Unitarity bounds with subthreshold and anomalous cuts for $b$-hadron decays

TL;DR

This paper generalizes the BGL parametrization to include subthreshold and anomalous cuts in form factors of $b$-hadron decays, enabling more accurate and systematic analyses from first principles.

Contribution

It introduces a new method to incorporate subthreshold and anomalous branch cuts into unitarity bounds for $b$-hadron decay form factors, extending the BGL framework.

Findings

Derived a generalized parametrization for form factors with additional branch cuts.

Established unitarity bounds accounting for subthreshold and anomalous cuts.

Facilitated more precise form factor analyses with reduced systematic uncertainties.

Abstract

We derive a generalisation of the Boyd-Grinstein-Lebed (BGL) parametrization. Most form factors (FFs) in $b$-hadron decays exhibit additional branch cuts -- namely subthreshold and anomalous branch cuts -- beyond the ``standard'' unitarity cut. These additional cuts cannot be adequately accounted for by the BGL parametrization. For instance, these cuts arise in the FFs for $B\to D^{(*)}$, $B\to K^{(*)}$, and $\Lambda_b\to \Lambda$ processes, which are particularly relevant from a phenomenological standpoint. We demonstrate how to parametrize such FFs and derive unitarity bounds in the presence of subthreshold and/or anomalous branch cuts. Our work paves the way for a wide range of new FF analyses based solely on first principles, thereby minimising systematic uncertainties.