Mass estimates of the SU(2) $0^{++}$ glueball from spectral methods

TL;DR

This paper introduces a spectral method using Tikhonov regularisation to estimate the SU(2) $0^{++}$ glueball mass spectrum from lattice QCD data, offering an alternative to traditional exponential decay analysis.

Contribution

It develops and tests a spectral density inversion technique for glueball mass estimation, demonstrating its effectiveness and providing new insights into excited states.

Findings

Ground state mass estimates agree with traditional methods.

Spectral density reveals potential excited states.

Method is competitive with Maximum Entropy Method.

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 inversion strategy based on Tikhonov regularisation. We test the method on a mesonic toy model, showing that our methodology is competitive with the traditional Maximum Entropy 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, using the published data of arXiv:1910.07756. Our estimates for the ground state mass are in good agreement with the traditional approach, 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. Spectroscopic analysis of glueball two-point functions therefore provides a straightforward and insightful alternative to the traditional method based on the large time exponential behaviour of the correlation functions.