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 B̄ → D(∗) form factors, both within and beyond the standard model to O(αs/mc,b, 1/mc,b), under truncation by this power counting. We show that the second-order power corrections to the zero-recoil normalization of the B̄ → D(∗)lν matrix elements (l = e, μ, τ) 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 B̄ → D(∗)τ ν̄ decay rates, lepton flavor universality violation ratios R(D(∗)), and the CKM matrix element |Vcb|. We point out some apparent errors in prior literature concerning the O(1/mcmb) corrections, and note a tension between commonly-used simplified dispersive bounds and current data. 1 ar X iv :2 20 6. 11 28 1v 1 [ he pph ] 2 2 Ju n 20 22