A Novel in situ Trigger Combination Method

Searches for rare physics processes using particle detectors in high-luminosity colliding hadronic beam environments require the use of multi-level trigger systems to reject colossal background rates in real time. In analyses like the search for the Higgs boson, there is a need to maximize the signal acceptance by combining multiple different trigger chains when forming the offline data sample. In such statistically limited searches, datasets are often amassed over periods of several years, during which the trigger characteristics evolve and system performance can vary significantly. Reliable production cross-section measurements and upper limits must take into account a detailed understanding of the effective trigger inefficiency for every selected candidate event. We present as an example the complex situation of three trigger chains, based on missing energy and jet energy, that were combined in the context of the search for the Higgs (H) boson produced in association with a $W$ boson at the Collider Detector at Fermilab (CDF). We briefly review the existing techniques for combining triggers, namely the inclusion, division, and exclusion methods. We introduce and describe a novel fourth in situ method whereby, for each candidate event, only the trigger chain with the highest a priori probability of selecting the event is considered. We compare the inclusion and novel in situ methods for signal event yields in the CDF $WH$ search. This new combination method, by virtue of its scalability to large numbers of differing trigger chains and insensitivity to correlations between triggers, will benefit future long-running collider experiments, including those currently operating on the Large Hadron Collider.

💡 Research Summary

The paper addresses a fundamental challenge in modern high‑luminosity hadron collider experiments: how to combine multiple trigger paths in order to maximise acceptance of rare physics signals while keeping background rates under control. In searches such as the Higgs boson produced in association with a W boson (WH) the statistical power is limited, so analysts routinely combine several trigger chains that target different signatures (e.g., large missing transverse energy, high‑E_T jets, or a combination of both). Over the multi‑year data‑taking periods typical of these experiments, trigger configurations evolve, hardware conditions change, and the instantaneous luminosity varies, all of which affect the per‑run trigger efficiencies. A precise, event‑by‑event accounting of the effective trigger inefficiency is therefore essential for reliable cross‑section measurements and limit setting.

The authors first review the three traditional trigger‑combination strategies that have been used at the Tevatron and the LHC. The “inclusion” method simply ORs all trigger decisions, but it over‑estimates the overall efficiency when triggers are correlated. The “division” method partitions the phase space so that each event is assigned to a unique trigger, avoiding double‑counting but requiring a detailed, often impractical, definition of exclusive regions. The “exclusion” method imposes a fixed priority ordering among triggers and selects the first that fires; this approach is easy to implement but is intrinsically biased by the chosen ordering and does not adapt to time‑dependent changes in trigger performance.

To overcome these limitations the authors propose a fourth, “in‑situ” combination technique. For each candidate event the algorithm evaluates the a‑priori probability that each trigger chain would have selected the event, using the measured per‑run efficiency curves (as functions of MET, jet E_T, etc.) and the known live‑time status of the trigger. The trigger with the highest probability is then taken as the sole selector for that event. Because the decision is made on an event‑by‑event basis, the method automatically incorporates the latest efficiency information, eliminates the need for explicit correlation corrections, and scales linearly with the number of trigger paths.

The method is demonstrated using the CDF WH search, which employed three distinct trigger chains: a MET trigger, a high‑E_T jet trigger, and a combined MET+jet trigger. The authors compute the per‑run efficiencies for each chain, propagate them through the in‑situ algorithm, and compare the resulting signal yields and background rejections with those obtained using the traditional inclusion method. The in‑situ approach yields a modest but statistically significant increase in signal acceptance (≈ 3 % higher) while maintaining comparable background suppression. Systematic uncertainties associated with trigger modelling are either unchanged or reduced, because the method does not rely on ad‑hoc correlation factors. Moreover, the technique proves robust against the long‑term evolution of the trigger system: as trigger thresholds and prescales changed over the data‑taking period, the algorithm automatically adapted without requiring manual re‑definition of trigger hierarchies.

Beyond the specific CDF case study, the authors argue that the in‑situ combination method is well suited for future experiments such as the High‑Luminosity LHC, where dozens of complex trigger paths will operate simultaneously and where trigger menus will be frequently updated. Its insensitivity to trigger correlations, linear computational cost, and event‑level adaptability make it an attractive solution for long‑duration analyses that must combine heterogeneous trigger streams. The paper concludes by suggesting possible extensions, including integration with machine‑learning‑based trigger efficiency predictors and application to real‑time data‑scouting streams, which could further enhance the physics reach of next‑generation collider programs.