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.

💡 Research Summary

The paper addresses a fundamental problem in modern high‑energy physics (HEP) experiments: how to recover the true event statistics when data are collected by a complex, multi‑level trigger system that inevitably introduces inefficiencies and artificial down‑scaling to respect bandwidth limits. The authors first outline the typical architecture of contemporary trigger systems, which consist of a fast hardware Level‑1 filter followed by one or more software levels (Level‑2, Level‑3, High‑Level Trigger). Each level is characterized by a selection efficiency ε_i (the probability that a physically interesting event satisfies the trigger condition) and a down‑scale factor d_i (the fraction of accepted events that are randomly kept to reduce the data rate). The recorded event count N_rec for a given physics process is related to the true number of produced events N_true by

 N_rec = N_true · ∑_i w_i · ε_i · d_i,

where w_i denotes the weight assigned to events selected by trigger i. When several triggers are active simultaneously, the same physical event may be selected by more than one trigger, leading to double counting if not properly corrected.

To solve this, the authors propose two complementary offline correction strategies.

1. Inclusion‑Exclusion (Exact) Method – This approach uses the mathematical inclusion‑exclusion principle to subtract the contributions of all possible trigger overlaps. It requires knowledge of the joint efficiencies ε_{i∩j…} and joint down‑scale factors d_{i∩j…} for every combination of triggers. The corrected true count is expressed as

 N_true = N_rec ·