A comparison of spectral reconstruction methods applied to non-zero temperature NRQCD meson correlation functions

TL;DR

This paper compares three spectral reconstruction methods—Maximum Likelihood, Backus Gilbert, and Kernel Ridge Regression—for analyzing bottomonium meson correlation functions at various temperatures using lattice QCD data.

Contribution

It introduces and evaluates the effectiveness of three different spectral reconstruction techniques applied to finite-temperature bottomonium data.

Findings

Maximum Likelihood provides reliable ground state extraction.

Backus Gilbert offers a model-independent spectral estimate.

Kernel Ridge Regression demonstrates promising machine learning capabilities.

Abstract

We present results from the fastsum collaboration's programme to determine the spectrum of the bottomonium system as a function of temperature. Three different methods of extracting spectral information are discussed: a Maximum Likelihood approach using a Gaussian spectral function for the ground state, the Backus Gilbert method, and the Kernel Ridge Regression machine learning procedure. We employ the fastsum anisotropic lattices with 2+1 dynamical quark flavours, with temperatures ranging from 47 to 375 MeV.