Baryon-baryon bound state in a 2+1 lattice QCD model with two flavors and strong coupling

Abstract

We consider baryon-baryon bound states in $\mathrm{S}\mathrm{U}(3)$ lattice QCD with two flavors, $2\ifmmode\times\else\texttimes\fi{}2$ spin matrices in $2+1$ dimensions, and in an imaginary time formulation. For small hopping parameter $0<\ensuremath{\kappa}\ensuremath{\ll}1$ and large glueball mass, we show the existence of an isospin $3/2$ baryon, with asymptotic mass $\ensuremath{-}3\mathrm{ln}\ensuremath{\kappa}$ and isolated dispersion curve. Baryon-baryon bound states of isospin zero and one are found with approximate binding energy ${\ensuremath{\kappa}}^{2}/8$ and ${\ensuremath{\kappa}}^{2}/24$, respectively, using a ladder approximation to a Bethe-Salpeter equation. The baryon-baryon interaction associated with the ladder approximation is an energy independent spatial range-one attractive potential with an $\mathcal{O}({\ensuremath{\kappa}}^{2})$ strength. The attractive potential does not have a meson exchange interpretation. Six-point gauge field correlations give rise to attraction and counterbalance the Pauli repulsion to give a vanishing zero-range potential. The overall range-one potential results from a complicated interaction between the isospin components of the constituent quarks of the baryons.