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

TL;DR

This paper introduces a geometric framework for heavy-quark transitions, revealing how infrared dressing leads to Berry holonomies that unify decay behaviors and explain longstanding puzzles in heavy-quark physics.

Contribution

It develops a novel geometric formulation of heavy-quark transitions incorporating non-Abelian holonomies and connects infrared dressing to observable decay phenomena.

Findings

Reproduces Isgur-Wise behavior with abelian phases

Identifies non-Abelian holonomies in sequential decays

Provides a geometric interpretation of mixing effects

Abstract

We propose a geometric formulation of heavy-quark transitions in which infrared-dressed states are adiabatically transported in the multidimensional recoil space and acquire Berry holonomies. Within this framework, single-step decays are governed by an abelian geometric phase and reproduce the standard Isgur-Wise behaviour, while sequential decays probe genuinely non-Abelian holonomies associated with a two-dimensional recoil space. The resulting geometric structure correlates different decay channels and provides a unified interpretation of mixing effects and quasi-degenerate states in heavy-quark phenomenology. This approach suggests that several long-standing puzzles arise as geometric consequences of infrared dressing rather than as accidental features of the microscopic dynamics.