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We investigate the semi-leptonic decays of $\bar B \to D^{(*)} \ell\bar\nu$in terms of the Heavy-Quark-Effective-Theory (HQET) parameterization for theform factors, which is described with the heavy quark expansion up to $\mathcalO(1/m_c^2)$ beyond the simple approximation considered in the original CLNparameterization. An analysis with this setup was first given in theliterature, and then we extend it to the comprehensive analyses including (i)simultaneous fit of $|V_{cb}|$ and the HQET parameters to availableexperimental full distribution data and theory constraints, and (ii) NewPhysics (NP) contributions of the $V_2$ and $T$ types to the decaydistributions and rates. For this purpose, we perform Bayesian fit analyses byusing Stan program, a state-of-the-art public platform for statisticalcomputation. Then, we show that our $|V_{cb}|$ fit results for the SM scenariosare close to the PDG combined average from the exclusive mode, and indicatesignificance of the angular distribution data. In turn, for the $\text{SM} +\text{NP}$ scenarios, our fit analyses find that non-zero NP contribution isfavored at the best fit point for both $\text{SM} + V_2$ and $\text{SM} + T$depending on the HQET parameterization model. A key feature is then realized inthe $\bar B \to D^{(*)} \tau\bar\nu$ observables. Our fit result of the HQETparameters in the $\text{SM} (+T)$ produces a consistent value for $R_D$ whilesmaller for $R_{D^*}$, compared with the previous SM prediction in the HFLAVreport. On the other hand, $\text{SM}+V_2$ points to smaller and larger valuesfor $R_D$ and $R_{D^*}$ than the SM predictions. In particular, the $R_{D^*}$deviation from the experimental measurement becomes smaller, which could beinteresting for future improvement on measurements at the Belle II experiment.

Bayesian fit analysis to full distribution data of $\bar B \to D^{(*)} \ell\bar\nu$: $|V_{cb}|$ determination and New Physics constraints