C-parameter hadronisation in the symmetric 3-jet limit and impact on αs fits

Hadronisation corrections are crucial in extractions of the strong coupling constant (alpha s) from event-shape distributions at lepton colliders. Although their dynamics cannot be understood rigorously using perturbative methods, their dominant effect on physical observables can be estimated in singular configurations sensitive to the emission of soft radiation. The differential distributions of some event-shape variables, notably the C parameter, feature two such singular points. We analytically compute the leading non-perturbative correction in the symmetric three-jet limit for the C parameter, and find that it differs by more than a factor of two from the known result in the two-jet limit. We estimate the impact of this result on strong coupling extractions, considering a range of functions to interpolate the hadronisation correction in the region between the 2 and 3-jet limits. Fitting data from ALEPH and JADE, we find that most interpolation choices increase the extracted alpha s, with effects of up to 4% relative to standard fits. This brings a new perspective on the long-standing discrepancy between certain event-shape alpha s fits and the world average.

Automated summary

Hadronisation corrections are crucial for extracting the strong coupling constant from event-shape distributions at lepton colliders. The leading non-perturbative correction in the symmetric three-jet limit for the C parameter differs significantly from the known result in the two-jet limit. Most interpolation choices in the region between the 2 and 3-jet limits increase the extracted alpha s by up to 4%, revealing a new perspective on the discrepancy between certain event-shape alpha s fits and the world average.