Constraints on exclusive branching fractions from moment measurements in inclusive decays

Florian U. Bernlochner; Dustin Biedermann; Heiko Lacker; Thomas Lück

doi:10.1140/epjc/s10052-014-2914-3

EPJ

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

Florian U. Bernlochner¹, Dustin Biedermann²^*, Heiko Lacker² and Thomas Lück¹

¹ University of Victoria, Victoria, British Columbia, V8W 3P, Canada
² Institut für Physik, Humboldt Universität zu Berlin, Newtonstr. 15, 12489 , Berlin, Germany

Received: 5 March 2014
Accepted: 19 May 2014
Published online: 24 June 2014

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.

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Constraints on exclusive branching fractions from moment measurements in inclusive decays

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