Combining Triggers in HEP data analysis

Modern high-energy physics experiments collect data using dedicated complex multi-level trigger systems which perform an online selection of potentially interesting events. In general, this selection suffers from inefficiencies. A further loss of statistics occurs when the rate of accepted events is artificially scaled down in order to meet bandwidth constraints. An offline analysis of the recorded data must correct for the resulting losses in order to determine the original statistics of the analysed data sample. This is particularly challenging when data samples recorded by several triggers are combined. In this paper, we present methods for the calculation of the offline corrections and study their statistical performance. Implications on building and operating trigger systems are discussed.