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

We propose a geometric framework for heavy–quark transitions in which the infrared dressing of heavy–light states is described through adiabatic Berry holonomies on the functional space of gauge configurations. Within this approach, the Berry curvature may carry a quantized functional flux, providing a geometric interpretation of the Isgur–Wise function and leading to a local exponential approximation in the vicinity of zero recoil. Sequential processes such as B→D**→D probe two independent recoil directions and therefore explore a two–dimensional region of the adiabatic manifold. In this case, the effective infrared dynamics naturally acquires a non–Abelian structure that, within the leading adiabatic approximation, is described by a local SU(2) holonomy acting on a quasi–degenerate infrared subspace. The corresponding heavy–quark form factors are obtained as channel-dependent projections of two common geometric eigenmodes, leading to correlated recoil dependence and a generally non-factorizable structure on the (w 1 ,w 2 ) plane. The resulting construction is compatible with the symmetry structure of HQET while providing a complementary geometric interpretation of heavy–quark transitions. It also predicts correlated patterns in sequential decay channels that may be tested in future analyses of Belle, Belle II, and LHCb data.