科研之友
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摘要
We consider a lattice SU(3) QCD model in 2 + 1 dimensions, with two flavors and 2 x 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 , and much smaller plaquette coupling . 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 and , 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 (of order ) which extend to jointly analytic function in and beta. We also prove that these points are the only mass spectrum up to slightly above the bound state masses. Precisely, we show, for and small , that the bound state masses are the only points in the mass spectrum in , for I = 0,1, and in , 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 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 kappa and beta) of the two-point correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy.
- 出版日期2013-7
