Vanishing of non-Abelian Berry phases in heavy solitonic baryons
Résumé
In this article, we show -- using a reasoning applicable to both the excitation spectrum in the chiral bag model and the hyperfine structure of diatomic molecules -- that the generic form of a nonabelian Berry potential appears in heavy quark effective theory (HQET) and that the Berry potential vanishes for the soliton-heavy meson bound state in the heavy-quark limit. The vanishing of the Berry potential in HQET is shown to be related to the restoration of heavy-quark symmetry in infinite heavy-quark-mass limit in close analogy to diatomic molecules at infinite internuclear separation. ----- Whenever a quantum system with a hierarchy of length scales is truncated, induced gauge potentials (known as Berry potentials) are naturally generated, reflecting on the degrees of freedom that are integrated out. Following Berry's work on abelian gauge structure, Wilczek and Zee generalized the concept to the nonabelian case for systems possessing degeneracies. In this paper, the authors show that the concept can equally be applied to hadron structure, in particular to excited light-quark baryons and baryons with one heavy quark (such as charm, bottom etc...). They show that the nonabelian Berry structure in heavy baryons resembles remarkably closely the one found in the chiral bag model for chiral baryons as well as that operative in diatomic molecules. Exploiting the generic structure of the Berry potential, they identify the heavy-quark symmetry of Isgur and Wise with the limit in which the Berry phase vanishes (or the induced gauge field becomes pure gauge) as the heavy-quark mass tends to infinity, in complete analogy to the diatomic molecule in which the electronic rotational invariance is restored as the internuclear distance goes to infinity. D.P. Min
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