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Baryon and Pseudoscalar Meson Octets within a Unified broken SU(6) symmetry

Luiz L. Lopes

TL;DR

The paper develops a unified broken $\mathrm{SU}(6)$ framework to fix vector-meson couplings for both baryon and pseudoscalar octets in dense neutron-star matter. By combining $\mathrm{SU}(3)$ flavor symmetry with $G$-Parity, it reduces the vector-coupling freedom to a single parameter $\alpha_V$, recovering expected kaon/antikaon interactions and the naive quark-isospin counting in the $\mathrm{SU}(6)$ limit. Numerical results show anti-kaon condensation softens the equation of state and competes with hyperon degrees of freedom, with the degree of stiffening or softening depending on $\alpha_V$; the neutron-star maximum mass is modestly affected but remains within observational bounds for several parameter choices. The approach provides a symmetry-based, parameter-constrained description of hadronic couplings relevant to hyperons and (anti)kaon condensation in dense matter, with implications for the composition and structure of neutron stars and potential experimental constraints on kaon potentials.

Abstract

In this work, I discuss neutron stars with hyperons and anti-kaon condensate. To fix their coupling constants with the vector mesons of the Quantum Hadrodynamics, I use a unified scheme imposing that the Yukawa coupling is an invariant under SU(3) and SU(6) groups. Combining with the G-Parity, I show that some expected results of the kaon and anti-kaon interaction with the nucleus are re-obtained. In the same sense, the naive quark-isospin counting rule is restored in the SU(6) limit. Furthermore, the G-Parity combined with the SU(3) gives us a clear picture of the role played by each meson in the kaon condensation. Numerical results show that the presence of anti-kaons severely compromises the stiffening of the EOS by breaking the SU(6) symmetry.

Baryon and Pseudoscalar Meson Octets within a Unified broken SU(6) symmetry

TL;DR

The paper develops a unified broken framework to fix vector-meson couplings for both baryon and pseudoscalar octets in dense neutron-star matter. By combining flavor symmetry with -Parity, it reduces the vector-coupling freedom to a single parameter , recovering expected kaon/antikaon interactions and the naive quark-isospin counting in the limit. Numerical results show anti-kaon condensation softens the equation of state and competes with hyperon degrees of freedom, with the degree of stiffening or softening depending on ; the neutron-star maximum mass is modestly affected but remains within observational bounds for several parameter choices. The approach provides a symmetry-based, parameter-constrained description of hadronic couplings relevant to hyperons and (anti)kaon condensation in dense matter, with implications for the composition and structure of neutron stars and potential experimental constraints on kaon potentials.

Abstract

In this work, I discuss neutron stars with hyperons and anti-kaon condensate. To fix their coupling constants with the vector mesons of the Quantum Hadrodynamics, I use a unified scheme imposing that the Yukawa coupling is an invariant under SU(3) and SU(6) groups. Combining with the G-Parity, I show that some expected results of the kaon and anti-kaon interaction with the nucleus are re-obtained. In the same sense, the naive quark-isospin counting rule is restored in the SU(6) limit. Furthermore, the G-Parity combined with the SU(3) gives us a clear picture of the role played by each meson in the kaon condensation. Numerical results show that the presence of anti-kaons severely compromises the stiffening of the EOS by breaking the SU(6) symmetry.

Paper Structure

This paper contains 7 sections, 49 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Formalism
  3. SU(3) and SU(6) symmetry groups for the hyperons-vector mesons coupling constants
  4. SU(3) and SU(6) symmetry groups for the pseudoscalar-vector meson couplings
  5. Numerical Results
  6. Additional Constraints
  7. Final Remarks

Figures (2)

  • Figure 1: Particle population for different values of $\alpha_V$ considering nucleons and anti-kaons (left) and nucleons, anti-kaons, and hyperons (right).
  • Figure 2: EOSs (top), adiabatic index (middle), and TOV solutions (bottom) within different values of $\alpha_V$. Figures on the left represent nucleons+anti-kaons matter, while figures on the right means nucleons+hyperons+anti-kaons.