Earth mover's distance as a measure of CP violation

TL;DR

This paper presents a novel unbinned test for detecting CP violation using Wasserstein distance, demonstrating comparable sensitivity to existing methods and offering improved computational efficiency for large datasets.

Contribution

Introducing a new Wasserstein distance-based test statistic for CP violation detection, with variants that improve computational performance and retain localization information.

Findings

Comparable sensitivity to energy tests in CP violation detection

Enhanced computational efficiency with binned and sliced Wasserstein variants

Effective application to Dalitz plot distributions of meson decays

Abstract

We introduce a new unbinned two sample test statistic sensitive to CP violation utilizing the optimal transport plan associated with the Wasserstein (earth mover's) distance. The efficacy of the test statistic is shown via two examples of CP asymmetric distributions with varying sample sizes: the Dalitz distributions of $B^0 \rightarrow K^+\pi^-\pi^0$ and of $D^0 \rightarrow \pi^+\pi^-\pi^0$ decays. The windowed version of the Wasserstein distance test statistic is shown to have comparable sensitivity to CP violation as the commonly used energy test statistic, but also retains information about the localized distributions of CP asymmetry over the Dalitz plot. For large statistic datasets we introduce two modified Wasserstein distance based test statistics -- the binned and the sliced Wasserstein distance statistics, which show comparable sensitivity to CP violation, but improved computing time and memory scalings. Finally, general extensions and applications of the introduced statistics are discussed.