# One-loop Angularity Distributions with Recoil using Soft-Collinear Effective Theory

## TL;DR

This paper develops a comprehensive Soft-Collinear Effective Theory framework to compute one-loop angularity distributions for all recoil-sensitive angularities, including previously uncalculated sub-leading effects, enhancing precision in QCD event shape analysis.

## Contribution

It provides the first one-loop calculations of angularity distributions for all values of the parameter b, incorporating recoil effects and extending theoretical understanding beyond the thrust limit.

## Key findings

- Agreement with Event2 generator results
- Identification of sub-leading singular contributions
- Recoil effects significantly impact peak region distributions

## Abstract

Angularities are event shapes whose sensitivity to the splitting angle of a collinear emission is controlled by a continuous parameter $b$, with $ -1 < b < \infty$. When measured with respect to the thrust axis, this class of QCD observables includes thrust ($b=1$) and jet broadening ($b=0$), the former being insensitive to the recoil of soft against collinear radiation, while the latter being maximally sensitive to it. Presently available analytic results for angularity distributions with $b \neq 0$ can be applied only close to the thrust limit since recoil effects have so far been neglected. As a first step to establish a comprehensive theoretical framework based on Soft-Collinear Effective Theory valid for all recoil-sensitive angularities, we compute for the first time angularity distributions at one-loop order in $\alpha_s$ for all values of $b$ taking into account recoil effects. In the differential cross section, these amount to novel sub-leading singular contributions and/or power corrections, where the former are characterized by fractional powers of the angularity and contribute appreciably close to the peak region, also for $b \gtrsim 0.5$. Our calculations are checked against various limits known in the literature and agree with the numerical output of the Event2 generator.