An analysis of Bayesian estimates for missing higher orders in perturbative calculations

Duhr, Claude; Huss, Alexander; Mazeliauskas, Aleksas; Szafron, Robert

doi:10.1007/jhep09(2021)122

An analysis of Bayesian estimates for missing higher orders in perturbative calculations

Journal Article · Mon Sep 20 00:00:00 EDT 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep09(2021)122· OSTI ID:1825077

Duhr, Claude ^[1]; Huss, Alexander ^[1]; ^[1]; Szafron, Robert ^[2]

European Organization for Nuclear Research (CERN), Geneva (Switzerland)
Brookhaven National Lab. (BNL), Upton, NY (United States)

With current high precision collider data, the reliable estimation of theoretical uncertainties due to missing higher orders (MHOs) in perturbation theory has become a pressing issue for collider phenomenology. Traditionally, the size of the MHOs is estimated through scale variation, a simple but ad hoc method without probabilistic interpretation. Bayesian approaches provide a compelling alternative to estimate the size of the MHOs, but it is not clear how to interpret the perturbative scales, like the factorisation and renormalisation scales, in a Bayesian framework. Recently, it was proposed that the scales can be incorporated as hidden parameters into a Bayesian model. In this paper, we thoroughly scrutinise Bayesian approaches to MHO estimation and systematically study the performance of different models on an extensive set of high-order calculations. We extend the framework in two significant ways. First, we define a new model that allows for asymmetric probability distributions. Second, we introduce a prescription to incorporate information on perturbative scales without interpreting them as hidden model parameters. We clarify how the two scale prescriptions bias the result towards specific scale choice, and we discuss and compare different Bayesian MHO estimates among themselves and to the traditional scale variation approach. Finally, we provide a practical prescription of how existing perturbative results at the standard scale variation points can be converted to 68%/95% credibility intervals in the Bayesian approach using the new public code MiHO.

View Accepted Manuscript (DOE)

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0012704

OSTI ID:: 1825077

Report Number(s):: BNL--222237-2021-JAAM

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 9 Vol. 2021; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders Bonvini, Marco The European Physical Journal C, Vol. 80, Issue 10 https://doi.org/10.1140/epjc/s10052-020-08545-z	journal	October 2020
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