Towards the application of the Maximum Entropy Method to finite temperature Upsilon Spectroscopy

TL;DR

This paper explores the use of the Maximum Entropy Method to extract spectral functions from finite temperature Upsilon correlation data, addressing the challenge of defining particle masses in thermal systems.

Contribution

It demonstrates the implementation and testing of the Maximum Entropy Method on zero temperature Upsilon correlation functions from NRQCD simulations.

Findings

Maximum Entropy Method successfully extracts spectral functions.

Different smearing functions impact the spectral results.

Method provides a new approach for finite temperature particle analysis.

Abstract

According to the Narnhofer Thirring Theorem interacting systems at finite temperature cannot be described by particles with a sharp dispersion law. It is therefore mandatory to develop new methods to extract particle masses at finite temperature. The Maximum Entropy method offers a path to obtain the spectral function of a particle correlation function directly. We have implemented the method and tested it with zero temperature Upsilon correlation functions obtained from an NRQCD simulation. Results for different smearing functions are discussed.