Unitarity bounds and form-factor predictions for $B$-meson decays

Abstract

This paper is organized around three main objectives. First, I review in a pedagogical way the unitarity bounds for form factors in $B$-meson decays, together with the parametrizations most commonly used in phenomenological analyses. These include BGL, BCL, CLN, and the Dispersive Matrix (DM) method. I also clarify the relation between BGL and DM, showing that they are two equivalent implementations of the same unitarity information. Second, I demonstrate that the standard BGL and DM constructions are strictly rigorous only when no subthreshold cuts are present. For $B$-meson decays, this requirement is fulfilled exclusively by the $B\to\pi$ FFs. To treat the generic case, I fully develop the GG parametrization introduced in previous work and show how the same logic extends to a DM-like construction. Third, I perform three combined analyses and obtain form-factor predictions over the full semileptonic region: one for $B\to\pi$ and $B_s\to K^{(*)}$, one for $B\to K^{(*)}$ and $B_s\to \phi$, and one for $B\to D^{(*)}$ and $B_s\to D_s^{(*)}$. All numerical results, posterior samples, analysis files, and plots are provided in the supplementary material (https://github.com/gubernari/suppl-unitb).