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

Abstract

Lepton flavor universality violations in semileptonic $b\to c$ transitions have garnered attention over a decade. For $R_{H_c}=\mathrm{BR}(H_b\to H_c\tau {\bar{\nu }}_{\tau })/\mathrm{BR}(H_b\to H_c\ell {\bar{\nu }}_{\ell })$ with $\ell$ being $e,\mu$, a sum rule among $R_D$, $R_{D^{\ast }}$ 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.

Comments: 20 pages, 4 figures, published from JHEP