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

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.

💡 Research Summary

In this work the authors investigate the single‑particle potentials of Λ and Σ hyperons in nuclear matter using hyperon‑nucleon (YN) interactions derived from chiral effective field theory (χEFT) up to next‑to‑next‑to‑leading order (N²LO). The YN potentials are constructed in the semi‑local momentum‑space (SMS) regularization scheme with several cutoff values (500, 550, 600 MeV) and are combined with nucleon‑nucleon forces also generated in the SMS framework. The many‑body problem is solved within the Brueckner‑Hartree‑Fock (BHF) approach, employing the continuous choice for the auxiliary single‑particle potential, which ensures self‑consistency of the G‑matrix.

At nuclear saturation density (ρ₀, corresponding to k_F = 1.35 fm⁻¹) the Λ potential U_Λ(k = 0) obtained with the SMS N²LO interactions lies between –41 and –46 MeV, while the NLO interactions give values between –34 and –39 MeV. These numbers are more attractive than the quasi‑empirical value extracted from hypernuclear data (≈ –30 MeV). The authors explain that the stronger attraction at higher chiral order originates from an enhanced ΛN–ΣN transition potential, which deepens the Λ binding in the medium. However, the N²LO calculation does not yet include explicit hyperon‑nucleon‑nucleon (YNN) three‑body forces, which first appear at this order. Consequently, the theoretical uncertainty estimated via the EKM (Epelbaum‑Krebs‑Meißner) truncation‑error method remains sizable, and the N²LO result is not fully compatible with the empirical value.

For the Σ hyperon the situation is markedly different. Earlier chiral YN models (e.g., NLO13 and NLO19) predicted a repulsive Σ potential (U_Σ ≈ +10 MeV) because the I = 3/2 ³S₁–³D₁ channel was strongly repulsive. Recent J‑PARC E40 measurements of Σ⁺p scattering impose tighter constraints on this channel. By refitting the SMS YN interactions to these data, the authors obtain Σ potentials that are weakly attractive at ρ₀ (U_Σ ranging from +10 to +30 MeV depending on the cutoff). A partial‑wave decomposition shows that the reduction of the repulsive contribution from the I = 3/2 ³S₁–³D₁ wave is the main driver of this change. The density dependence of U_Σ is also presented: for most SMS NLO and N²LO interactions the potential remains attractive up to about 1.5 ρ₀, turning repulsive only for the 500 MeV cutoff at higher densities. In pure neutron matter the Σ⁻ potential is predicted to be repulsive (≈ +9 MeV at ρ₀), reflecting the larger Fermi momentum in that environment.

The authors quantify theoretical uncertainties using the EKM prescription, which combines the expected chiral expansion parameter Q (taken as p/Λ_b with p≈k_F) and the observed differences between successive orders. For Λ, the LO and NLO bands (± 7 MeV) comfortably encompass the empirical value, while the N²LO band (± 4 MeV) is narrower but still does not overlap the empirical –30 MeV because three‑body forces are omitted. For Σ, the uncertainty bands are smaller because the NLO and N²LO results are already close to each other; nevertheless, the attractive nature up to 1.5 ρ₀ is robust within the estimated errors. The uncertainty grows rapidly with density, especially in pure neutron matter where the Fermi momentum is larger.

In the concluding discussion the authors stress that a complete N²LO calculation must incorporate YNN three‑body forces, which can be generated either by solving the Bethe‑Faddeev equations or by employing density‑dependent effective two‑body interactions derived from integrating out the third nucleon. They caution against the on‑shell approximation previously used in hypernuclear few‑body studies and advocate for more consistent treatments. The present results, especially the revised Σ attraction informed by J‑PARC data, have important implications for the equation of state of dense matter and for the possible appearance of hyperons in neutron stars.

Overall, the paper delivers a systematic χEFT‑based analysis of hyperon single‑particle potentials, demonstrates the impact of recent scattering data on the Σ sector, provides a quantitative error budget, and outlines the next steps required—most notably the inclusion of YNN three‑body forces—to achieve reliable predictions for astrophysical applications.