Measurements of multijet event isotropies using optimal transport with the ATLAS detector

A measurement of novel event shapes characterizing the isotropy of collider events is performed in 139 fb$^{-1}$ of proton--proton collisions with $\sqrt{s}=13$ TeV centre-of-mass energy recorded with the ATLAS detector at CERN's Large Hadron Collider. These event shapes are defined as the distance between collider events and isotropic reference geometries with cylindrical and circular symmetries. The evaluation of this distance is framed as an optimal transport problem, using the `energy-mover's distance.' The event-shape variables are corrected for detector effects, and measured triple-differentially in inclusive bins of jet multiplicity the scalar sum of the leading jet pair transverse momentum. The measured distributions are provided as an inputs to future Monte Carlo tuning campaigns and other QCD studies utilizing event-shape distributions.