Semileptonic sum rules in heavy-to-light charm decays

Abstract

We investigate semileptonic sum rules in heavy-to-light charm decays, motivated by analogous relations in $b\to c$ and $b\to u$ transitions. Focusing on the $c\to d\overline{\ell }\nu$ decays, $D\to \pi \overline{\ell }\nu$, $D\to \rho \overline{\ell }\nu$, and ${\Lambda }_c\to n\overline{\ell }\nu$, we examine a relation among their lepton-flavor universality ratios $R_H^{\mu e}$. Although the charm sum rule is less precise than the relations in bottom-hadron decays, current low-energy and high-$p_T$ constraints on new physics restrict the actual deviation from the relation to below the percent level. The relation can therefore provide a useful consistency check of charm semileptonic measurements. As an application, we derive a prediction for the yet-unmeasured ratio $R_n^{\mu e}$ in ${\Lambda }_c\to n\overline{\ell }\nu$.

26 pages, 6 figures, 2 tables