Existence of diproton-like particles in 3 þ 1 lattice QCD with two flavors and strong coupling.

Abstract

Starting from quarks, gluons, and their dynamics, we consider the existence of two-baryon bound states of total isospin I ¼ 1 in an imaginary-time formulation of a strongly coupled 3 þ 1-dimensional SUð3Þc lattice QCD with two flavors and 4 4 spin matrices, defined using the Wilson action. For a small hopping parameter >0 and a much smaller gauge coupling 0< 1 (heavy quarks and large glueball mass), using a ladder approximation to a lattice Bethe-Salpeter equation, diproton-like bound states are found in the I ¼ 1 isospin sector, with asymptotic masses 6 ln and binding energies of order 2. By isospin symmetry, for each diproton there is also a dineutron bound state with the same mass and binding energy. The dominant two-baryon interaction is an energy-independent spatial range-one potential with an Oð 2Þ strength. There is also an attraction arising from gauge field correlations associated with six overlapping bonds, but it is subdominant. The overall range-one potential results from a quark-antiquark exchange with no meson exchange interpretation (wrong spin indices). The repulsive or attractive nature of the interaction does depend on the isospin and spin of the two-baryon states. A novel representation in term of permanents is obtained for the spin, isospin interaction between the baryons, which is valid for any isospin sector.