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

We analyze the isovector vector form factors of $D$, $D^{\ast }$, $B$, and $B^{\ast }$ 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.