Heavy quark symmetry behind b → c semileptonic sum rule

A bstract Lepton flavor universality violations in semileptonic b → c transitions have garnered attention over a decade. For R₇₂=BR (H₁ H₂) /BR (H₁ H₂) with ℓ being e, μ, a sum rule among R D, R₃^{*} and R Λ 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.