Likelihood-Based Unsupervised Anomaly Detection in CMS Dijet Events

Anomaly detection, the identification of collision events that deviate from Standard Model expectations, is one of the most promising model-agnostic strategies for new-physics searches at the Large Hadron Collider. Searching for rare events in learned low-dimensional representations removes the need to commit to hand-crafted observables a priori, but sacrifices the immediate physical interpretation those observables provide. For anomaly detection to enter a discovery pipeline, flagged events must therefore be diagnosed locally, both to distinguish potential new physics from mismodeling or detector effects and to identify observables for targeted follow-up searches. We evaluate supervised and self-supervised neural embedding strategies on COLLIDE-2V, a 750-million-event dataset simulated under realistic High-Luminosity LHC conditions, using the reconstruction error of an autoencoder trained in the learned latent space as the anomaly score. Across the configurations and benchmark signals considered, supervised objectives, which exploit simulation process labels during training, generally outperform their self-supervised counterparts and, in their best configurations, improve on an autoencoder trained directly on kinematic features, raising the signal efficiency at 10% background acceptance on all held-out processes. We further introduce a local diagnostic pipeline that fits a Gaussian Mixture Model to the SM latent space, profiles each component through high-level observables without process labels, localizes the flagged events, and ranks observables by their local discriminating power. The ranking recovers the defining kinematics of the held-out processes, while correlating the anomaly score with the same observables quantifies how closely the score tracks them, revealing cases where the most discriminating observable is not the one the score follows most closely.

We report a search for dark matter (DM) produced in association with a leptonically decaying $Z$ boson at $\sqrt{s}=13$ TeV using CMS Run 2015D open data corresponding to an integrated luminosity of $2.32\,\mathrm{fb}^{-1}$ together with simplified-model Monte Carlo simulation. Events are selected in the mono-$Z\rightarrow\ell^+\ell^-$ final state in both the $μμ$ and $ee$ channels. Forty kinematic observables are extracted from MINIAOD and MINIAODSIM, cleaned with physics-motivated selections, and reduced to a 37-dimensional feature vector. Five Neural Spline Flows are trained independently to model Standard Model background and mediator-specific DM signal densities. The per-event test statistic is constructed from the log-likelihood ratio between the signal and background density estimates, providing sensitivity across the full kinematic phase space without requiring a hard upper $\mathrm{MET}$ threshold. A simultaneous profile-likelihood fit combining the two channels yields observed (expected) 95% confidence level upper limits on the signal-strength parameter of $μ<0.0177$ ($0.0018$) for the scalar mediator, $μ<0.0362$ ($0.0039$) for the vector mediator, and $μ<0.0498$ ($0.0069$) for the axial-vector mediator. The observed limits are weaker than expected because of a residual high-$\mathrm{MET}$ background-modeling discrepancy rather than evidence for a DM signal. To our knowledge, this is the first application of Neural Spline Flow likelihood-ratio scoring to a mono-$Z$ dark matter search using CMS Run 2015D open data simultaneously in the $μμ$ and $ee$ channels.

Machine-learned anomaly detection is reshaping searches for new physics, but it has outrun the statistics used to interpret it. A raw anomaly score has no calibrated meaning, a model that scans many regions inflates the look-elsewhere effect, and the asymptotic significances the field relies on are blind to the background mismodelling that anomaly detectors are especially prone to. We propose a calibration layer, built on conformal prediction, that turns any anomaly score into a defensible significance with distribution-free, finite-sample guarantees. Conformal prediction converts scores into valid local p-values, weighted and Mondrian variants repair the sideband-to-signal-region exchangeability failures that resonant searches suffer, and a Gross-Vitells step carries the result through to a look-elsewhere-aware global significance. The layer does two things at once. It exposes miscalibration that the standard pipeline cannot see, and it corrects it without retraining the detector. On public LHC Olympics data, a classifier develops a substructure-mass correlation that makes sideband-calibrated background p-values anti-conservative. Taken at face value, this manufactures a $\sim 46σ$ excess from background sculpting alone, which the label-free weighted correction removes, restoring an honest null. When run as a blind wide-mass bump hunt, the standard asymptotic and unweighted procedures fabricate $\gtrsim10σ$ excesses and $\approx5σ$ excesses even in signal-free windows, while the conformal layer raises no false alarms and its global false-positive rate is verified on background-only pseudoexperiments. The result is an auditable, detector-agnostic path from an uncalibrated score to a trials-factor-aware significance, ready to be folded into experimental anomaly searches.