Non–Abelian Recoil Geometry and Infrared Holonomies in Heavy–Quark Transitions

We explore a geometric framework for heavy–quark transitions in which infrared–dressed states are adiabatically transported in recoil space and acquire Berry holonomies. Within this approach, single–step transitions provide the simplest setting for discussing possible geometric effects associated with the infrared dressing cloud, while sequential decays involve a multidimensional recoil manifold that may support non–Abelian holonomies. Assuming the existence of a suitable quasi–degenerate infrared sector, the resulting geometric structure can be described in terms of an effective [Formula: see text] holonomy. The corresponding geometric modes provide a convenient basis for parametrizing possible infrared contributions and correlations among different decay channels. As an illustrative application, we investigate whether such a geometric framework can shed light on the long–standing [Formula: see text] versus [Formula: see text] puzzle. Within a simple effective model, the resulting geometric correlations lead naturally to ratios of partial widths of order unity, [Formula: see text]. We also discuss the possible relevance of the same geometric language for quasi–degenerate hadronic systems and near–threshold exotic states.