$ΛNN$ input to neutron stars from hypernuclear data

TL;DR

The paper addresses how the Lambda-nucleon and Lambda-nucleon-nucleon interactions shape the Lambda-nucleus optical potential and its implications for neutron-star cores. It employs a density-dependent potential $V_{Lambda}(\rho)=V^{(2)}(\rho)+V^{(3)}(\rho)$, incorporating Pauli correlations and a quadratic density term, and constrains the depths $D^{(2)}_\Lambda$, $D^{(3)}_\Lambda$, and the total $D_\Lambda$ by fitting 21 Lambda single-particle binding energies, including $1d_\Lambda$ and $1f_\Lambda$ states. The extracted values at nuclear-matter density $\rho_0$ are $D^{(2)}_\Lambda=-37.5\pm0.7$ MeV, $D^{(3)}_\Lambda=+9.8\pm1.2$ MeV, and $D_\Lambda=-27.7\pm0.5$ MeV, with a notable need to suppress the $\rho^2$ term for neutron-rich cores; the sizable repulsive three-body contribution helps address the hyperon puzzle by preventing early hyperon appearance in dense matter. The results favor a consistent isospin-dependent framework and motivate forthcoming experiments (e.g., JLab E12-15-008) and EFT-based tests to further constrain hyperon interactions in dense environments.

Abstract

This work is a sequel to our two 2023 publications [PLB 837 137669, NPA 1039 122725] where fitting 14 1$s_Λ$ and 1$p_Λ$ single-particle binding energies in hypernuclei across the periodic table led to a well-defined $Λ$-nucleus optical potential. The potential consists of a Pauli modified linear-density ($ΛN$) and a quadratic-density ($ΛNN$) terms. The present work reports on extending the above analysis to 21 $Λ$ single-particle data points input by including 1$d_Λ$ and 1$f_Λ$ states in medium-weight and heavy hypernuclei. The upgraded results for the $ΛN$ and $ΛNN$ potential depths at nuclear-matter density $ρ_0=0.17$~fm$^{-3}$, $D^{(2)}_Λ=-37.5\mp 0.7$~MeV and $D^{(3)}_Λ=+9.8\pm 1.2$~MeV together with the total depth $D_Λ=-27.7\pm 0.5$~MeV, agree within errors with the earlier results. The $Λ$ hypernuclear overbinding associated with the $ΛN$-induced potential depth $D^{(2)}_Λ$ agrees quantitatively with a recent combined analysis of low-energy $Λp$ scattering data and correlation functions [PLB 850 (2024) 138550]. These results, particularly the size of the repulsive $D^{(3)}_Λ$, provide an essential input towards resolving the 'hyperon puzzle' in the core of neutron stars. We also show that a key property of our $ΛNN$-induced potential term, i.e. a need to suppress the quadratic-density $ΛNN$ term involving an excess neutron and a $N=Z$ core nucleon, can be tested in the forthcoming JLab E12-15-008 experiment.

Figures (3)

• Figure 1: $B_{\Lambda}^{1s,1p}(A)$ values across the periodic table as calculated in models X (upper) and Y (lower), compared with data points, including uncertainties. Continuous lines connect calculated values. Figure updating Fig. 3 in Ref. FGa23a. The upper part, model X, uses the full $\rho^2$ term. The lower part, model Y, replaces $\rho^2$ by a reduced form, decoupling (N$-$Z) excess neutrons from $2Z$ symmetric-core nucleons, see text. The dashed lines are for $\rho^2$ replaced by $F\rho^2$, with a suppression factor $F$ given by Eq. (\ref{['eq:F']}) below.
• Figure 2: $\chi^2$ fits to the full 1$s_\Lambda$ and $1p_\Lambda$ data (solid black lines) and when excluding $^{12}_{~\Lambda}$B and $^{13}_{~\Lambda}$C (dashed red lines). Also shown are predictions of 1$d_\Lambda$ and 1$f_\Lambda$ binding energies for the latter choice.
• Figure 3: $B_\Lambda(^{48}_{~\Lambda}{\rm K})-B_\Lambda(^{40}_{~\Lambda}{\rm K} )$ values for 1$s_{\Lambda}$ and 1$p_{\Lambda}$ states, with and without applying the suppression factor $F$, as a function of the neutron-skin of $^{48}_{~\Lambda}$K, see text.