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

Abstract

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 Lüscher’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-N[subscript c] 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([superscript 1]S[subscript 0]), NN([superscript 3]S[subscript 1]) and 1/√2](Ξ[superscript 0]n+Ξ[superscript -]p)([superscript 3]S[subscript 1]) channels unambiguously exhibit a single bound state, while the irrep containing the Σ[superscript +]p([superscript 3]S[subscript 1]) 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.