & RIKEN) １． Introduction ２． Formulation ３． Results ４． Summary 2016/11/22 NSMAT2016 1

１． Introduction Three-body force in the 3 baryon system ⇒ It is needed many physics category Few-body system physics • Nuclear matter physics • Its origin is unclear Neutron star physics • …… • Theoretical approach 2 π -exchange potential model （ Fujita&Miyazawa ） • Phenomenological procedure • Chiral effective-field theory • Lattice QCD • …… • 2016/11/22 NSMAT2016 2

Approach by a quark model q q 9-quark 3-baryon system （ 3-cluster 9-body system ） q q q q ⇒ Three-body force may be appearance of the constituent effects ? Toki, Suzuki, Hecht ： PRC26 (1982) 736 Suzuki, Hecht ： PRC29 (1984) 1586 q Kinematical ： quark-Pauli effect Maltman ： NPA439 (1985) 648 • Takeuchi, Shimizu ： PLB179 (1986) 197 q q Dynamical ： quark-quark interaction through quark-exchange • 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 2016/11/22 NSMAT2016 3

Model space Exotic Decouplet Hyper- hadron baryon Nuclei nuclei In this talk charm & ∆ - resonance up & down strange bottom PRC94,035803 (2016) Kinematics Norm kernel Quark-Pauli effect Quark Hamiltonian (kinematics) Kinetic-energy Confinement & Heavy-quark Dynamics Color-Coulombic symmetry Short-range Color-magnetic repulsion Fujita-Miyazawa π - exchange effect three-body force 2016/11/22 NSMAT2016 4

Present talk Estimation of the quark-Pauli effect in the B 8 B 8 B 8 systems through the eigen-value of the RGM norm-kernel (no parameter) Three-body baryonic repulsion originated from quark-kinematics Does the quark-Pauli blocking effect play a prominent role to support the neutron star with 2-times solar-mass ? 2016/11/22 NSMAT2016 5

2 ． Formulation 9-quark 3-baryon wave-function We assume the color-singlet for 3 q -cluster 2016/11/22 NSMAT2016 6

Eigen-value equation Antisymmetrizer µ S a = 0 ： Pauli forbidden state µ S a ~ 0 ： almost Pauli forbidden state so much repulsive that µ S a is smaller The degree to which 3-baryons are reluctant to overlap each other 2016/11/22 NSMAT2016 7

Antisymmetrizer 2-baryon system Antisymmetrizer 20 terms baryon-exchange operator quark -exchange operator 1 3 6 5 2 4 3-baryon system D-term 2B-term ① ③ 762 terms ② 2016/11/22 NSMAT2016 8

3 ． Results 2016/11/22 NSMAT2016 9

Review of the B 8 B 8 case Almost Pauli forbidden state only in the 2-channel µ S a = 2/9 Σ N(I=3/2) 3 S -state They have the same Origin of repulsive Σ nuclear potential flavor-SU(3) irreducible representation µ S a = 2/9 ΞΞ (I=0) 3 S -state 2016/11/22 NSMAT2016 10

B 8 B 8 B 8 system Eigen-value components : ( color ) × ( spin-flavor ) Color-singlet condition in each 3 q -cluster ① ③ ② We do not need to calculate ③ -type 2016/11/22 NSMAT2016 11

PRC94,035803 (2016) Total Spin ½ case Λ nn Σ - nn Ξ - Ξ - n ΛΛ n Ξ - nn Σ - Σ - n 2016/11/22 NSMAT2016 12

PRC94,035803 (2016) Total Spin ½ case Λ nn Σ - nn Ξ - Ξ - n ΛΛ n Strong Pauli-repulsion Ξ - nn Σ - Σ - n 2016/11/22 NSMAT2016 13

PRC94,035803 (2016) Total Spin 3/2 case Σ - Λ n Ξ - Σ - n Ξ - Σ - Λ 2016/11/22 NSMAT2016 14

PRC94,035803 (2016) Total Spin 3/2 case Σ - Λ n Strong Pauli-repulsion Ξ - Σ - n Ξ - Σ - Λ 2016/11/22 NSMAT2016 15

Contribution from exchange-diagram ① among 3-baryons breakdown µ S a ③ ② 3-body terms : Replusive tendency 3-body terms: Λ nn Replusive tendency Σ − nn Ξ − nn 3-body terms: Replusive tendency 2016/11/22 NSMAT2016 16

４． Summary PRC94,035803 (2016) We investigated the quark-Pauli effects in the B 8 B 8 B 8 systems by estimating the • eigenvalue of the RGM normalization kernel. ( no parameter ) Almost Pauli-forbidden state • Total spin 1/2 Σ NN(I=2)= Σ − nn , ΣΣ N(5/2) = Σ − Σ − n , ΞΞΛ−ΞΞΣ (0), ΞΞΞ (1/2) Total spin 3/2 Σ NN(1), ΣΣΝ−ΣΛΝ (3/2) = Σ − Λ n , ΞΣ N(2) = Ξ − Σ − n , ΞΞΛ (0), ΞΞΣ (1) The Pauli blocking effect is weak in the Λ nn system • No additional No quark-Pauli repulsion effectively works for Λ repulsion for Λ The Pauli blocking effect is strong in the Σ − nn system • The appearance of Σ − is suppressed in the neutron star interior ・ Estimation of the kinetic-energy term ・ Estimation of the interaction term Future ・ including decouplet baryon … 2016/11/22 NSMAT2016 17