Relativistic corrections to the form factors of $B_c$ into $P$-wave orbitally excited charmonium

TL;DR

This paper calculates relativistic corrections to form factors of the $B_c$ meson decaying into P-wave charmonium, revealing significant effects on decay rates and aiding future experimental tests at LHCb.

Contribution

It provides the first analytic computation of next-to-leading order relativistic corrections to these form factors within nonrelativistic QCD.

Findings

Relativistic corrections significantly increase decay branching ratios.

Form factors are affected notably by relativistic effects.

Results are relevant for phenomenological analysis at LHCb.

Abstract

We investigated the form factors of the $B_{c}$ meson into $P$-wave orbitally excited charmonium using the nonrelativistic QCD effective theory. Through the analytic computation, the next-to-leading order relativistic corrections to the form factors were obtained, and the asymptotic expressions were studied in the infinite bottom quark mass limit. Employing the general form factors, we discussed the exclusive decays of the $B_{c}$ meson into $P$-wave orbitally excited charmonium and a light meson. We found that the relativistic corrections lead to a large correction for the form factors, which makes the branching ratios of the decay channels $\mathcal{B}(B_{c} ^{\pm }\to \chi _{cJ}(h_c) +\pi ^{\pm }(K^{\pm }))$ larger. These results are useful for the phenomenological analysis of the $B_{c}$ meson decays into $P$-wave charmonium, which shall be tested in the LHCb experiments.