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

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.

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