Bayesian inference of non-positive spectral functions in quantum field theory

TL;DR

This paper extends a Bayesian deconvolution method to handle non-positive spectral functions in quantum field theory, enabling more accurate reconstructions of spectra with negative features, exemplified by gluon spectral functions in QCD.

Contribution

The paper introduces a generalized Bayesian approach for non-positive spectral functions, maintaining key properties and allowing hyperparameter integration, with applications demonstrated on QCD-inspired spectra.

Findings

Successfully reconstructs non-positive spectral functions

Preserves scale invariance in the Bayesian framework

Effective in analyzing gluon spectral functions in QCD

Abstract

We present the generalization to non positive definite spectral functions of a recently proposed Bayesian deconvolution approach (BR method). The novel prior used here retains many of the beneficial analytic properties of the original method, in particular it allows us to integrate out the hyperparameter $\alpha$ directly. To preserve the underlying axiom of scale invariance, we introduce a second default-model related function, whose role is discussed. Our reconstruction prescription is contrasted with existing direct methods, as well as with an approach where shift functions are introduced to compensate for negative spectral features. A mock spectrum analysis inspired by the study of gluon spectral functions in QCD illustrates the capabilities of this new approach.