On sum rules for semi-leptonic b → c and b → u decays

Abstract

Abstract The semi-leptonic b → clν processes are receiving a lot of attention, as the lepton flavor universality (LFU) violation has been hinted by the measured ratios R D ∗ $$ {R}_{D^{\left(\ast \right)}} $$ = Γ(B → D (∗) τν)/Γ(B → D (∗) ℓν) for ℓ = e, μ. Recently, it has also been pointed out that the baryonic counterpart, R Λ c $$ {R}_{\Lambda_c} $$ = Γ(Λ b → Λ c τν)/Γ(Λ b → Λ c ℓν), has a strong correlation with R D ∗ $$ {R}_{D^{\left(\ast \right)}} $$ , referred to as the R ratio sum rule in this paper. The correlation is almost independent of the new physics (NP) implication and hence can predict R Λ c $$ {R}_{\Lambda_c} $$ from the measured R D ∗ $$ {R}_{D^{\left(\ast \right)}} $$ . On the other hand, we have fewer measurements and/or theoretical studies of the semi-leptonic b → ulν processes, although the same arguments can be applied to the ratios R π , R ρ , and R p as above. Since these processes are measurable at the ongoing LHCb run-3 and/or Belle II experiments, precise studies on them are important as well. In this paper, we obtain the semi-analytic formulae for all the aforementioned R X ratios in the presence of NP contributions by using the available lattice QCD and/or light-cone sum rule fits to the form factors. Two novel points are highlighted: (i) We evaluate uncertainties of R X including both the Standard Model (SM) and NP terms, inherited from the form factor fits, and discuss how the uncertainties affect the R ratio sum rules. (ii) We obtain the R ratio sum rule among the semi-leptonic b → ulν processes for the first time, which provides a complementary motivation for observing these processes. In addition, based on our numerical results, we investigate how the different NP scenarios work in the b → c and b → u sectors and perform a combined study in the framework of SM effective field theory with specific flavor symmetries.

Keywords

• Semi-Leptonic Decays
• Specific BSM Phenomenology
• SMEFT