Abstract
We present a study of fits to exclusive ${B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ measurements for the determination of the Cabibbo-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 (LQCD) measurements of form factors at nonzero 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 Monte Carlo method using a Cholesky decomposition of the covariance matrix. Using additional input from lattice QCD calculations of form factors at nonzero 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 LQCD inputs and assuming a value of $\mathcal{F}(1)=0.904\ifmmode\pm\else\textpm\fi{}0.012$, we find $|{V}_{cb}|=(38.48\ifmmode\pm\else\textpm\fi{}0.32\ifmmode\pm\else\textpm\fi{}0.97\ifmmode\pm\else\textpm\fi{}0.46)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ in BGL(2,2,2) and $(38.42\ifmmode\pm\else\textpm\fi{}0.35\ifmmode\pm\else\textpm\fi{}1.05\ifmmode\pm\else\textpm\fi{}0.46)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ in CLNnoHQS, where the errors are statistical, systematic, and related to $\mathcal{F}(1)$, respectively.
Highlights
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 (LQCD) measurements of form factors at nonzero hadronic recoil from the JLQCD Collaboration
To avoid bias from high systematic error correlations, we employ a novel technique in the field of B-physics phenomenology with a toy Monte Carlo method using a Cholesky decomposition of the covariance matrix
The Cabibbo-Kobayashi-Maskawa matrix element jVcbj is a fundamental parameter of the Standard Model, describing the weak decay of b quarks, and must be measured
Summary
The Cabibbo-Kobayashi-Maskawa matrix element jVcbj is a fundamental parameter of the Standard Model, describing the weak decay of b quarks, and must be measured. The 2019 untagged Belle measurement of jVcbj [4] measured binned yields of B0 → DÃ−lþνl and fits to the CLN and BGL parametrizations, measuring F ð1ÞηEWjVcbj 1⁄4 ð35.06Æ0.15Æ0.56Þ×10−3 and ð34.93 Æ 0.23 Æ 0.59Þ × 10−3, respectively, where the latter is determined at a fixed order of power series truncation, defined later. These results showed consistency between the two parametrizations at a given order in the BGL expansion, in contrast to the results based on a preliminary measurement with tagged Belle data [5], as covered by Refs.
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