Anomalous thresholds in $B\to (P,V)\gamma^*$ form factors

TL;DR

This paper investigates how anomalous thresholds influence the non-local form factors in $B$ meson decays to light mesons and photons, revealing that these effects are generally small on the $ ho(770)$ resonance but can be significant off-peak, with implications for decay analysis.

Contribution

The study provides a detailed dispersive framework for understanding anomalous thresholds in $B$ decay form factors, including phenomenological estimates and potential extensions to higher states and charm loops.

Findings

Anomalous effects are suppressed on the $ ho(770)$ resonance.

Off-peak anomalous effects can reach about 10% of the form factors.

The dispersive framework aids in interpreting $B o (P,V) o ext{leptons}$ decays.

Abstract

We study the effects of anomalous thresholds on the non-local form factors describing the hadronization of the light-quark contribution to $B\to(P,V)\gamma^*$ transitions. Starting from a comprehensive discussion of anomalous thresholds in the triangle loop function for different mass configurations, we detail how the dispersion relation for $\pi\pi$ intermediate states is affected by contour deformations mandated by the anomalous branch points. Phenomenological estimates of the size of the anomalous contributions to the form factors are provided with couplings determined from measured branching fractions and Dalitz plot distributions. Our key finding is that anomalous effects are suppressed on the $\rho(770)$ resonance, while off-peak the effects can become as large as $\mathcal{O}(10\%)$ of the full (light-quark-loop induced) non-local form factors. We comment on future generalizations towards higher intermediate states and the charm loop, outlining how the dispersive framework established in this work could help improve the non-local form factors needed as input for a robust interpretation of $B\to (P,V)\ell^+\ell^-$ decays.