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

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 $\bar{B} \to D^{(*)}$ 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 $\bar{B} \to D^{(*)} l \nu$ 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 $\bar{B} \to D^{(*)} \tau \bar\nu$ decay rates, lepton flavor universality violation ratios $R(D^{(*)})$, and the CKM matrix element $|V_{cb}|$. We point out some apparent errors in prior literature concerning the $\mathcal{O}(1/m_cm_b)$ corrections, and note a tension between commonly-used simplified dispersive bounds and current data.