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

TL;DR

This paper introduces a new method using theory nuisance parameters to more accurately estimate uncertainties from missing higher orders in perturbative calculations, improving upon traditional scale variation methods.

Contribution

It proposes a simple prescription with theory nuisance parameters to directly encode missing higher order terms and estimate uncertainties more reliably.

Findings

TNP-based estimates match scale variations when well-behaved.

TNP method improves uncertainty estimates where scale variation underestimates.

Application to LHC processes at NLO and NNLO demonstrates effectiveness.

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.