Abstract
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.
Highlights
Ure of 1% uncertainty from the Particle Data Group (PDG) average masks significant discrepancies between different extractions
The use of Monte Carlo (MC) event generators has long been criticised on two main grounds: they are tuned on less accurate perturbative calculations, and the separation between perturbative and non-perturbative components cannot be related to today’s highest-accuracy perturbative calculations
We found that the leading hadronisation correction at the Sudakov shoulder (C = 3/4) is over a factor of two smaller than the corresponding value in the two-jet (C = 0) limit
Summary
These particular event-shape and jet-rate fits are among the most precise of a wide variety of fits to e+e− hadronic final-state data [4,5,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Existing fits calculate the hadronisation correction around the first singular point, C = 0 and extend it to the whole C-parameter spectrum. To obtain a perturbative prediction that is accurate across the whole physical spectrum, we need to match the resummed NNLL calculation to the fixed order result. The hadronisation corrections to the C parameter distribution can be described in terms of an expansion in negative powers of the centre of mass energy Q. Equation (7) includes terms to subtract the contributions already accounted for in the perturbative calculation [13,18,45] The determination of the latter is not without subtleties, in that it assumes that non-inclusive corrections to such renormalon subtraction are described by the same multiplicative M factor as for the coefficient of α0(μ2I ). The shift in the C-parameter induced by a small-kt gluer is [27,39]
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