On the Statistical Interpretation of Discoveries in LHC Data

We examine discovery criteria at the Large Hadron Collider (LHC) within a model-independent framework, with particular emphasis on the statistical signatures of new physics. This study is motivated by the recent shift from model-specific searches based on a small number of distributions to broad, model-agnostic strategies, which offer substantially greater sensitivity to unexpected phenomena. We revisit the well-known criterion of a local statistical significance of $5\,\sigma$ for the observation of new phenomena in invariant-mass distributions and discuss how this threshold should be modified to account for look-elsewhere effects arising not only from multiple bins within a given distribution, but also from the simultaneous consideration of multiple distributions. We present a simple but statistically conservative relation between local and global significances in the presence of multiple invariant-mass distributions at the LHC, which can serve as a useful first approximation for planning future measurements.