The measured $\bar{ B}\to D^{ (*)} l \bar\nu$ decay rates for light leptons ($l=e,\mu$) constrain all $\bar{ B}\to D^{ (*)}$ semileptonic form factors, by including both the leading and ${ \cal O}(\Lambda_{ \text{ QCD}}/m_{ c,b})$ subleading Isgur-Wise functions in the heavy quark effective theory. We perform a novel combined fit to the $\bar{ B}\to D^{ (*)} l \bar\nu$ decay distributions to predict the $\bar{ B} \to D^{ (*)} \tau\bar\nu$ rates and determine the CKM matrix element $|V_{ cb}|$. Most theoretical and experimental papers have neglected uncertainties in the predictions for form factor ratios at order $\Lambda_{ \text{ QCD}}/m_{ c,b}$, which we include. We also calculate ${ \cal O}(\Lambda_{ \text{ QCD}}/m_{ c,b})$ and ${ \cal O}(\alpha_s)$ contributions to semileptonic $\bar{ B}\to D^{ (*)} \ell \bar\nu$ decays for all possible $b \to c$ currents. This result has not been available for the tensor current form factors, and for two of those, which are ${ \cal O}(\Lambda_{ \text{ QCD}}/m_{ c,b})$, the corrections are of the same order as approximations used in the literature. These results allow us to determine with improved precision how new physics may affect the $\bar{ B}\to D^{ (*)} \tau\bar\nu$ rates. Our predictions can be systematically improved with more data; they need not rely on lattice QCD results, although these can be incorporated.
Categories: hep-ph