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The estimation of the K\"all\'en-Lehmann spectral density from gaugeinvariant lattice QCD two point correlation functions is proposed, and exploredvia an inversion strategy based on Tikhonov regularisation. We test the methodon a mesonic toy model, showing that our methodology is competitive with thetraditional Maximum Entropy Method. As proof of concept the SU(2) glueballspectrum for the quantum numbers $J^{PC}=0^{++}$ is investigated, for variousvalues of the lattice spacing, using the published data of arXiv:1910.07756.Our estimates for the ground state mass are in good agreement with thetraditional approach, which is based on the large time exponential behaviour ofthe correlation functions. Furthermore, the spectral density also containshints of excites states in the spectrum. Spectroscopic analysis of glueballtwo-point functions therefore provides a straightforward and insightfulalternative to the traditional method based on the large time exponentialbehaviour of the correlation functions.

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