Model independent analysis of semileptonic $B$ decays to $D^{\ast \ast }$ for arbitrary new physics

Abstract

We explore semileptonic $B$ decays to the four lightest excited charm mesons, $D^{\ast \ast }=\{D_0^{\ast },D_1^{\ast },$ $D_1,D_2^{\ast }\}$, for nonzero charged lepton mass and for all $b\to c\ell \bar{\nu }$ four-Fermi interactions, including calculation of the $\mathcal{O}({\Lambda }_{\text{QCD}}/m_{c,b})$ and $\mathcal{O}({\alpha }_s)$ corrections to the heavy quark limit for all form factors. In the heavy quark limit some form factors are suppressed at zero recoil, therefore, the $\mathcal{O}({\Lambda }_{\text{QCD}}/m_{c,b})$ corrections can be very important. The $D^{\ast \ast }$ rates exhibit sensitivities to new physics in $b\to c\tau \bar{\nu }$ mediated decays complementary to the $D$ and $D^{\ast }$ modes. Since they are also important backgrounds to $B\to D^{(\ast )}\tau \bar{\nu }$, the correct interpretation of future semitauonic $B\to D^{(\ast )}$ rate measurements requires consistent treatment of both the $D^{\ast \ast }$ backgrounds and the signals. Our results allow more precise and more reliable calculations of these $B\to D^{\ast \ast }\ell \bar{\nu }$ decays, and are systematically improvable by better data on the $e$ and $\mu$ modes. As an example, we show that the $D^{\ast \ast }$ rates are more sensitive to a new $\bar{c}{\sigma }_{\mu \nu }b$ tensor interaction than the $D^{(\ast )}$ rates.

Comments: 17 pages, 4 figures, 5 tables; published version