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

Abstract

Inspired by a series of unexpected measurements of semileptonic decays mediated via $b\to c$ 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.

arXiv comment12 pages, 2 figures, 4 tables

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• Footprints of New Physics in $b\to c\tau \nu$ Transitions
• New physics solutions for $R_D$ and $R_{D^{\ast }}$
• Model independent investigation of the $R_{J/\psi ,{\eta }_c}$ and ratios of decay widths of semileptonic $B_c$ decays into a P-wave charmonium
• Semileptonic $B_c$ decays to $P-$wave charmonium and the nature of ${\chi }_{c1}(3872)$
• Revisiting nonfactorizable contributions to factorization-forbidden decays of $B$ mesons to charmonium
• $B_c$ to $A$ Transition Form Factors and Semileptonic Decays in Self-consistent Covariant Light-front Approach
• Correlated study on some $B_c\to P$ and $B_c\to S$ wave channels in light of new inputs
• Nonleptonic $B_c$ decay rates from model independent relations
• Study of Form Factors and Observables in $B_c^{-}\to {\bar{D}}^{(\ast )0}{\ell }^{-}{\bar{\nu }}_{\ell }$ and $B_c^{-}\to D^{(\ast )-}{\ell }^{+}{\ell }^{-}$ decays