U-spin symmetry energy and hyperon puzzle in $\Lambda$-admixed neutron stars

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 standard I-spin counterpart for the interactions among nucleons, namely the nuclear symmetry energy $E_{\mathrm{sym}}(n_{\mathrm{b}})$, characterizes the variation of binding energy as the neutron to proton ratio in a nuclear system. We propose the U-spin symmetry energy $E_{\mathrm{U}}(n_{\mathrm{b}})$ for hyperonic matter to characterize the variation of binding energy with the inclusion of hyperons. In particular, we include $\Lambda$ hyperons in dense matter and neglect contributions from other hyperons, then constrain $E_{\mathrm{U}}(n_{\mathrm{b}})$ using nuclear physics and astrophysical observations through a Bayesian inference approach. Our results show that $E_{\mathrm{U}}(n_{\mathrm{b}})$ is much smaller than 9$E_{\mathrm{sym}}(n_{\mathrm{b}})$, indicating a substantially weaker dependence of the adopted binding energy functional on the U-spin asymmetry than on the corresponding I-spin asymmetry. Consequently, the $\Lambda$ hyperon potential increases significantly with density and becomes repulsive at higher densities, leading to more than 50\% probability for the emergence of $\Lambda$ hyperons in the posterior, which are likely to vanish again at densities $n_{\mathrm{b}}\gtrsim 5n_0$. In scenarios where $\Lambda$ hyperons do emerge, the onset density $n_{\mathrm{b}}^{\Lambda }$ typically falls in the range $2n_0$--$5n_0$, corresponding to central densities of neutron stars more massive than $1.0{\mathrm{M}}_{\odot }$.