Relativistic corrections to the form factors of $B_c$ into $S$-wave Charmonium

Understand

We investigate the form factors of $B_c$ meson into $S$-wave charmonium within the nonrelativistic QCD effective theory and obtain the next-to-leading order relativistic corrections to the form factors, where both the $B_c$ meson and the charmonium are treated as the nonrelativistic bound states.

• Treating the charm quark as a light quark in the limit \ $m_c/m_b\to 0$, some form factors are identical at the maximum recoil point, which are consistent with the predictions in the heavy-quark effective theory and the large-energy effective theory.
• Considering that the branching ratios of $B^+_c \to J/\psi D_s^+$ and $B^+_c \to J/\psi D_s^{*+}$ have been measured by the LHCb and ATLAS Collaborations recently, we employ the form factors of $B_c$ meson into $S$-wave charmonium at the next-to-leading order accuracy to these two decay channels and obtain more precise predictions of their decay rates.
• Numerical results indicate that the factorizable diagrams dominate the contribution in these two channels, while the colour-suppressed and the annihilation diagrams contribute less than 10 percent.