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

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