Study of the $\rm B_c^\pm$ lifetime measurement using the exclusive decay $\rm B_c^\pm \rightarrow J/\psi(\mu^+\mu^-) \pi^\pm$ at LHCb

This note describes a Monte Carlo study of the $\rm B_c^\pm$ lifetime measurement using the exclusive decay $\rm B_c^\pm\rightarrow J/\psi(\mu^+\mu^-) \pi^\pm$ at LHCb. In order to reduce the systematic uncertainty introduced by the limited knowledge of the $p_{\rm T}$($\rm B_c^\pm$) distribution, the sample was divided into two $p_{\rm T}$($\rm B_c^\pm$) intervals, 5 GeV/$c<p_{\rm T}{\rm(B_c^\pm)}<12$ GeV/$c$ and $p_{\rm T}{\rm (B_c^\pm)} \geq$ 12 GeV/$c$. A combined mass-lifetime fit was performed in the two $p_{\rm T}$($\rm B_c^\pm$) intervals simultaneously. A statistical uncertainty below 30 fs can be achieved with 1 fb$^{-1}$ of data for a signal yield of 100 (260) events and a $B/S$ ratio of 6 (1) in the first (second) $p_{\rm T}$($\rm B_c^\pm$) bin.