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

Abstract

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 < κ 1, and much smaller plaquette coupling β, 0 < β κ. 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 κ and mm ≈ −2 ln κ, 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 κ2) which extend to jointly analytic function in κ and β.We also prove that these points are the only mass spectrum up to slightly above the bound state masses. Precisely, we show, for α0 = 1 4, α1 = 1 12, α2 = 1 2, α3 = 34 and small δ > 0, that the bound state masses 2m − I ± are the only points in the mass spectrum in (0, 2m − I ± + δαI κ2), for I = 0, 1, and in (0, 2m − (1 + δ)αI κ2), 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 κ2 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 κ and β) of the two-point correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy.