Constraints on exclusive branching fractions $${\mathcal {B}}_i(B^+\rightarrow X_c^il^+\nu )$$ B i ( B + → X c i l + ν ) from moment measurements in inclusive $$B\rightarrow X_cl\nu $$ B → X c l ν decays

Abstract

As an alternative to direct measurements, we extract the branching fractions \({\mathcal {B}}_i(B^+\rightarrow X_c^il^+\nu )\) 1 with \(X_c^i=D,D^*,D_0,D'_1,D_1,D_2,D',D'^{*}\) and non-resonant final states \((D^{(*)}\pi )_{nr}\), from a fit to electron energy, hadronic mass and combined hadronic mass–energy moments measured in inclusive \(B\rightarrow X_cl\nu \) decays. The fit is performed by constraining the sum of exclusive branching fractions to the measured \({\mathcal {B}} (B^+\rightarrow X_c l^+\nu )\) value, and with different sets of additional constraints for the directly measured branching fractions. There is no fit scenario in which a single branching fraction can close the gap between \({\mathcal {B}} (B^+\rightarrow X_c l^+\nu )\) and the sum of known branching fractions \({\mathcal {B}}_i(B^+\rightarrow X_c^il^+\nu )\). The fitted \({\mathcal {B}}(B^+\rightarrow \overline{D}^{*0}l^+\nu )\) is found to be significantly larger than its direct measurement. \({\mathcal {B}}(B^+\rightarrow \overline{D}^0l^+\nu )\) is in good agreement with the direct measurement; when \({\mathcal {B}}(B^+\rightarrow \overline{D}^{*0} l^+\nu )\) is constrained the fitted \({\mathcal {B}}(B^+\rightarrow \overline{D}^0l^+\nu )\) increases. Within large uncertainties, \({\mathcal {B}}(B^+\rightarrow \overline{D}'^0_1l^+\nu )\) agrees with direct measurements. Depending on the fit scenario, \({\mathcal {B}}(B^+\rightarrow \overline{D}^0_0l^+\nu )\) is consistent with or larger than its direct measurement. The fit is not able to easily disentangle \(B^+\rightarrow \overline{D}^0_1l^+\nu \) and \(B^+\rightarrow \overline{D}^0_2l^+\nu \), and tends to increase the sum of these two branching fractions. \({\mathcal {B}} (B^+\rightarrow (D^{(*)}\pi )_{nr}l^+\nu )\) with non-resonant \((D^{(*)}\pi )_{nr}\) final states is found to be of the order \(0.3~\%\). No indication is found for significant contributions from so far unmeasured \(B^+\rightarrow \overline{D}'^{(*)0}l^+\nu \) decays.