[Paper Review] Hyperons in nuclear matter

Tsuyoshi Miyatsu, Kenji Saito|arXiv (Cornell University)|Mar 11, 2009

High-Energy Particle Collisions Research10 citations

TL;DR

This paper applies the chiral quark-meson coupling (CQMC) model to hyperons in nuclear matter, self-consistently including one-gluon exchange (OGE) and pion-cloud effects. The OGE-induced hyperfine interaction strongly splits baryon spectra, making the Λ hyperon feel a significantly more attractive mean field than Σ or Ξ, explaining the experimental difficulty in forming Σ or Ξ hypernuclei.

ABSTRACT

The chiral version of the QMC model, in which the effect of gluon and pion exchanges is included self-consistently, is applied to the hyperons in a nuclear medium. The hyperfine interaction due to the gluon exchange plays an important role in the in-medium baryon spectra, while the pion-cloud effect is relatively small. At the quark mean-field level, the $Λ$ feels more attractive force than the Σor Ξin matter.

Motivation & Objective

• To investigate the role of quark-level dynamics, particularly gluon and pion exchanges, in determining hyperon properties in nuclear matter.
• To explain the experimental scarcity of Σ and Ξ hypernuclei by analyzing the in-medium potential and mass splitting of hyperons.
• To assess the importance of the one-gluon exchange (OGE) hyperfine interaction versus pion-cloud effects in the chiral quark-meson coupling (CQMC) framework.
• To determine how the scalar and vector mean fields, combined with quark-level interactions, affect the effective masses and potentials of Λ, Σ, and Ξ hyperons in dense matter.

Proposed method

• Adopts the chiral quark-meson coupling (CQMC) model, an extension of the QMC model incorporating chiral symmetry via the cloudy bag model (CBM) with linearized pion fields.
• Uses a Lagrangian density including quark fields, bag constant, pion-quark pseudoscalar/pseudovector coupling, and gluon-quark interaction with color-magnetic terms.
• Calculates the Hartree-Fock (HF) energy correction for pion-quark interaction using Hubbard's prescription to include direct and exchange contributions.
• Evaluates the one-gluon exchange (OGE) contribution to hyperon masses via the color magnetic interaction term ΔE_G^mg = (α_s/R)[a_00M_00 + a_0sM_0s + a_ssM_ss], with coefficients a_ij from SU(6) wavefunctions.
• Computes the quark magnetic moment M_ij as a function of quark mass and bag radius R, using M_ij(m_i,m_j,R) = (3/R^3)μ(m_i,R)μ(m_j,R)I(δ_i,δ_j).
• Analyzes the in-medium potential u_v - u_s = (n/3)g_ωω - (M_Y - M_Y^*) for Λ, Σ, and Ξ, comparing cases with and without pion-cloud effects.

Experimental results

Research questions

• RQ1 How does the one-gluon exchange (OGE) hyperfine interaction affect the in-medium spectra of Λ, Σ, and Ξ hyperons in nuclear matter?
• RQ2 To what extent does the pion-cloud effect modify the masses and potentials of hyperons in dense nuclear matter?
• RQ3 Why is the Λ hyperon more strongly bound in nuclear matter than the Σ or Ξ hyperons, and how does this relate to experimental observations of hypernuclei?
• RQ4 Does the CQMC model predict a violation of the simple scaling law δM_H^*/δM_N^* ∝ (number of light quarks in H), and if so, why?
• RQ5 How do the scalar (σ) and vector (ω) mean fields, combined with OGE and pion effects, shape the effective potential for hyperons in nuclear matter?

Key findings

• The OGE-induced color magnetic interaction dominates the in-medium hyperon spectra, with the Δ-N mass splitting significantly enhanced due to the M_00 term.
• The Λ hyperon experiences a much stronger attractive mean field than the Σ or Ξ hyperons, as evidenced by δM_Λ^* > δM_Σ^* > δM_Ξ^* in matter, consistent with the lack of observed Σ or Ξ hypernuclei.
• The pion-cloud effect is relatively small, contributing only minor mass shifts, while the OGE effect is crucial for splitting the Σ and Ξ masses from the Λ.
• The mass difference M_Y^* - M_Λ^* in matter increases with baryon density ρ_B, indicating that Σ and Ξ are less bound than Λ in dense matter.
• Beyond ρ_B/ρ_0 ≈ 1.3, the potential for the Ξ hyperon becomes deeper than that for the Σ, due to the OGE contribution -4M_0s + M_ss, which exceeds the Σ's -M_00 + 4M_0s.
• The CQMC model violates the simple QMC scaling law δM_H^*/δM_N^* ∝ (number of light quarks), due to the non-uniform impact of OGE and pion effects on different hyperons.