QCD corrections to the $B_c$ to charmonia semi-leptonic decays

Understand

We present a detailed analysis on the $B_c$ meson semi-leptonic decays, $B_c \to \eta_c (J/\psi) \ell \nu$, up to next-to-leading order (NLO) QCD correction.

• We adopt the principle of maximum conformality (PMC) to set the renormalization scales for those decays.
• After applying the PMC scale setting, we determine the optimal renormalization scale for the $B_c\to\eta_c(J/\psi)$ transition form factors (TFFs).
• Because of the same $\{\beta_0\}$-terms, the optimal PMC scales at the NLO level are the same for all those TFFs, i.e.