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

Thomas Spriggs,Jon-Ivar Skullerud,Ben Page,Chris Allton,Gert Aarts,Rachel Horohan D’Arcy,Maria-Paola Lombardo,Sam Offler,Timothy Burns,Seyong Kim,Sinead M Ryan,Benjamin Jäger

doi:10.1051/epjconf/202225805011

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.

Highlights

There has been a great deal of interest in onia systems in the context of heavy-ion collision experiments, since the proposal they behave as a proxy for the temperature [1]
Project, in which the long-term aim is to test and compare these and other methods, using the same lattice dataset in order to extract the best estimates of the bottomonium spectrum at finite temperature
Because the b-quark’s mass is larger than any other mass scale, it can be approximated as a non-relativistic particle and the NRQCD e↵ective theory can be used for its dynamics

Summary

Introduction

There has been a great deal of interest in onia systems in the context of heavy-ion collision experiments, since the proposal they behave as a proxy for the temperature [1]. The fastsum collaboration has had a long programme of studying the bottomonium spectrum at non-zero temperature using the NRQCD method [3], principally using the Maximum Entropy Method [4]. We have determined both S- and P-wave masses and determined upper bounds for the state’s widths. We extend this work here to include three new analysis techniques to determine the bottomonium spectrum, including the widths of the states These approaches are: a Maximum Likelihood approach using a Gaussian spectral function for the ground state Project, in which the long-term aim is to test and compare these and other methods, using the same lattice dataset in order to extract the best estimates of the bottomonium spectrum at finite temperature

Lattice Method

Gaussian Maximum Likelihood

Backus Gilbert

Kernel Ridge Regression

Conclusion