Revisiting fits to $B^{0} \to D^{*-} \ell^{+} \nu_{\ell}$ to measure $|V_{cb}|$ with novel methods and preliminary LQCD data at non-zero recoil

Abstract

We present a study of fits to exclusive $B^{0} \to D^{*-} \ell^{+} \nu_{\ell}$ measurements for the determination of the Cabbibo-Kobayashi-Maskawa matrix element magnitude $|V_{cb}|$, based on the most recent Belle untagged measurement. Results are obtained with the Caprini-Lellouch-Neubert (CLN) and Boyd-Grinstein-Lebed (BGL) form factor parametrizations, with and without the inclusion of preliminary Lattice QCD measurements of form factors at non-zero hadronic recoil from the JLQCD collaboration. The CLN and BGL fits are also studied in different scenarios with reduced theoretical assumptions, and at higher order expansions, respectively. To avoid bias from high systematic error correlations we employ a novel technique in the field of $B$-physics phenomenology with a toy MC using a Cholesky decomposition of the covariance matrix. Using additional input from Lattice QCD calculations of form factors at non-zero recoil, in collaboration with JLQCD, allows for well-defined fit results with reduced model dependence in CLN and BGL. The results obtained are consistent between different configurations, ultimately providing a method for a more model-independent exclusive measurement of $|V_{cb}|$. Using preliminary inputs, $\mathcal{F}(1)\eta_{\rm EW}|V_{cb}|$ is found to be approximately $(35.02 \pm 0.29 \pm 0.88) \times 10^{-3}$ in BGL(2,2,2) and $(34.96 \pm 0.32 \pm 0.96) \times 10^{-3}$ in CLNnoHQS.