Next-to-leading order QCD calculation of $B_c$ to charmonium tensor form factors

TL;DR

This paper calculates the next-to-leading order QCD corrections to $B_c$ meson decay form factors into charmonium states using NRQCD, providing analytical results, asymptotic behaviors, and numerical evaluations.

Contribution

It provides the first full analytical NLO QCD corrections for $B_c$ to charmonium tensor form factors within the NRQCD framework, including asymptotic analysis and numerical results.

Findings

Analytical NLO corrections for $B_c$ to $ o ext{charmonium}$ tensor form factors.

Asymptotic behaviors of form factors in heavy quark limits.

Numerical results across the physical region.

Abstract

We present a next-to-leading order (NLO) QCD corrections to $B_c\to \eta_c$ and $B_c\to J/\psi$ tensor form factors within nonrelativistic QCD (NRQCD) framework. The full analytical results for $B_c$ to S-wave charmonium tensor form factors are obtained. We also studied the asymptotic behaviours of tensor form factors in hierarchy heavy quark limit, i.e. $m_b\to\infty,~ m_c\to\infty, ~\mathrm{and }~m_c/m_b\to0$. A compact expression for tensor form factors are given analytically in the hierarchy heavy quark limit. The relation among different form factors is also analyzed especially at large momentum recoil point. The numerical results for the $B_c$ to charmonium tensor form factors in all the physical region are given in the end.