In-medium hyperon potentials and the quarkyonic hyperon onset: charged $\Sigma$'s in $\beta$-equilibrium and the neutrino connection

Abstract

Quarkyonic matter resolves the neutron-star hyperon puzzle statistically: neutrons fill low-momentum $d$-quark phase space, shifting the $S=-1$ threshold from $\text{muB}=M_Y$ to $2M_Y-M_N$ and suppressing residual softening by $1/{\text{Nc}}^3$ in the Fujimoto--Kojo--McLerran (FKM) mechanism. We dress FKM's IdylliQ model with in-medium potentials, constrained by hypernuclear data and neutrino-induced hyperon FSI, and find: (i) the dressed onset, ${\text{muB}}^{\mathrm{onset}}=(2M_Y-M_N)+2U_Y-\text{UN}$, carries $U_Y$ at weight 2, with $d{n}_{\mathrm{onset}}/d{U}_Y\simeq 0.3\text{nz}$ per $10\text{MeV}$, twice the leverage. (ii) A self-consistent neutron potential enters at weight $-2$, so protection needs $\text{UN}(n_{\mathrm{onset}})\lesssim +96\text{MeV}$. (iii) With leptons in $\beta$ equilibrium, the ${\Sigma }^{-}$ ($dds$) onset becomes $\text{mue}\ge 258\text{MeV}+\text{US}-\text{UN}$, never reached inside a $2\text{Msun}$ core: ${\Sigma }^{-}$ switches from first hyperon to forbidden and the $\Sigma$ ordering inverts. (iv) The $\text{kY}\ge \text{kbu}$ continuation gives TOV softening below $0.05\text{Msun}$ in the FKM ansatz family and below $0.025\text{Msun}$ for the realistic interacting star, $4$--$8$ below hadronic models. In the family this is a ceiling; generally it is a floor, since hyperons above $\text{kbu}$ are omitted. (v) In an interacting low-density sector calibrated to $\text{Mmax}=2.12\text{Msun}$, core strangeness is controlled by $(\text{UL}(\text{nz}),c_{\Lambda })$: at $\text{UL}(\text{nz})=-28\text{MeV}$, the maximum-mass star is hyperon-free once the supra-saturation $YNN$ turn-over exceeds a few-MeV threshold $c_{\Lambda }^{\ast }$. Projected SBND+DUNE FSI precision pins $\text{UL}(\text{nz})$ but leaves $c_{\Lambda }$ -- to which neutrino data are blind -- decisive: with the heavy-ion prior, $P(\mathrm{hyperon}\text{mbox}-\mathrm{free}\mathrm{core})=0.90$, versus $0.89$ from priors alone, prior-dominated rather than measured. The sharpest observable is differential: $d\text{Mmax}/d{U}_Y$ is an order of magnitude smaller than in mean-field models, discriminating the two resolutions.

Comments: 9 pages, 6 figures