$b \to c$ semileptonic sum rule: orbitally excited hadrons

TL;DR

This paper derives sum rules for semileptonic $b o c$ decays involving excited charm hadrons, highlighting the importance of hadronic form factors and deviations from the small-velocity limit.

Contribution

It constructs new sum rules based on heavy quark symmetry for orbitally excited charm hadrons in semileptonic $b o c$ transitions and analyzes deviations from idealized limits.

Findings

Deviations increase with excited hadrons involved.

Tensor contributions can induce sizable effects.

Current form factors are insufficiently constrained.

Abstract

We study semileptonic sum rules for $b \to c \tau \overline{\nu}$ transitions involving orbitally excited charm hadrons. Starting from the amplitude-level relation implied by the heavy quark symmetry, we construct sum rules relating these decays. We then examine deviations from the small-velocity limit. Our numerical analysis shows that the deviations generally increase once excited hadrons are involved, with tensor contributions often inducing sizable effects. At present, however, the relevant form factors are not yet sufficiently constrained. Further improvements in the hadronic inputs are essential for these sum rules to yield robust predictions for the corresponding lepton-universality ratios.