Event selection of $\rm B_c^\pm \rightarrow J/\psi(\mu^+\mu^-) \pi^\pm$ and estimate of the event yield

In this note, a Monte Carlo study of the $\rm B_c^\pm \rightarrow J/\psi(\mu^+\mu^-) \pi^\pm$ selection at the LHCb experiment is presented. Using a simulated $\rm B_c^\pm$ signal sample and the relevant background samples, event selection criteria were determined. The key selection cuts were optimized to improve the signal-to-background ratio. The background is difficult to evaluate as the background Monte Carlo statistics is limited. To do an estimate of the background level, the correlations between the key selection criteria were studied. The key selection cuts were divided into two almost uncorrelated sets. They were imposed independently to obtain their background rejection rates, whose product was taken as the total rejection rate. About $311 \pm 5 \mbox{(stat.)}$ signal events are expected for a data set which corresponds to an integrated luminosity of 1 fb$^{-1}$. A $B/S$ ratio of 2 is found.