Heavy quark symmetry behind $b \to c$ semileptonic sum rule

TL;DR

This paper explores a sum rule relating different semileptonic decay ratios in heavy quark systems, derived from heavy quark symmetry, and discusses how real-world corrections affect this relation.

Contribution

It derives an exact sum rule based on heavy quark symmetry and analyzes the impact of model-dependent corrections in practical scenarios.

Findings

Sum rule holds exactly in the heavy quark limit.

Model-dependent corrections modify the sum rule.

Provides a framework to test lepton flavor universality.

Abstract

Lepton flavor universality violations in semileptonic $b \to c$ transitions have garnered attention over a decade. For $R_{H_c}={\rm{BR}}(H_b\to H_c \tau\bar\nu_\tau)/{\rm{BR}}(H_b\to H_c \ell\bar\nu_\ell)$ with $\ell$ being $e,\, \mu$, a sum rule among $R_{D}$, $R_{D^*}$ and $R_{\Lambda_c}$ was proposed to check consistency in the experimental results independently of new physics models. We revisit this relation from the perspective of the heavy quark symmetry. We derive a sum rule holding exactly in the heavy quark limit and clarify how model-dependent corrections are introduced in a realistic situation.