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

Abstract

The measured $\bar{B}\to D^{(*)} l \barν$ decay rates for light leptons ($l=e,μ$) constrain all $\bar{B}\to D^{(*)}$ semileptonic form factors, by including both the leading and ${\cal O}(Λ_{\text{QCD}}/m_{c,b})$ subleading Isgur-Wise functions in the heavy quark effective theory. We perform a novel combined fit to the $\bar{B}\to D^{(*)} l \barν$ decay distributions to predict the $\bar{B} \to D^{(*)} τ\barν$ 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 $Λ_{\text{QCD}}/m_{c,b}$, which we include. We also calculate ${\cal O}(Λ_{\text{QCD}}/m_{c,b})$ and ${\cal O}(α_s)$ contributions to semileptonic $\bar{B}\to D^{(*)} \ell \barν$ 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 ${\cal O}(Λ_{\text{QCD}}/m_{c,b})$, 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 $\bar{B}\to D^{(*)} τ\barν$ rates. Our predictions can be systematically improved with more data; they need not rely on lattice QCD results, although these can be incorporated.

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