Data driven trigger efficiency determination at LHCb

We demonstrate in detail the trigger efficiency evaluation of the LHCb trigger system purely on data with the so-called TISTOS method. The discussion includes an explicit overview of the uncertainty propagation. Additionally, we present a way to reduce the systematic uncertainty of the TISTOS method by binning the phase space. As an example, the binning is performed in the $B$ meson phase space for $B^+ \to J/\psi K^+$ decays. A large sample of simulated events is used to determine the systematic uncertainties. Following the procedure discussed in this note, the trigger efficiency can be correctly determined for any dataset of sufficient size, including a realistic determination of systematic uncertainties. The developed method is used to measure the trigger efficiency of $B^+ \to J/\psi K^+$ events in a dataset corresponding to an integrated luminosity of 3 fb$^{-1}$, collected in 2011 and 2012. The numerical values determined here have been used for the 3 fb$^{-1}$ measurement of the branching fraction of the rare decay $B^0_s \to \mu^+ \mu^-$.