Baryons and Low-Density Baryonic Matter in 1+1 Dimensional Large N_c QCD with Heavy Quarks

Abstract

This paper studies baryons and baryonic matter in the combined large N_c and heavy quark mass limits of QCD in 1+1 dimension. In this non-relativistic limit, baryons are composed of N_c quarks that interact, at leading order in N_c, through a color Coulomb potential. Using variational techniques, very accurate calculations of single baryon masses and interaction energies of low-density baryon crystal are performed. These results are used to cross-check a general numerical approach applicable for arbitrary quark masses and baryon densities recently proposed by Bringoltz, which is based on a lattice in a finite box with periodic boundary conditions. The Bringoltz method differs from a previous approach of Salcedo, et al. in its treatment of a finite box effect - namely gauge configurations that wind around the box. One might expect these effects to be small for large enough boxes, in which the baryon density approaches zero to high accuracy at the edges. However, the effects of these windings appear to be quite large even in such boxes. The large mass infinite volume calculations performed here are consistent with the results of numerical calculations using the Bringoltz method. The calculation of the baryon crystal interaction energy requires the assumption that at low-densities the ground state is composed of individual baryons, each in a color-singlet state and orthogonal to each other. This assumption is plausible but ad hoc in that one can construct configurations in which the entire state is color-singlet but cannot be broken into individual color-singlet baryons. The interaction energy of low-density baryon crystals calculated with the assumption is consistent with numerical results based on Bringoltz's approach suggesting that the assumption is justified. This further supports a similar assumption that was made in 3+1 dimensions, where no alternative means of calculation exist.