Abstract
Inspired by a series of unexpected measurements of semileptonic decays mediated via $b\rightarrow c $ charged current interactions, we explore semileptonic $B_c$ decays to the four lightest $P$-wave charmonium states, $\chi_{c0}, \chi_{c1}, \chi_{c2}, h_c$, by the recently developed improved perturbative QCD formalism, in which the charm quark mass effect is included both in the Sudakov factor and the hard kernels. We first directly evaluate the concerned transition form factors with vector and axial-vector currents in the region of small momentum transfer squared, and then recast them to the full kinematical region by adopting the exponential parametrization. The obtained form factors are used to evaluate the semileptonic decay branching ratios, which can reach the order of $10^{-3}$, letting the corresponding measurement appear feasible. For a better analysis, a comparison of our results with the predictions of other models is provided. We also present the ratios between the tau and light lepton branching ratios and the polarization contributions in the relevant processes, which still need experimental tests in the ongoing and forthcoming experiments. Any significant deviations from the Standard Model results may provide some hints of new physics effects.
Highlights
A number of experimental measurements involving semitauonic decays of the charged current b → cτντ transitions have shown interesting deviations from their Standard Model (SM) expectations, though the significance of the excess is low due to the large statistical uncertainties
The investigation of the corresponding P-wave charmonium modes is of special interest and further provides complementary information on physics beyond the SM
We gave predictions on the ratio between the tau and light lepton branching ratio RðXÞ, which are smaller than our previous calculation of RðJ=ψÞ due to the suppression from the phase space
Summary
A number of experimental measurements involving semitauonic decays of the charged current b → cτντ transitions have shown interesting deviations from their Standard Model (SM) expectations, though the significance of the excess is low due to the large statistical uncertainties. The possible NP effects in the semileptonic decays have been discussed recently in several papers [18,19,20,21,22,23,24,25,26]. Essential to the study of the semileptonic decays is the calculation of the invariant form factors describing the corresponding hadronic transitions. The relativistic corrections to the form factors of the Bc meson into P-wave orbitally excited charmonium have been investigated using the nonrelativistic QCD effective theory (NRQCD) [40].
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