# Integrated and Differential Accuracy in Resummed Cross Sections

## TL;DR

This paper introduces the $\sigma$-improved scheme, a method to enhance the consistency and uncertainty estimation of resummed cross sections by including higher-order terms and using profile scales, demonstrated on thrust distribution.

## Contribution

The paper proposes a novel $\sigma$-improved scheme that improves the agreement between the spectrum and cumulant in resummed QCD predictions, with a generic algorithm for profile scale determination.

## Key findings

- Improved agreement between spectrum and cumulant predictions.
- Robust uncertainty estimates for integrated spectra.
- Application to thrust distribution at various perturbative orders.

## Abstract

Standard QCD resummation techniques provide precise predictions for the spectrum and the cumulant of a given observable. The integrated spectrum and the cumulant differ by higher-order terms which, however, can be numerically significant. In this paper we propose a method, which we call the $\sigma\text{-improved}$ scheme, to resolve this issue. It consists of two steps: (i) include higher-order terms in the spectrum to improve the agreement with the cumulant central value, and (ii) employ profile scales that encode correlations between different points to give robust uncertainty estimates for the integrated spectrum. We provide a generic algorithm for determining such profile scales, and show the application to the thrust distribution in $e^+e^-$ collisions at NLL$'$+NLO and NNLL$'$+NNLO.