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  • Letter
  • Open Access

Robust estimates of theoretical uncertainties at fixed-order in perturbation theory

Matthew A. Lim1,* and Rene Poncelet2,†

  • *Contact author: m.a.lim@sussex.ac.uk
  • †Contact author: rene.poncelet@ifj.edu.pl
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Phys. Rev. D 112, L111901 – Published 11 December, 2025

DOI: https://doi.org/10.1103/7g5k-4y3v

Abstract

Calculations truncated at a fixed order in perturbation theory are accompanied by an associated theoretical uncertainty, which encodes the missing higher orders (MHOU). This is typically estimated by a scale variation procedure, which has well-known shortcomings. In this work, we propose a simple prescription to directly encode the missing higher order terms using theory nuisance parameters (TNPs) and estimate the uncertainty by their variation. We study multiple processes relevant for Large Hadron Collider physics at next-to-leading and next-to-next-to-leading order in perturbation theory, obtaining MHOU estimates for differential observables in each case. In cases where scale variations are well-behaved we are able to replicate their effects using TNPs, while we find significant improvement in cases where scale variation typically underestimates the uncertainty.

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Information

Phys. Rev. D 112, L111901– Published 11 December, 2025
  • Received 15 January 2025
  • Accepted 29 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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