Low-energy scattering and effective interactions of two baryons at mπ∼450 MeV from lattice quantum chromodynamics

Abstract

The interactions between two octet baryons are studied at low energies using lattice quantum chromodynamics (LQCD) with larger-than-physical quark masses corresponding to a pion mass of ${m}_{\ensuremath{\pi}}\ensuremath{\sim}450\text{ }\text{ }\mathrm{MeV}$ and a kaon mass of ${m}_{K}\ensuremath{\sim}596\text{ }\text{ }\mathrm{MeV}$. The two-baryon systems that are analyzed range from strangeness $S=0$ to $S=\ensuremath{-}4$ and include the spin-singlet and triplet $NN$, $\mathrm{\ensuremath{\Sigma}}N$ ($I=3/2$), and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}$ states, the spin-singlet $\mathrm{\ensuremath{\Sigma}}\mathrm{\ensuremath{\Sigma}}$ ($I=2$) and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Sigma}}$ ($I=3/2$) states, and the spin-triplet $\mathrm{\ensuremath{\Xi}}N$ ($I=0$) state. The corresponding $s$-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable are extracted using L\"uscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet $\mathrm{\ensuremath{\Sigma}}N$ and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}$ channels are found to be repulsive and do not support bound states. Using results from previous studies of these systems at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with available experimental values and phenomenological predictions. The low-energy coefficients in pionless effective field theory (EFT) relevant for two-baryon interactions, including those responsible for $SU(3)$ flavor-symmetry breaking, are constrained. The $SU(3)$ flavor symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the $SU(6)$ spin-flavor symmetry, predicted at large ${N}_{c}$. A remnant of an accidental $SU(16)$ symmetry found previously at a larger pion mass is further observed. The $SU(6)$-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading $SU(3)$ flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD.