Three-baryon interaction generated by determinant interaction of quarks

Akira Ohnishi,Kenji Morita,Kouji Kashiwa

doi:10.1093/ptep/ptx095

Akira Ohnishi, Kenji Morita + Show 1 more

Open Access

https://doi.org/10.1093/ptep/ptx095

Copy DOI

Abstract

We discuss the three-baryon interaction generated by the determinant interaction of quarks, known as the Kobayashi-Maskawa-'t Hooft (KMT) interaction. The expectation value of the KMT interaction operator is calculated in fully-antisymmetrized quark-cluster model wave functions for one-, two- and three-octet baryon states. The three-baryon potential from the KMT interaction is found to be repulsive for $NN\Lambda$ and $N\Lambda\Lambda$ systems, while it is zero for the $NNN$ system. The strength and range of the three-baryon potential are found to be comparable to those for the $NNN$ three-body potential obtained in lattice QCD simulations. The contribution to the $\Lambda$ single particle potential in nuclear matter is found to be 0.28 MeV and 0.73 MeV in neutron matter and symmetric nuclear matter at normal nuclear density, respectively. These repulsive forces are not enough to solve the hyperon puzzle, but may be measured in high-precision hyperisotope experiments.

Highlights

The discovery of 2-solar-mass neutron stars [1,2] has cast doubt on the equation of state (EOS)based on conventional nuclear physics
One of the ideas is to assume that the crossover transition [8,9] from nuclear matter to quark matter takes place at relatively low density, 2–3ρ0, with ρ0 0.16 fm−3 being the normal nuclear matter density, instead of the often assumed first-order deconfinement phase transition at high density
We find that the color factor is ±1 when there is no quark exchange among baryons (a1, a2, a3)

Summary

Introduction

The discovery of 2-solar-mass neutron stars [1,2] has cast doubt on the equation of state (EOS). The 3B interaction from the KMT interaction has favorable features to resolve the hyperon puzzle It acts only on systems including strange quarks, and it is probably repulsive because of the negative value of gD. In this treatment, we do not need to set the quark condensate qq , which appears in other diagrams, and there is no contribution to the N − mass difference [37], since we need u, d, and s quarks in the 3 quarks for the KMT interaction to work. 3, we quantify the 3B potential generated by the KMT interaction based on the 3-baryon wave function and discuss its implication to the hyperon puzzle.

One-baryon state

Two-baryon states

Three-baryon states

KMT operator and its expectation value

Summary