Analytical description of missing transverse-momentum trigger rates in ATLAS with 7 and 8 TeV data

The missing transverse-momentum (MET) trigger of the ATLAS experiment is based on the measurement of the energy deposited over the full calorimeter acceptance. The MET trigger rate for a fixed threshold therefore strongly depends on the number of collisions per bunch crossing produced by the CERN LHC. For useful trigger thresholds, the MET trigger rate is dominated by mismeasuement giving rise to an apparent transverse-momentum imbalance, rather than particles escaping the detector. This note presents an analytic model for the resulting MET distribution, which arises from two main sources. At low MET values, detector resolution effects dominate. These depend on the scalar sum of the transverse projection of energies measured in the event and on the mean number \mu of collisions per bunch crossing (a measure of the LHC instantaneous luminosity). In this region, the MET trigger rate decreases exponentially with the trigger’s MET threshold value. However, in the same region the absolute rate of a fixed threshold trigger increases exponentially with increasing \mu, making it very hard to obtain reliable rate predictions for high-luminosity LHC runs. On the other hand, large MET events arise primarily from error in the determination of single-jet transverse-momenta. The trigger rates for high MET thresholds are basically independent of SumET and only depend on \mu, and behave in a fashion similar to that of single-jet triggers with hight threshold on jet transverse-momentum. Event-by-event, the two contributions to MET add up vectorially with a random angle between them. Hence, the overall distribution is modeled as a random overlap of the stochastic contribution due to the finite calorimeter resolution, dominating at low energy and representing the biggest fraction of events, and the hard tail of large MET values induced by jet momentum mismeasurements. Trigger rate predictions based on this model are presented for the high-luminosity LHC runs.