Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints

TL;DR

This paper employs dispersive methods combined with chiral and heavy-quark symmetries to analyze the vector form factors of $D$, $D^*$, $B$, and $B^*$ mesons, including resonance effects and anomalous thresholds.

Contribution

It introduces a model-independent dispersive framework incorporating all symmetry constraints and analyzes the analytic structure of heavy meson form factors, including anomalous thresholds.

Findings

Determined $ ho$ resonance couplings to heavy mesons via pole residues.

Analyzed the analytic properties and anomalous thresholds of form factors.

Provided a comprehensive dispersive analysis consistent with symmetries.

Abstract

We analyze the isovector vector form factors of $D$, $D^*$, $B$, and $B^*$ mesons at low energies. We employ all constraints due to chiral and heavy-quark symmetry, and include the physics of resonant pion-pion rescattering in a model-independent way, using dispersion theory. Special attention is paid to the analytic properties of these form factors, which include anomalous thresholds due to triangle diagrams that are located on the physical Riemann sheets in some of the form factors. We extract the couplings of the $\rho(770)$ resonance to all these heavy mesons by determining the appropriate pole residues.