Properties of Baryons Containing a Heavy Quark in the Skyrme Model

Abstract

The properties of baryons containing one heavy quark are studied in the Skyrme model, where they are treated as bound states of a heavy meson with an $SU(2)$ chiral soliton. In the large $N_c$ limit, the baryon spectrum is an infinite tower of degenerate states with isospin and spin of the light degrees of freedom $I=s_{\ell }=0,1,2,\dots$, and total spin $s=\text{abs}{s}_{\ell }\pm 1/2$. Exotic states with no quark model analogues in the large $N_c$ limit are found to be unbound. The ${\Sigma }_c-{\Lambda }_c$ mass difference is computed and found to be in good agreement with experiment. The ${\Sigma }_c{\Sigma }_c\pi$ and ${\Sigma }_c{\Lambda }_c\pi$ coupling constants are calculated to leading order in $N_c$ in terms of $g_A$, the axial coupling constant of the nucleon. We discuss the extension of our results to $SU(3)$ chiral solitons.

Comments: (28 pages, 0 figures, uses harvmac.tex)