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

## TL;DR

This paper performs a comprehensive analysis of semileptonic B decays to D and D* mesons, incorporating uncertainties and higher-order corrections to improve predictions of decay rates, CKM matrix element |V_cb|, and potential new physics effects.

## Contribution

It introduces a novel combined fit method including subleading Isgur-Wise functions and uncertainties, providing more precise predictions for decay rates and new physics constraints.

## Key findings

- Predicted B to D(*) tau nu decay rates with improved accuracy.
- Quantified uncertainties in form factor ratios at order Λ_QCD/m_c,b.
- Assessed potential impacts of new physics on semileptonic decay rates.

## Abstract

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.