Kallen-Lehmann spectral representation of the scalar SU(2) glueball

The estimation of the Kallen-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 Yamanaka et al. (Phys Rev D 102(5):054507, https://doi.org/ 10.1103/PhysRevD. 102.054507, arXiv:1910.07756 [hep-lat], 2020). 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.

Automated summary

This study proposes and explores a method for estimating the Kallen-Lehmann spectral density from gauge invariant lattice QCD two point correlation functions through an appropriate inversion method. As a proof of concept, the SU(2) glueball spectrum with quantum numbers J(PC) = 0(++) is investigated, with different values of the lattice spacing. The estimates for the ground state mass are in good agreement with the traditional approach based on the large time exponential behavior of the correlation functions, and hints of excited states in the spectrum are found in the spectral density.