Methodology for the Simulation of Single-Muon and Di-Muon Trigger Rates at the CMS Experiment in the Presence of PileöUp

At the Large Hadron Collider at CERN, an average of 17.3 inelastic interactions will occur per beam crossing at design luminosity. Muon trigger rates in the presence of this pile-up can be simulated in two different ways. Firstly, the trigger response can be simulated for single interactions and the effect of piling up such interactions can then be taken into account, analytically. Secondly, interactions can be superimposed in order to construct beam crossings as they will occur at the LHC and the trigger response can be simulated for these beam crossings. The application of the first method to singleömuon and diömuon trigger rates is discussed. The obtained rates are exact but interference effects of particles from multiple interactions contributing to the same trigger object are neglected. The second method includes these interference effects, explicitly. It can be used to study any ty pe of trigger condition, including topological multi-object triggers. If crossings were constructed from completely unbiased minimum bias events, an excessive number of events would be required to obtain accurate trigger rates. A technique to pile up interactions that are generated in bins of muon transverse momentum therefore has been developed which allows to obtain accurate trigger rates up to high trigger thresholds with much smaller datasets. It has been applied to the construction of a sample of crossings used for the study of diömuon trigger rates in the Compact Muon Solenoid experiment.