K\"all\'en-Lehmann Spectral Representation of the Scalar SU(2) Glueball

TL;DR

This paper introduces a method to extract the K"allén-Lehmann spectral density from lattice QCD data to estimate the scalar SU(2) glueball spectrum, providing a new perspective on glueball states and their excitations.

Contribution

It proposes a novel inversion technique to determine the spectral density from lattice correlators, applied to the SU(2) glueball spectrum, and validates results against traditional methods.

Findings

Ground state mass estimates agree with traditional methods

Spectral density reveals potential excited states

Method successfully extracts spectral information from lattice data

Abstract

The estimation of the K\"all\'en-Lehmann spectral density from gauge invariant lattice QCD two point correlation functions is proposed, and explored via an appropriate inversion method. As proof of concept the SU(2) glueball spectrum for the quantum numbers $J^{PC} = 0^{++}$ is investigated for various values of the lattice spacing. The spectral density and the glueball spectrum are estimated using the published data of arXiv:1910.07756. Our estimates for the ground state mass are in good agreement with the traditional approach published therein, which is based on the large time exponential behaviour of the correlation functions. Furthermore, the spectral density also contains hints of excites states in the spectrum.