Constrained second-order power corrections in HQET: $R(D^{(\ast )})$, $|V_{cb}|$, and new physics

Abstract

We postulate a supplemental power counting within the heavy quark effective theory, that results in a small, highly-constrained set of second-order power corrections, compared to the standard approach. We determine all $\bar{B}\to D^{(\ast )}$ form factors, both within and beyond the standard model to $\mathcal{O}({\alpha }_s/m_{c,b},1/m_{c,b}^2)$, under truncation by this power counting. We show that the second-order power corrections to the zero-recoil normalization of the $\bar{B}\to D^{(\ast )}l\nu$ matrix elements ($l=e$, $\mu$, $\tau$) are fully determined by hadron mass parameters, and are in good agreement with lattice QCD (LQCD) predictions. We develop a parametrization of these form factors under the postulated truncation, that achieves excellent fits to the available LQCD predictions and experimental data, and we provide precise updated predictions for the $\bar{B}\to D^{(\ast )}\tau \bar{\nu }$ decay rates, lepton flavor universality violation ratios $R(D^{(\ast )})$, and the CKM matrix element $|V_{cb}|$. We point out some apparent errors in prior literature concerning the $\mathcal{O}(1/m_c{m}_b)$ corrections, and note a tension between commonly-used simplified dispersive bounds and current data.

arXiv comment85 pages, 11 figures, 19 tables; published version; minor typos corrected

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• First Measurement of $R(X_{\tau /\ell })$ as an Inclusive Test of the $b\to c\tau \nu$ Anomaly
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