Measurement of the branching fraction ratio $\mathcal{B}(B_c^+ \rightarrow \psi(2S)\pi^+)/\mathcal{B}(B_c^+ \rightarrow J/\psi \pi^+)$

Using $pp$ collision data collected by LHCb at center-of-mass energies $\sqrt{s}$ = 7 TeV and 8 TeV, corresponding to an integrated luminosity of 3 fb$^{-1}$, the ratio of the branching fraction of the $B_c^+ \rightarrow \psi(2S)\pi^+$ decay relative to that of the $B_c^+ \rightarrow J/\psi\pi^+$ decay is measured to be 0.268 $\pm$ 0.032 (stat) $\pm$ 0.007 (syst) $\pm$ 0.006 (BF). The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainties on the branching fractions of the $J/\psi \rightarrow \mu^+\mu^-$ and $\psi(2S) \rightarrow \mu^+\mu^-$ decays. This measurement is consistent with the previous LHCb result, and the statistical uncertainty is halved.