https://doi.org/10.1140/epjc/s10052-022-10213-3
Regular Article - Theoretical Physics
Källén–Lehmann spectral representation of the scalar SU(2) glueball
1
Department of Physics, KU Leuven Campus Kortrijk–Kulak, Etienne Sabbelaan 53 bus 7657, 8500, Kortrijk, Belgium
2
Department of Physics and Astronomy, Ghent University, Krijgslaan 281-S9, 9000, Ghent, Belgium
3
Department of Physics, CFisUC, University of Coimbra, 3004-516, Coimbra, Portugal
Received:
25
June
2021
Accepted:
12
March
2022
Published online:
23
March
2022
The estimation of the Källén–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 
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.
© The Author(s) 2022
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