U-spin symmetry energy and hyperon puzzle

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 binding energy with the inclusion of hyperons. In particular, being the lightest hyperon, $\Lambda$ 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, the $\Lambda$ hyperon potential increases significantly with density and becomes repulsive at high densities. The results indicate that there is more than 50\% probability for the emergence of $\Lambda$ hyperons in posterior EOSs, which are likely to vanish at densities $n_\mathrm{b} \gtrsim 5\,n_0$. In scenarios where $\Lambda$ hyperons do emerge, the onset density $n_{\mathrm{b}}^\Lambda$ is typically within the range of $2\,n_0$--$5\,n_0$, corresponding to neutron stars more massive than $1.0\,\rm{M_\odot}$.