Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors.

We consider a lattice SU(3) QCD model in 2 + 1 dimensions, with two flavors and 2 ? 2 spin matrices. An imaginary time functional integral formulation with Wilson?s action is used in the strong coupling regime, i.e. small hopping parameter 0 < ? 1, and much smaller plaquette coupling ?, 0 < ? ?. In this regime, it is known that the low-lying energy-momentum spectrum contains isolated dispersion curves identified with baryons and mesons with asymptotic masses m ? ?3 ln ? and mm ? ?2 ln ?, respectively. We prove the existence of two (labelled by ?) two-baryon bound states for each of the total isospin sectors I = 0, 1 and we obtain, in each case, the exact binding energies I ? (of order ?2) which extend to jointly analytic function in ? and ?.We also prove that these points are the only mass spectrum up to slightly above the bound state masses. Precisely, we show, for ?0 = 1 4, ?1 = 1 12, ?2 = 1 2, ?3 = 34 and small ? > 0, that the bound state masses 2m ? I ? are the only points in the mass spectrum in (0, 2m ? I ? + ??I ?2), for I = 0, 1, and in (0, 2m ? (1 + ?)?I ?2), for I = 2, 3. These results are exact and validate our previous results obtained in a ladder approximation. The method employs suitable two- and four-point correlations with spectral representations and a lattice Bethe-Salpeter equation. For I = 0, 1, a quark, antiquark space-range one potential of order ?2 is found to be the dominant contribution to the two-baryon interaction and the interaction of the individual quark isospins of one baryon with those of the other is described by permanents. A novel spectral free decomposition (but spectral representation motivated, for real ? and ?) of the two-point correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy