Abstract
We investigate the semi-leptonic decays of $B D^(*) \ell\bar\nu$
in terms of the Heavy-Quark-Effective-Theory (HQET) parameterization for the
form factors, which is described with the heavy quark expansion up to $\mathcal
O(1/m_c^2)$ beyond the simple approximation considered in the original CLN
parameterization. An analysis with this setup was first given in the
literature, and then we extend it to the comprehensive analyses including (i)
simultaneous fit of $|V_cb|$ and the HQET parameters to available
experimental full distribution data and theory constraints, and (ii) New
Physics (NP) contributions of the $V_2$ and $T$ types to the decay
distributions and rates. For this purpose, we perform Bayesian fit analyses by
using Stan program, a state-of-the-art public platform for statistical
computation. Then, we show that our $|V_cb|$ fit results for the SM scenarios
are close to the PDG combined average from the exclusive mode, and indicate
significance of the angular distribution data. In turn, for the $SM +
NP$ scenarios, our fit analyses find that non-zero NP contribution is
favored at the best fit point for both $SM + V_2$ and $SM + T$
depending on the HQET parameterization model. A key feature is then realized in
the $B D^(*) \tau\bar\nu$ observables. Our fit result of the HQET
parameters in the $SM (+T)$ produces a consistent value for $R_D$ while
smaller for $R_D^*$, compared with the previous SM prediction in the HFLAV
report. On the other hand, $SM+V_2$ points to smaller and larger values
for $R_D$ and $R_D^*$ than the SM predictions. In particular, the $R_D^*$
deviation from the experimental measurement becomes smaller, which could be
interesting for future improvement on measurements at the Belle~II experiment.
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