U-spin symmetry energy and hyperon puzzle

TL;DR

This work introduces the U-spin symmetry energy $E_\mathrm{U}(n_\mathrm{b})$ as an analogue to the nuclear symmetry energy $E_\mathrm{sym}(n_\mathrm{b})$ to characterize how hyperons affect binding in dense matter, focusing on the lightest hyperon, the $\Lambda$. Using a polytropic EOS framework and Bayesian inference that combines nuclear data (HICs and $\chi$EFT) with astrophysical NS observations (masses and radii), the authors constrain four key parameters and derived quantities. They find $E_\mathrm{U}(n_\mathrm{b})$ is markedly smaller than $9E_\mathrm{sym}(n_\mathrm{b})$, indicating much weaker $N$-$\Lambda$ attraction and driving the $\Lambda$ potential to become repulsive at high density; as a result, the emergence of $\Lambda$ hyperons in neutron stars is suppressed in most cases ( probability $>80\%$ of no appearance ), with onset densities $n_\mathrm{b}^\Lambda \gtrsim 0.8\ \mathrm{fm}^{-3}$ and corresponding NS masses typically $M\gtrsim 1.7\ M_\odot$. The constrained EOSs satisfy causality and require no hyperon cores in most observed NSs, offering a coherent resolution to the Hyperon Puzzle within the current data framework. Future extensions could incorporate more extensive hyperon sectors and refined EOS parametrizations.

Abstract

By combining the (u,d) I-spin doublets or (d,s) U-spin doublets, the SU(3) flavor symmetry of light quarks can be decomposed into SU(2)$_I\times$U(1)$_Y$ or SU(2)$_U\times$U(1)$_Q$ subgroups, which have been widely adopted to categorize hadrons and their decay properties. The I-spin counterpart for the interactions among nucleons has been extensively investigated, i.e., the nuclear symmetry energy $E_\mathrm{sym}(n_\mathrm{b})$, which characterizes the variation of binding energy as the neutron to proton ratio in a nuclear system. In this work, we propose U-spin symmetry energy $E_\mathrm{U}(n_\mathrm{b})$ for hyperonic matter to characterize the variation of the binding energy with the inclusion of hyperons. In particular, being the lightest hyperon, $Λ$ hyperons are included in dense matter, where the U-spin symmetry energy $E_\mathrm{U}(n_\mathrm{b})$ is fixed according to state-of-the-art constraints from nuclear physics and astrophysical observations using Bayesian inference approach. It is found that $E_\mathrm{U}(n_\mathrm{b})$ is much smaller than that of $E_\mathrm{sym}(n_\mathrm{b})$, indicating much stronger proton-neutron attraction than that of nucleon-hyperon pairs. Consequently, $Λ$ hyperon potential increases significantly and becomes repulsive at large density, where there is more than 80\% probability that $Λ$ hyperons do not emerge in neutron stars. For those undergoing emergence within neutron stars, the onset density of $Λ$ hyperons $n_\mathrm{b}^Λ$ is typically larger than $\sim$0.8 fm$^{-3}$, corresponding to neutron stars more massive than 1.7 $M_\odot$.

Figures (7)

• Figure 1: Posterior probability distribution functions of the saturation properties (in MeV) and onset densities $n_\mathrm{b}^\Lambda$ (in fm$^{-3}$) of $\Lambda$ hyperons in neutron stars as well as their correlations inferred from the Bayesian analysis of both nuclear and astrophysical constraints listed in Table \ref{['Tab:HIC']} and Table \ref{['Tab:data_astro']} employing Prior 1 as indicated in Table \ref{['Tab:prior']}. The red (yellow) curves indicate the 68% (90%) credible regions, while there is only 17.12% probability that $\Lambda$ hyperons emerge within the density range shown here.
• Figure 2: Same as Fig. \ref{['Fig:para1']} but adopting Prior 2 with only 15.68% probability that $\Lambda$ hyperons emerge within the density range.
• Figure 3: Mass-radius relations of neutron stars predicted adopting the parameters corresponding to those indicated in Fig. \ref{['Fig:para1']} (upper panel) and Fig. \ref{['Fig:para2']} (lower panel) employing Prior 1 and Prior 2. The posterior 68% (red) and 90% (yellow) credible regions of neutron star masses and radii in the Bayesian analysis are presented as well. The red solid circles indicate the critical neutron stars with the emergence of $\Lambda$ hyperons at their centers, while the grey curves indicate the acausal region with $c_s>1$ in the center.
• Figure 4: Left: Energy per baryon $\varepsilon/n_{\rm{b}}$, pressure $P$, and speed of sound $c_s$ of neutron star matter; Right: The corresponding I-spin and U-spin asymmetry parameters $\delta$ and $\delta_\mathrm{U}$, where the direct Urca processes take place once $\delta<0.704$ if $\delta_\mathrm{U}=1$. The results presented here are inferred from the Bayesian analysis employing Prior 1.
• Figure 5: Constrained $E_{0}(n_\mathrm{b})$, $E_\mathrm{sym}(n_\mathrm{b})$, and $E_\mathrm{U}(n_\mathrm{b})$ for Eq. \ref{['Eq:Et']} employing Prior 1, where the red (yellow) curves indicate the 68% (90%) credible regions.