Two-Sample Testing for Monte Carlo Evaluation in Particle Physics: Challenges and Opportunities

Monte Carlo (MC) simulation is central to modern particle physics, where evaluating the fidelity of simulated samples against reference distributions is a fundamental yet under-standardized task. We present \texttt{MCBench}, a modular benchmark suite for assessing MC sampling quality using distributional distance metrics, including the sliced Wasserstein distance and the maximum mean discrepancy (MMD). Applied to the high-dimensional, structured distributions arising in high-energy physics, the choice of test metric and kernel is known to affect sensitivity in high-dimensional settings \citep{Gretton2012optimal}. Whether modern learned or adaptive testing methods can provide improved sensitivity for the structured distributions arising in particle physics remains an open and practically important question. We describe the architecture of \texttt{MCBench}, illustrate key challenges posed by physics data, and outline concrete opportunities for distribution-distance-based hypothesis testing methods to advance the evaluation of physics simulators.