Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

Yannis Burnier and Alexander Rothkopf
Phys. Rev. Lett. 111, 182003 – Published 31 October 2013

Abstract

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33TC.

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  • Received 1 August 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.182003

© 2013 American Physical Society

Authors & Affiliations

Yannis Burnier and Alexander Rothkopf

  • Albert Einstein Center for Fundamental Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland

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Issue

Vol. 111, Iss. 18 — 1 November 2013

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