Baryons and low-density baryonic matter in(1+1)-dimensional large-NcQCD 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. This regime allows for a simple physical picture, which is computationally tractable. In this nonrelativistic limit, baryons are composed of ${N}_{c}$ quarks that interact, at leading order in ${N}_{c}$, through a color Coulomb potential. Using variational techniques, single baryon masses and interaction energies of low-density baryon crystal are calculated. The single baryon calculations are very accurate and can be used as a crosscheck to the general numerical approach based on Hamiltonian methods for baryons and baryonic matter in 1+1 dimension for arbitrary quark mass recently proposed by Bringoltz, which is based on a lattice in a finite box. It is noteworthy that the Bringoltz method differs from a previous approach developed by Salcedo et al. in its treatment of an effect due to the finite box size with periodic boundary conditions---namely, the existence of gauge configurations which wind around the box. As these are finite volume effects, one might expect them to be small for boxes that are large enough so that the baryon density approaches zero to high accuracy at the edges of the box. 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 approach and confirm the importance of gauge fields that wrap around for finite systems. 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 color-singlet states, with wave functions orthogonal to one another. While plausible, this assumption is somewhat 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. However, the interaction energy of low-density baryon crystals calculated with this assumption is consistent with numerical results based on Bringoltz's approach. This suggests that the assumptions regarding the color structure is justified in 1+1 dimension. This is useful, as it supports a similar assumption that was made in 3+1 dimensions, where there is no alternative means of calculation.