Angular Analysis of $B \to D^{*}\ell \bar{\nu}_{\ell}$ from Lattice and Experiment: $|V_{cb}|$ and New Physics Constraints

Abstract

We present a combined angular analysis within and beyond the Standard Model (SM) of experimental measurements for the $B \to D^{*}\ell \bar{\nu}_{\ell}$ angular coefficients provided by the Belle collaboration, together with lattice-calculated hadronic form-factor data from the HPQCD, JLQCD, and FNAL/MILC collaborations. We focus on determining the CKM matrix element $|V_{cb}|$ and constraining a set of Wilson coefficients associated with new physics (NP) mediated by scalar and tensor currents. SM predictions for the angular coefficients are obtained using form-factor parameterisations based on the Boyd-Grinstein-Lebed (BGL) ansatz, with unitarity constraints imposed as Bayesian priors. Experimental and theoretical data are analysed jointly by considering the cases $\ell = e, \mu$ separately and comparing with the massless approximation. For the latter, we determine $|V_{cb}| = 0.03997(71)$, with no resolution of the exclusive-inclusive puzzle. Using the full expressions for the angular coefficients in the presence of scalar, vector, and tensor currents, the corresponding Wilson coefficients are constrained through a joint Bayesian fit to lattice and experimental data. By including the renormalisation group evolution of the Wilson coefficients in the SM effective field theory (SMEFT), these constraints translate into bounds on the effective scale of potential heavy NP at the TeV scale. We find, at the $68\%$ confidence level, that NP mediated by a scalar leptoquark and a vector leptoquark/colourless scalar boson are excluded at the effective scales 1.0 and 2.5 TeV, respectively.