Eventshape

Eventshape refers to a class of observables used in high-energy physics to characterize the geometric distribution of final-state particles produced in a collision event. These measures summarize how energy and momentum are arranged in space and serve as a link between experimental data and theoretical predictions of quantum chromodynamics (QCD). They are particularly useful for testing perturbative QCD, studying hadronization, and tuning Monte Carlo event generators.

Common event shapes include thrust, sphericity, the C-parameter, jet broadening, and jet masses. Thrust, for example, is defined by finding a unit vector that maximizes the sum of the projections of particle momenta along that direction, normalized by the total momentum. The thrust value ranges from 1/2 for a completely spherical event to 1 for a perfectly collimated, pencil-like event. The sphericity approach uses the momentum tensor constructed from particle momenta, with eigenvalues used to quantify how isotropic the event is; the sphericity is typically related to the sum of the smaller eigenvalues.

Calculation of event shapes generally uses reconstructed particle momenta from detectors, often in the center-of-mass frame for electron–positron collisions, though shapes are also studied at hadron colliders. Observables can be infrared- and collinear-safe to enable reliable theoretical predictions, or they can be designed to study specific aspects of parton showers and hadronization.

Applications of event shapes include testing QCD predictions, extracting the strong coupling constant, comparing different Monte Carlo models, and tuning simulations. In hadron collisions, initial-state radiation and multiple parton interactions introduce additional complexity, but event shapes remain valuable for probing the dynamics of QCD and for improving the modeling of complex final states.