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

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

Abstract

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 amore »« less

Authors:

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)

Publication Date:: Mon Sep 20 00:00:00 EDT 2021

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States)

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

OSTI Identifier:: 1825077

Report Number(s):: BNL-222237-2021-JAAM
Journal ID: ISSN 1029-8479; TRN: US2215777

Grant/Contract Number:: SC0012704

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2021; Journal Issue: 9; Journal ID: ISSN 1029-8479

Publisher:: Springer Nature

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QCD Phenomenology; NLO Computations

Citation Formats


                    Duhr, Claude, Huss, Alexander, Mazeliauskas, Aleksas, and Szafron, Robert. An analysis of Bayesian estimates for missing higher orders in perturbative calculations.  United States: N. p., 2021. 
Web.  doi:10.1007/jhep09(2021)122.

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                    Duhr, Claude, Huss, Alexander, Mazeliauskas, Aleksas, & Szafron, Robert. An analysis of Bayesian estimates for missing higher orders in perturbative calculations.  United States.  https://doi.org/10.1007/jhep09(2021)122

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                    Duhr, Claude, Huss, Alexander, Mazeliauskas, Aleksas, and Szafron, Robert. Mon .  
"An analysis of Bayesian estimates for missing higher orders in perturbative calculations".  United States.  https://doi.org/10.1007/jhep09(2021)122.  https://www.osti.gov/servlets/purl/1825077.

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@article{osti_1825077,

  title        = {An analysis of Bayesian estimates for missing higher orders in perturbative calculations},

  author       = {Duhr, Claude and Huss, Alexander and Mazeliauskas, Aleksas and Szafron, Robert},

  abstractNote = {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.},

  doi          = {10.1007/jhep09(2021)122},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 9,

  volume       = 2021,

  place        = {United States},

  year         = {Mon Sep 20 00:00:00 EDT 2021},

  month        = {Mon Sep 20 00:00:00 EDT 2021}

}

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

Abstract

Citation Formats

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Four-loop photon quark form factor and cusp anomalous dimension in the large-N c limit of QCD journal, March 2017

Logarithmically enhanced Euler-Heisenberg Lagrangian contribution to the electron gyromagnetic factor journal, November 2020

Revised and improved value of the QED tenth-order electron anomalous magnetic moment journal, February 2018

Complete two-loop correction to the bound-electron g factor journal, August 2005

A prediction for the 4-loop β function in QCD journal, May 1997

Renormalization-scale-invariant continuation of truncated QCD (QED) series — an analysis beyond large-β0 approximation journal, April 1998

Stevenson's optimized perturbation theory applied to factorization and mass scheme dependence journal, January 1982

One-loop binding corrections to the electron g factor journal, September 2017

Leptoproduction and Drell-Yan processes beyond the leading approximation in chromodynamics journal, October 1978

Analytic bound-state solutions in a relativistic two-body formalism with applications in muonium and positronium journal, September 1977

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Higher-order corrections in threshold resummation journal, October 2005

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The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions journal, January 2016

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Padé-improved estimates of hadronic Higgs decay rates journal, July 2000

Positronium Hyperfine Splitting: Analytical Value at O ( m α 6 ) journal, January 1999

High precision determination of the gluon fusion Higgs boson cross-section at the LHC journal, May 2016

Four-loop non-singlet splitting functions in the planar limit and beyond journal, October 2017

Renormalization-prescription ambiguity in perturbative quantum chromodynamics: Has Stevenson found the solution? journal, October 1982

Convergence of the expansion of the Laplace-Borel integral in perturbative QCD improved by conformal mapping journal, July 2000

The three-loop splitting functions in QCD: the non-singlet case journal, June 2004

The full four-loop cusp anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills and QCD journal, April 2020

The three-loop relation between the and the pole quark masses journal, June 2000

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NNLO QCD corrections to Higgs pair production via vector boson fusion at hadron colliders
journal, March 2014

Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
journal, May 2019

Numerical calculation of high-order QED contributions to the electron anomalous magnetic moment
journal, October 2018

On the consistent use of scale variations in PDF fits and predictions
journal, March 2019

High-precision calculation of the 4-loop contribution to the electron g -2 in QED
journal, September 2017

Renormalization group improved perturbative QCD
journal, September 1980

Vector boson fusion at next-to-next-to-leading order in QCD: Standard model Higgs boson and beyond
journal, February 2012

Structure-function approach to vector-boson scattering in pp collisions
journal, December 1992

David Draper and E. I. George, and a rejoinder by the authors
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Scheme Variations of the QCD Coupling and Hadronic $τ$ Decays
journal, October 2016

Tenth-Order QED Contribution to the Electron $g - 2$ and an Improved Value of the Fine Structure Constant
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Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops
journal, February 2015

Higgs boson production at hadron colliders in NNLO QCD
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Physical resurgent extrapolation
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Complete renormalization group improvement — avoiding factorization and renormalization scale dependence in QCD predictions
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Higgs production and decay: analytic results at next-to-leading order QCD
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journal, August 1991

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journal, August 1981

The Sudakov form factor at four loops in maximal super Yang-Mills theory
journal, January 2018

An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations
journal, February 2015

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journal, August 1991

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journal, March 2017

Logarithmically enhanced Euler-Heisenberg Lagrangian contribution to the electron gyromagnetic factor
journal, November 2020

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journal, February 2018

Complete two-loop correction to the bound-electron $g$ factor
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journal, May 1997

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journal, April 1998

Stevenson's optimized perturbation theory applied to factorization and mass scheme dependence
journal, January 1982

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journal, September 2017

Leptoproduction and Drell-Yan processes beyond the leading approximation in chromodynamics
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journal, September 1977

Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors
journal, April 2020

Sense and nonsense in the renormalization-scheme-dependence problem
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Higher-order corrections in threshold resummation
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Two-Loop Binding Corrections to the Electron Gyromagnetic Factor
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Renormalization-scheme-invariant QCD and QED: The method of effective charges
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The QCD renormalization group equation and the elimination of fixed-order scheme-and-scale ambiguities using the principle of maximum conformality
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Quantifying correlated truncation errors in effective field theory
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Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop
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N3LO corrections to jet production in deep inelastic scattering using the Projection-to-Born method
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Asymptotic improvement of resummations and perturbative predictions in quantum field theory
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A planar four-loop form factor and cusp anomalous dimension in QCD
journal, May 2016

Padé-improved estimates of hadronic Higgs decay rates
journal, July 2000

Positronium Hyperfine Splitting: Analytical Value at $O ({m α}^{6})$
journal, January 1999

High precision determination of the gluon fusion Higgs boson cross-section at the LHC
journal, May 2016

Four-loop non-singlet splitting functions in the planar limit and beyond
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Renormalization-prescription ambiguity in perturbative quantum chromodynamics: Has Stevenson found the solution?
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Convergence of the expansion of the Laplace-Borel integral in perturbative QCD improved by conformal mapping
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The three-loop splitting functions in QCD: the non-singlet case
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α _s and the τ hadronic width: fixed-order, contour- improved and higher-order perturbation theory
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Generalization of the Brodsky-Lepage-Mackenzie optimization within the ${β}$ -expansion and the principle of maximal conformality
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Padé approximants, Borel transforms and renormalons: the Bjorken sum rule as a case study
journal, January 1996

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journal, October 2020

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journal, October 2013

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journal, August 2003

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journal, April 2015

Order $α^{7} \ln (1 / α)$ Contribution to Positronium Hyperfine Splitting
journal, December 2000

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Large- n f contributions to the four-loop splitting functions in QCD
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