Improved perturbative QCD formalism for $B_c$ meson decays

TL;DR

This paper develops an improved perturbative QCD approach incorporating charm quark mass effects for $B_c$ meson decays, enabling more accurate predictions of decay rates and form factors, especially for the $B_c^+ o J/ \, $ channel.

Contribution

It introduces a $k_T$ resummation formalism with charm mass effects into pQCD for $B_c$ decays, enhancing theoretical precision for heavy meson decay calculations.

Findings

The imaginary part of the $B_c o J/$ transition form factor is power suppressed.

The $B_c^+ o J/ \, $ branching ratio is estimated to be not lower than $10^{-3}$.

The formalism can be extended to other $B_c$ decay channels.

Abstract

We derive the $k_T$ resummation for doubly heavy-flavored $B_c$ meson decays by including the charm quark mass effect into the known formula for a heavy-light system. The resultant Sudakov factor is employed in the perutrbative QCD study of the "golden channel" $B_c^+ \to J/\psi \pi^+$. With a reasonable model for the $B_c$ meson distribution amplitude, which maintains approximate on-shell conditions of both the partonic bottom and charm quarks, it is observed that the imaginary piece of the $B_c \to J/\psi$ transition form factor appears to be power suppressed, and the $B_c^+ \to J/\psi \pi^+$ branching ratio is not lower than $10^{-3}$. The above improved perutrbative QCD formalism is applicable to $B_c$ meson decays to other charmonia and charmed mesons.