Baryon-baryon interactions and spin-flavor symmetry from lattice quantum chromodynamics

Lattice quantum chromodynamics is used to constrain the interactions of two octet baryons at the $SU(3)$ flavor-symmetric point, with quark masses that are heavier than those in nature (equal to that of the physical strange quark mass and corresponding to a pion mass of ≈806 MeV). Specifically, the S-wave scattering phase shifts of two-baryon systems at low energies are obtained with the application of L\"uscher's formalism, mapping the energy eigenvalues of two interacting baryons in a finite volume to the two-particle scattering amplitudes below the relevant inelastic thresholds. The leading-order low-energy scattering parameters in the two-nucleon systems that were previously obtained at these quark masses are determined with a refined analysis, and the scattering parameters in two other channels containing the Σ and Ξ baryons are constrained for the first time. It is found that the values of these parameters are consistent with an approximate $SU(6)$ spin-flavor symmetry in the nuclear and hypernuclear forces that is predicted in the large-Nc limit of QCD. The two distinct $SU(6)$-invariant interactions between two baryons are constrained for the first time at this value of the quark masses, and their values indicate an approximate accidental $SU(16)$ symmetry. The $SU(3)$ irreps containing the NN(¹S₀), NN(³S₁) and 1√2(Ξ⁰n+Ξ^-p)(³S₁) channels unambiguously exhibit a single bound state, while the irrep containing the Σ⁺p(³S₁) channel exhibits a state that is consistent with either a bound state or a scattering state close to threshold. These results are in agreement with the previous conclusions of the NPLQCD collaboration regarding the existence of two-nucleon bound states at this value of the quark masses.