Measurement of the branching fraction ratio ${\cal B}(B_{c}^{+} \to \psi(2S)\pi^+)/{\cal B}(B_{c}^{+} \to J/\psi\pi^+)$

Using the $pp$ collision data collected by LHCb at center-of-mass energies $\sqrt{s} \, = 7 \, {\rm TeV} \,$ and $8 \, {\rm TeV} \,$, corresponding to an integrated luminosity of $3 \, \mathrm{fb}^{-1} \,$, the ratio of the branching fraction of the $B_{c}^{+} \to \psi(2S)\pi^+$ decay relative to that of the $B_{c}^{+} \to J/\psi\pi^+$ decay is measured to be ${0.268 \pm 0.032\mathrm{\,(stat)} \pm 0.007\mathrm{\,(syst)} \pm 0.006\,(\mathrm{BF}) }$. The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainties on the branching fractions of the $J/\psi \to \mu^{+}\mu^{-}$ and $\psi(2S) \to \mu^{+}\mu^{-}$ decays. To enhance the signal significance with limited $B_{c}^{+}$ statistics, the boosted decision tree selection is used to separate the signal and background effectively. The systematic uncertainties are discussed extensively. This measurement is consistent with the previous LHCb result, and the statistical uncertainty is halved.