Kaon-meson coupling from SU(3) flavour symmetry and application to antikaon condensed dense matter in neutron star

TL;DR

The work presents the first application of SU(3) flavour symmetry to determine antikaon couplings to vector mesons in dense neutron-star matter, using two parameter-tracking schemes and a fixed antikaon potential depth of $U_{ar{K}}=-130$ MeV within a DDRH/RMF framework based on DDME2. By deriving kaon–vector couplings from SU(3) and enforcing ideal mixing, it demonstrates that larger SU(3) parameters $\alpha_m$ and $ obreak ext{ }z_m$ yield a progressively stiffer EOS, delay the onset of $K^-$ condensation, and raise the maximum neutron-star mass, bringing many configurations into agreement with observed massive pulsars. The results indicate a second-order phase transition to antikaon-condensed matter, with $ar{K}^0$ condensation typically absent, and underscore the sensitivity of neutron-star core composition and structure to the underlying flavour-symmetry structure of hadron interactions. Overall, the SU(3)-based couplings constrain the dense-matter EOS and have important implications for the mass-radius relation and the presence of strange degrees of freedom in neutron stars.

Abstract

Observations of massive pulsars suggest that the central density of neutron stars can exceed several times the nuclear saturation density, creating a favourable environment for the appearance of exotic states, such as strange and non-strange baryons, meson condensates, and deconfined quark matter. The antikaon condensate is the most studied and plausible candidate among meson condensates. However, little is known about the exact interaction mechanisms between antikaons and mediator mesons. In this work, we investigate these interactions by, for the first time, employing SU(3) flavor symmetry to study antikaon condensation in dense matter. We determine hadron couplings in the mesonic sector using SU(3) flavour symmetry. Among the three key parameters we calculate $θ_v$, the mixing angle between the octet meson $ω_8$ and the singlet meson $φ_1$; the ratio of the octet to singlet couplings $z$; and leave the weight factor that balances the symmetric and antisymmetric couplings $α_v$ as a free parameter to explore its impact on the system. Using this approach, we derive the couplings for antikaon interactions with both singlet and octet mesons in the nonet vector meson family and examine the corresponding implications for dense matter featuring antikaon condensation. Our findings reveal that the equation of state for dense matter becomes progressively stiffer with increasing values of $α_v$, which delays the onset of antikaon condensation and increases the maximum achievable mass of neutron stars.

Figures (4)

• Figure 1: Color online: The variation of particle fractions $x_i$ with the normalized baryon number density in NK matter for $U_{\bar{K}} = -130$ MeV. Left panels: for different $\alpha_m$. The upper panel corresponds to $\alpha_b = \alpha_m$, the middle panel to $\alpha_b = 2\alpha_m$, and the lower panel to $\alpha_b = \alpha_m/2$. Right panels: for different $z_m$. The upper panel shows the case $z_b = z_m$, the middle panel $z_b = 2z_m$, and the lower panel $z_b = z_m/2$. The solid lines and the dashed lines are for $\alpha_m,z_m = 0.2$ and $0.4$, respectively. The vertical lines denote the central matter densities corresponding to the maximum mass NS configuration for the respective EOS models.
• Figure 2: Color online: The variation of particle fractions $x_i$ with normalised baryon number density in NK matter for the case of QMIC case for $U_{\bar{K}}=-130$ MeV. The vertical line denotes the same fact as in Fig. \ref{['fig:abundances']}.
• Figure 3: Color online: The variation of pressure with energy density in NK matter for $U_{\bar{K}} = -130$ MeV. Left panels: for different $\alpha_m$. The upper panel corresponds to $\alpha_b = \alpha_m$, the middle panel to $\alpha_b = 2\alpha_m$, and the lower panel to $\alpha_b = \alpha_m/2$. Right panels: for different $z_m$. The upper panel shows the case $z_b = z_m$, the middle panel $z_b = 2z_m$, and the lower panel $z_b = z_m/2$. The solid line represents $\alpha_m, z_m = 0.2$, the dashed line represents $\alpha_m, z_m = 0.4$, dotted and double-dashed lines represent QMIC and the case of pure nucleonic matter, respectively.
• Figure 4: Color online: The variation of mass with radius in NK matter for $U_{\bar{K}} = -130$ MeV. The observed mass included in the figure is of PSR J0952-607 (M = 2.35 ± 0.17$M_\odot$ ) 2022ApJ...934L..17R. Left panels: for different $\alpha_m$. The upper panel corresponds to $\alpha_b = \alpha_m$, the middle panel to $\alpha_b = 2\alpha_m$, and the lower panel to $\alpha_b = \alpha_m/2$. Right panels: for different $z_m$. The upper panel shows the case $z_b = z_m$, the middle panel $z_b = 2z_m$, and the lower panel $z_b = z_m/2$. The solid line represents $\alpha_m, z_m = 0.2$, the dashed line represents $\alpha_m, z_m = 0.4$, thick solid black, and the double-dashed lines represent QMIC and the case of pure nucleonic matter, respectively.