On the universality of the Milan factor for 1/Q power corrections to jet shapes

TL;DR

This work shows that two-loop calculations render the 1/Q power corrections to jet-shape observables universally rescaled by the Milan factor across a broad class of variables, including thrust, C-parameter, jet masses, and jet broadening, with EEC extending the same correction outside back-to-back kinematics. Using a dispersive, renormalon-based framework and an infrared matching scale μ_I, the authors merge perturbative and non-perturbative contributions to yield a shift in perturbative spectra governed by a single NP parameter P, multiplied by a universal factor M. The analysis provides explicit expressions for the radiators, trigger functions, and the processed moments A1 and A1′ that characterize the leading 1/Q corrections, and discusses the resulting scale dependence, scheme dependence, and potential higher-order uncertainties. The results enable practical phenomenology by delivering renormalon-safe, resummed predictions for jet-shape distributions, and they anticipate fractional powers in certain semi-inclusive observables (e.g., Drell-Yan q_T=0) that warrant further experimental and theoretical study.

Abstract

We perform the two-loop analysis of the 1/Q power corrections to jet-shape variables. This step is necessary for producing reliable theoretical predictions for the relative magnitudes of genuine confinement effects. We show that the rescaling factor recently derived for the thrust case (the Milan factor) remains the same for the class of observables which includes the C-parameter, invariant jet masses, jet broadening and the energy-energy correlation measure. We list the expressions which should be used for extracting 1/Q power effects in jet shapes. We also envisage large non-perturbative effects, characterised by fractional powers of Q, in certain semi-inclusive observables such as the height of the spectrum of Drell-Yan lepton pairs with invariant mass Q and transverse momentum Q_t=0, and back-to-back energy flows in e^+e^- and DIS.