Baryon-baryon bound states from first principles in 3+1 lattice QCD with two flavors and strong coupling

We determine baryon-baryon bound states in (3+1)-dimensional SU(3) lattice QCD with two flavors, 4×4 spin matrices, and in an imaginary time formulation. For small hopping parameter κ>0 and large glueball mass (strong coupling), we show the existence of three-quark isospin 1/2 particles (proton and neutron) and isospin 3/2 baryons (delta particles), with asymptotic masses −3lnκ and isolated dispersion curves. Baryon-baryon bound states of isospin zero are found with binding energy of order κ2, using a ladder approximation to a lattice Bethe-Salpeter equation. The dominant baryon-baryon interaction is an energy-independent spatial range-one attractive potential with an O(κ2) strength. There is also attraction arising from gauge field correlations associated with six overlapping bonds, but it is counterbalanced by Pauli repulsion to give a vanishing zero-range potential. The overall range-one potential results from a quark, antiquark exchange with no meson exchange interpretation; the repulsive or attractive nature of the interaction depends on the isospin and spin of the two-baryon state.