A Geometric Interpretation of Heavy-Quark Transitions and the Emergent SU(2) Structure
Jorge Gamboa, Natalia A. Tapia Arellano
TL;DR
The paper develops a geometric, Berry-phase description of heavy-quark transitions in QCD, identifying an abelian Berry holonomy that yields the Isgur–Wise function for single-recoil decays and an emergent SU(2) holonomy for sequential decays B → D^{**} → D. It shows that infrared dressing of heavy-light states is topologically organized into quantized flux sectors, giving rise to universal geometric modes and channel-dependent projections that correlate heavy-quark form factors across channels. The framework provides a principled origin for the exponential falloff near zero recoil, explains the 1/2 vs 3/2 puzzle via non-Abelian holonomies, and makes falsifiable predictions for recoil-plane correlations, angular distributions, and tauonic enhancements. It also connects these geometric insights to established HQET constructs like Bjorken–Uraltsev sum rules, while offering concrete experimental signatures for Belle, Belle II, BaBar, and LHCb. Overall, the work proposes a topological, holonomy-based extension of HQET that links infrared QCD geometry to heavy-quark phenomenology with clear avenues for experimental validation.
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.