Combined analysis of semileptonic $B$ decays to $D$ and $D^{\ast }$: $R(D^{(\ast )})$, $|V_{cb}|$, and new physics

Abstract

The measured $\bar{B}\to D^{(\ast )}l\bar{\nu }$ decay rates for light leptons ($l=e,\mu$) constrain all $\bar{B}\to D^{(\ast )}$ semileptonic form factors, by including both the leading and $\mathcal{O}({\Lambda }_{\text{QCD}}/m_{c,b})$ subleading Isgur-Wise functions in the heavy quark effective theory. We perform a novel combined fit to the $\bar{B}\to D^{(\ast )}l\bar{\nu }$ decay distributions to predict the $\bar{B}\to D^{(\ast )}\tau \bar{\nu }$ 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 $\mathcal{O}({\Lambda }_{\text{QCD}}/m_{c,b})$ and $\mathcal{O}({\alpha }_s)$ contributions to semileptonic $\bar{B}\to D^{(\ast )}\ell \bar{\nu }$ 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 $\mathcal{O}({\Lambda }_{\text{QCD}}/m_{c,b})$, 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 $\bar{B}\to D^{(\ast )}\tau \bar{\nu }$ rates. Our predictions can be systematically improved with more data; they need not rely on lattice QCD results, although these can be incorporated.

Comments: 32 pages, 5 figures, 11 tables; v2: additional fit scenario added; plots 3 & 4 corrected; numerical results unchanged; v3: transcription of Eqs (A1a,b) corrected; all results unchanged; v4: corrected typo in eq 19b