Heavy quark symmetry behind b → c semileptonic sum rule

Lepton flavor universality violations in semileptonic b → c transitions have garnered attention over a decade. For \({R}_{{H}_{c}}={\text{BR}}\left({H}_{b}\to {H}_{c}\tau {\overline{\nu }}_{\tau }\right)/{\text{BR}}\left({H}_{b}\to {H}_{c}{\ell}{\overline{\nu }}_{{\ell}}\right)\) with ℓ being e, μ, a sum rule among R_D, \({R}_{{D}^{*}}\) and R_Λc 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.