H-dibaryon matter in the Skyrme model on a hypersphere

Abstract

We study the properties of H-dibaryon matter through the SO(3) Skyrmion solution on a three-dimensional hypersphere S³. As the density increases, the swelling of H-dibaryon is found. Above a critical density, the system becomes uniform in terms of the baryon density. In this uniform phase, the critical order parameter is largely reduced, which can be interpreted as the chiral symmetry restoration. From the comparison with the SO(2)×SO(2) solution, the SO(3) soliton is found to be the true ground state for high density system with R≤0.64 fm in the B=2 sector with N_f=3.

Introduction

Recently exotic hadron states have been studied elaborately. Among them, an H-dibaryon has been an object of many works [1]as a hopeful candidate of q⁶ state since the prediction by Jaffe [2]in the MIT bag model. Lots of theoretical studies have been made on the problem of the H-dibaryon, and have predicted the H-dibaryon mass below the ΛΛ threshold 1, 3. The Skyrme model was first applied to the H-dibaryon by Balachandran et al. proposing the B=2 SO(3) soliton configuration, which has the symmetric configuration in terms of the flavor SU(3) 4, 5. They obtained the H-dibaryon mass lighter than two Λ's (M_H∼1.92M_B) in the SU(3) flavor symmetric limit.

Experimentally, several candidate events have been reported 6, 7, but any conclusive result for its existence is not obtained yet. The binding energy of two Λ's in a double hypernucleus places a restriction on the H-mass. A double hypernucleus event found at KEK [8]implies that the lower limit of the H-dibaryon mass is a few tens of MeV below the ΛΛ threshold.

The possibility of the existence of H-dibaryon matter in a high-density neutron star is pointed out by Tamagaki et al. [9]. In their argument, the compactness of the H-dibaryon radius is an important assumption on the existence of H-dibaryon matter, although the size of H-dibaryon may vary in the dense system as the nucleon swelling phenomenon in nuclear matter [10]. If so, nuclear matter may decay into H-matter at a critical density ρ_c=6∼9ρ₀ (ρ₀=0.17 fm⁻³) before the phase transition into quark-gluon plasma.

The properties of nuclear matter at high densities have been investigated in many ways. Castillejo et al. studied Skyrmion matter by placing SU(2) hedgehog Skyrmions on a lattice and show that the deconfinement phase transition and the chiral symmetry restoration occur above a critical density [11]. Manton and Ruback obtained the similar results by a simple and mathematically sophisticated approach. Instead of placing many Skyrmions in the flat space $\text{R}{}^3$, Skyrmion matter is approximated by one Skyrmion on an S³ hypersphere with radius R. They showed that beyond a critical density the lowest energy solution is given by the “identity map” and the baryon density distributes uniformly on the hypersphere [12]. In this phase, the spacially averaged value of the chiral order parameter becomes zero, which may imply the chiral symmetry restoration at high densities. This phase transition was investigated also in the case of two Skyrmions on S³ [13]. The result is qualitatively the same as one Skyrmion case on S³, and they concluded that these behaviors are a general tendency in the Skyrme model.

In this paper, we investigate the feature of H-dibaryon matter by using the SO(3) Skyrmion with baryon number 2 located on S³ hypersphere. We study how the QCD phase transition occurs in this situation. We study also how the size of the H-dibaryon varies in high-density H-matter. For simplicity on the mathematical and physical insight, we deal with the chiral limit in this paper.