NNLO beam functions for angularity distributions

TL;DR

This paper computes NNLO beam functions for seven angularity observables, enhancing precision in collider event shape analysis and enabling NNLL' resummation in deep inelastic scattering.

Contribution

It provides the first NNLO calculations of quark and gluon beam functions for angularities, extending automated SCET-2 methods to SCET-1 observables.

Findings

Computed NNLO beam functions for seven angularities.

Results enable NNLL' resummation of DIS angularity distributions.

Automated framework successfully adapted for SCET-1 cases.

Abstract

The popular class of angularity event shapes provides a wealth of information on the hadronic final-state distribution in collider events. While initially proposed for $e^+ e^-$ collisions, angularities have more recently attracted considerable interest as a jet substructure observable at hadron colliders. Moreover, angularities can be measured as a global event shape in deep inelastic electron-nucleon scattering (DIS), and the respective factorisation theorem contains a beam function that parametrises the collinear initial-state radiation. In the present work, we compute the quark and gluon beam functions for seven different angularities to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on an automated framework that was previously developed for SCET-2 observables, and which we transfer in the current work to the generic SCET-1 case. Our results are relevant for resumming DIS angularity distributions at NNLL$'$ accuracy.