Hyperon single-particle potentials in nuclear matter based on baryon-baryon interactions derived within chiral effective field theory

TL;DR

The study investigates hyperon single-particle potentials in nuclear matter using chiral effective field theory–based YN interactions up to N$^2$LO with semi-local SMS regularization, constrained by J-PARC E40 data. Employing a self-consistent Brueckner-Hartree-Fock approach with continuous single-particle potentials, it extracts $U_ extGamma$ for $ extLambda$ and $ extSigma$ in symmetric and neutron-rich matter, and provides a systematic uncertainty estimate via the EKM truncation scheme. The results indicate $U_ extLambda( ho_0)$ is broadly attractive and slightly more so than some quasi-empirical values, while $U_ extSigma$ is weakly attractive at $ ho_0$ for most NLO/N$^2$LO interactions, with LO predicting repulsion; the behavior in dense matter is sensitive to channel couplings, especially in the $I=3/2$ sector constrained by E40 data. A caveat is that full N$^2$LO accuracy requires including $YNN$ three-body forces, motivating future work on either explicit three-body calculations or density-dependent two-body reductions to achieve a consistent description relevant for neutron-star EoS.

Abstract

An analysis of the Lambda and Sigma single-particle potentials is presented, based on YN interactions derived within chiral effective field theory up to next-to-next-to-leading order (N$^2$LO). The self-consistent Brueckner-Hartree-Fock framework is employed within the continuous choice for the single-particle potential. The result for the Lambda single-particle potential is comparable to the ones obtained with previous chiral YN interactions up to next-to-leading order (NLO). The Sigma single-particle potential is found weakly attractive, in contrast to earlier weakly repulsive results, reflecting new constraints from the recent J-PARC E40 data on $Σ^+p$ scattering. An estimate of the theoretical uncertainty of the single-particle potentials is provided.

Figures (4)

• Figure 1: Density dependence of the $\Lambda$ single-particle potential in symmetric nuclear matter. The bar symbolizes the quasi-empirical value Gal:2016boi.
• Figure 2: ${\Sigma}^+p$ scattering results Haidenbauer:2023qhf. Left: $^3S_1$ phase shift. Center: Differential cross section at $500$ MeV/c. Right: Integrated ${\Sigma}^+p$ cross section. Solid, dashed, and dash-dotted lines are the results for the SMS N$^2$LO(550)$^a$, N$^2$LO(550)$^b$, and NLO(550) potentials, respectively. The band represents the results of the NLO19 potential from Ref. Haidenbauer:2019boi. The E40 data J-PARCE40:2022nvq are indicated by filled circles.
• Figure 3: Density dependence of the $\Sigma$ single-particle potential in symmetric nuclear matter. The bar indicates results from phenomenological analyses Gal:2016boi.
• Figure 4: Uncertainty estimate of the $\Lambda$ and $\Sigma$ single-particle potentials in symmetric nuclear matter and of the $\Sigma^-$ single-particle potential in pure neutron matter, from left to right. The SMS NLO and N$^2$LO$^b$ interactions with cutoff $550$ MeV are employed, while for SMS LO the potential with $700$ MeV cutoff is used. The bars symbolize the values from Ref. Gal:2016boi.