Anomalous scaling of linear power corrections

TL;DR

This paper demonstrates that non-perturbative power corrections in hadronic observables exhibit an anomalous scaling behavior, which can be simplified to an exponential form under certain conditions, aiding precision collider physics.

Contribution

It introduces a simplified exponential form for anomalous scaling of power corrections, extending beyond the two-jet limit and within a specific hadron mass scheme.

Findings

Scaling is modified by an anomalous dimension.

The exponential form applies to key observables like thrust and C-parameter.

The approach works beyond the two-jet limit.

Abstract

Non-perturbative corrections to hadronic observables represent a critical obstacle to increasing accuracy at colliders. Long taken to scale simply as $1/Q$, where $Q$ is the centre-of-mass scattering energy, recent work has opened the path towards calculating the anomalous dimension that modifies that scaling. A priori, the problem is complex, requiring a resummation involving arbitrary numbers of large-angle and low-energy gluons. Within a specific framework for kinematic recoil, we show that it reduces to a simple exponential for key observables like the thrust, $C$-parameter and energy correlators. This simplicity holds for a specific hadron mass scheme, and also even beyond the two-jet limit.