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

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 $b\to c\mathrm{\ell }\bar{\nu }$ four-Fermi interactions, including calculation of the $\mathcal{O}({\mathrm{\Lambda }}_{\text{QCD}}\mathrm{/}{m}_{c,b})$ 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 ${\cal O}(\Lambda_$\text{QCD}$/m_{c,b})$correctionscanbeveryimportant\mathrm{.}The$D^{**}$ratesexhibitsensitivitiestonewphysicsin$b\to c\tau\bar\nu$ 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 $B\to D^{\ast \ast }\mathrm{\ell }\bar{\nu }$ 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 $\bar c, \sigma_{\mu\nu} b$tensorinteractionthanthe$D^{(*)}$ rates.