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 $\approx 806\mathtt{MeV}$). 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 values of the leading-order low-energy scattering parameters in the irreducible representations of SU(3) are consistent with an approximate SU(6) spin-flavor symmetry in the nuclear and hypernuclear forces that is predicted in the large-$N_c$ limit of QCD. The two distinct SU(6)-invariant interactions between two baryons are constrained at this value of the quark masses, and their values indicate an approximate accidental SU(16) symmetry. The SU(3) irreducible representations containing the $NN({}^1{S}_0)$, $NN({}^3{S}_1)$ and $\frac{1}{\sqrt{2}}({\Xi }^{0}n+{\Xi }^{-}p)({}^3{S}_1)$ channels unambiguously exhibit a single bound state, while the irreducible representation containing the ${\Sigma }^{+}p({}^3{S}_1)$ 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.

Comments: 49 pages, 21 figures, 14 tables. v2: Minor wording improvements and updated references