Semileptonic $B_{(s)}$ decays to excited charmed mesons with $e,\mu,\tau$ and searching for new physics with $R(D^{**})$
Semileptonic $B$ meson decays into the four lightest excited charmed meson states ($D_0^*$, $D_1^*$, $D_1$, and $D_2^*$) and their counterparts with $s$ quarks are investigated, including the full lepton mass dependence. We derive the standard model predictions for the differential branching fractions, as well as predictions for the ratios of the semi-tauonic and light lepton semileptonic branching fractions. These can be systematically improved using future measurements of the total or differential semileptonic rates to $e$ and $\mu$, as well as the two-body hadronic branching fractions with a pion, related by factorization to the semileptonic rate at maximal recoil. To illustrate the different sensitivities to new physics, we explore the dependence of the ratio of semi-tauonic and light-lepton branching fractions on the type-II and type-III two-Higgs-doublet model parameters, $\tan\beta$ and $m_{H}^\pm$, for all four states.