Semileptonic decays of $B_c$ meson to $P$-wave charmonium states

TL;DR

This paper calculates semileptonic decay rates of the $B_c$ meson to P-wave charmonium states using an improved perturbative QCD approach, providing predictions for branching ratios and polarization observables to aid experimental tests and new physics searches.

Contribution

It introduces an improved pQCD formalism including charm quark mass effects to evaluate transition form factors for $B_c$ decays to P-wave charmonium states, extending previous models.

Findings

Branching ratios can reach order of 10^{-3}

Form factors are evaluated across the full kinematic range

Predictions for tau and light lepton ratio and polarization are provided

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.