A Geometric Interpretation of Heavy-Quark Transitions and the Emergent SU(2) Structure

TL;DR

This paper introduces a geometric framework using Berry holonomies to interpret heavy-light mesons, revealing an SU(2) structure that explains form factors and correlations in heavy-quark transitions.

Contribution

It provides a novel geometric interpretation of heavy-quark transitions, linking Berry curvature and holonomies to SU(2) structures and form factors in HQET.

Findings

Quantized Berry flux explains Isgur-Wise function form

SU(2) holonomy describes non-Abelian structure in transitions

Predicts correlations and angular patterns in heavy-quark phenomenology

Abstract

We propose a geometric interpretation of heavy-light mesons in which their infrared dressing is described through adiabatic Berry holonomies on the functional space of gauge configurations. Within this framework the Berry curvature associated with the infrared cloud carries a quantized functional flux, providing a simple and structural origin for the exponential form of the Isgur-Wise function in single-recoil transitions. Sequential processes such as $B \rightarrow D^{**} \rightarrow D$ probe two independent recoil directions and explore a two-dimensional region of the adiabatic manifold. In this setting the quantized flux naturally leads to a minimal non-Abelian structure which can be described effectively by an SU(2) holonomy. Heavy-quark form factors then appear as channel-dependent projections of two universal geometric modes, giving rise to correlated slopes, non-factorizable curvature in the $(w_{1},w_{2})$ plane, and characteristic angular patterns. These features are consistent with the symmetry structure of HQET while providing additional correlations among excited channels. The resulting framework offers a complementary viewpoint on heavy-quark phenomenology and suggests several experimentally testable signatures in multi-step semileptonic transitions.