Properties of hyperons in nuclear matter from chiral hyperon-nucleon interactions at next-to-next-to-leading order

TL;DR

This work analyzes the in-medium properties of $Λ$ and $Σ$ hyperons in infinite nuclear matter using semilocal momentum-space regularized (SMS) hyperon-nucleon interactions up to $N^2LO$ in chiral EFT, paired with a consistent SMS nucleon-nucleon force, within Brueckner-Hartree-Fock theory with continuous choice. It provides a first systematic uncertainty estimate for the hyperon single-particle potentials via chiral truncation (EKM) and examines convergence and regulator dependence across orders. The main findings are that $U_{Λ}(k=0)$ at saturation density is in the $-41$ to $-46$ MeV range for $N^2LO$ and similar to $NLO$ results, while $U_{Σ}(k=0)$ is more attractive with SMS due to updated $ ext{Σ}N$ constraints, though sensitive to isospin channels; the study also finds notable differences from older $NLO13/NLO19$ results driven by the $I=3/2$ sector. The authors highlight the need to include leading three-body forces ($YNN$) for a fully converged description and discuss plans to extend to higher densities and refine the $P$- and $D$-wave sectors with additional data and higher-order EFT.

Abstract

The $Λ$ and $Σ$ single-particle potentials in infinite nuclear matter are analyzed within a recently established chiral hyperon-nucleon ($YN$) interaction up to N$^2$LO in combination with an nucleon-nucleon interaction derived in the same scheme. The self-consistent Brueckner-Hartree-Fock method with the continuous choice of the single-particle potential is employed. It is found that the $Λ$ single-particle potential is comparable to the results achieved with the NLO $YN$ interaction from 2019. The resulting $Σ$ potential becomes more attractive compared to the previous NLO results due to the constraint from the recent $ΣN$ differential cross section data measured in the J-PARC E40 experiment. An estimate of the theoretical uncertainty of the single-particle potentials is provided in terms of the truncation error in the chiral expansion.

Figures (14)

• Figure 1: Diagrams contributing to the $YN$ potential at LO (top), NLO (center), and N$^2$LO (bottom) in chiral EFT. Solid and dashed lines denote octet baryons and pseudoscalar mesons, respectively.
• Figure 2: Nucleon single-particle potentials in symmetric nuclear matter (top) and pure neutron matter (bottom) at $\rho_0$. N$^3$LO(450) and N$^3$LO(500) refer to the N$^3$LO NN potential by Entem and Machleidt Entem:2003ft with corresponding cutoff, while the SMS N$^4$LO$^+$ potential is by Reinert et al.Reinert:2017usi.
• Figure 3: Total energy per particle in both symmetric nuclear matter and pure neutron matter. Results are shown for the N$^3$LO Entem:2003ft and SMS N$^4$LO$^+$Reinert:2017usi$NN$ potentials. The empirical value at the nuclear matter saturation point, $E/A=-16$ MeV, is indicated by a circle.
• Figure 4: Momentum dependence of the ${\Lambda}$ single-particle potentials in symmetric nuclear matter at $\rho_0$.
• Figure 5: Momentum dependence of $U_{\Lambda}$ in symmetric nuclear matter for $\rho/\rho_0=(0.5,1.0,2.0)$, corresponding to the Fermi momenta $k_F=(1.07,1.35,1.7)~{\rm fm}^{-1}$. The SMS N$^2$LO(500) $YN$ potential is employed.