Constrained second-order power corrections in HQET: R(D(*)) , |Vcb| , and new physics

Abstract

We postulate a supplemental power counting within the heavy quark effective theory (HQET) that results in a small, highly constrained set of second-order power corrections, compared to the standard approach. We determine all $\overline{B}\ensuremath{\rightarrow}{D}^{(*)}$ form factors, both within and beyond the standard model to $\mathcal{O}({\ensuremath{\alpha}}_{s}/{m}_{c,b},1/{m}_{c,b}^{2})$, under truncation by this power counting. We show that the second-order power corrections to the zero-recoil normalization of the $\overline{B}\ensuremath{\rightarrow}{D}^{(*)}l\ensuremath{\nu}$ matrix elements ($l=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$) 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 $\overline{B}\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\tau}\overline{\ensuremath{\nu}}$ decay rates, lepton flavor universality violation ratios $R({D}^{(*)})$, and the Cabibbo-Kobayashi-Maskawa 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.