Particle theory

Abstract:

Hadronisation corrections are crucial in extractions of the strong coupling constant (αs) 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 αs, with effects of up to 4% relative to standard fits. This brings a new perspective on the long-standing discrepancy between certain event-shape αs fits and the world average.

Abstract:

Hodge numbers of Calabi-Yau manifolds depend non-trivially on the underlying manifold data and they present an interesting challenge for machine learning. In this letter we consider the data set of complete intersection Calabi-Yau four-folds, a set of about 900,000 topological types, and study supervised learning of the Hodge numbers h1,1 and h3,1 for these manifolds. We find that h1,1 can be successfully learned (to 96% precision) by fully connected classifier and regressor networks. While both types of networks fail for h3,1, we show that a more complicated two-branch network, combined with feature enhancement, can act as an efficient regressor (to 98% precision) for h3,1, at least for a subset of the data. This hints at the existence of an, as yet unknown, formula for Hodge numbers.