Baryons Containing a Heavy Quark as Solitons ⋆ ( REVISED

The possibility of interpreting baryons containing a single heavy quark as bound states of solitons (that arise in the nonlinear sigma model) and heavy mesons is explored. Particular attention is paid to the parity of the bound states and to the role of heavy quark symmetry. ⋆ Work supported in part by the U.S. Dept. of Energy under Contract no. DEAC-03-81ER40050 and under grant no. DE-FG03-90ER40546, and by the National Science Foundation under a Presidential Young Investigator award no. PHY-8958081. Many properties of baryons B containing light u and d quarks suggest that they can be represented as solitons. For example, they have a mass of order 1/α and the cross section for ee → BB̄ is of order e−1/α, where α = 1/Nc is taken as a small quantity. Skyrme originally suggested that baryons are solitons in the chiral Lagrangian (i.e. nonlinear sigma model) used to describe pion self interactions. The solitons of the chiral Lagrangian have the right quantum numbers to be QCD baryons, provided one includes the Wess-Zumino term. The model of QCD baryons as solitons has been used to compute many of their properties.5,6 The same large Nc power counting that suggests that baryons containing only light quarks are solitons, also suggests that baryons containing a single heavy quark Q (mQ ≫ ΛQCD) can be represented as solitons. Recently there has been considerable progress in understanding the properties of hadrons containing a single heavy quark. In the limit mQ → ∞, QCD has a heavy quark spin-flavor symmetry7,8 that determines many properties of hadrons containing a single heavy quark. In the mQ → ∞ limit, the total angular momentum of the light degrees of freedom (i.e. light quarks and gluons), ~ Sl = ~ S − ~ SQ , (1) is conserved. Consequently mesons and baryons containing a single heavy quark can be labeled by sl, and provided sl 6= 0, they come in degenerate doublets with total spins s± = sl ± 1/2 (2) formed by combining the spin of the heavy quark with the angular momentum of the light degrees of freedom. Callan and Klebanov originally suggested an interpretation of baryons containing a heavy quark as bound states of solitons of the pion chiral Lagrangian with mesons containing a heavy quark.10,11 In this paper we examine this model for heavy baryons. An important aspect of this work is that the consequences of heavy quark symmetry