Hadronisation corrections are crucial in extractions of the strong coupling constant 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.
I will discuss the calculation of the leading non-perturbative correction in the symmetric three-jet limit for this observable, and find that it differs by more than a factor of two from the known result in the two-jet limit. This result is used to estimate the uncertainty due to the description of non-perturbative corrections in strong coupling extractions from experimental data, finding effects of up to 3-4% 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.
