Estimation of the chances to find new phenomena at the LHC in a model-agnostic combinatorial analysis

In this paper, we estimate the number of event topologies that have the potential to be produced in $pp$ collisions at the Large Hadron Collider (LHC) without violating kinematic and other constraints. We use numerical calculations and combinatorics, guided by large-scale Monte Carlo simulations of Standard Model (SM) processes. Then, we set the upper limit on the probability that new physics may escape detection, assuming a model-agnostic approach. The calculated probability is unexpectedly large, and the fact that the LHC has not found new physics until now is not entirely surprising. We argue that the optimal direction for maximizing the chances of finding new physics is to use unsupervised machine learning for anomaly detection or algorithms designed for event classification.