Källén-Lehmann Spectral Representation of the Scalar SU(2) Glueball

Abstract

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 $J^{PC}=0^{++}$ 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.

17 pages, 9 figures

References in corpus (18)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• The Physics of Glueballs
• The Status of Glueballs
• The Experimental Status of Glueballs
• Quarkonium correlators and spectral functions at zero and finite temperature
• Charmonium at high temperature in two-flavor QCD
• The glueball spectrum of SU(3) gauge theory in 3+1 dimension
• SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology
• Glueball masses from an infrared moment problem and nonperturbative Landau gauge
• Scalar isoscalar mesons and the scalar glueball from radiative $J/\psi$ decays
• Glueball scattering cross section in lattice SU(2) Yang-Mills theory
• Spectrum of scalar and pseudoscalar glueballs from functional methods
• Dark matter scattering cross section and dynamics in dark Yang-Mills theory
• Spectral functions and critical dynamics of the $O(4)$ model from classical-statistical lattice simulations
• Bayesian inference of non-positive spectral functions in quantum field theory
• Quark propagator in Minkowski space
• Decay of Boson Stars with Application to Glueballs and Other Real Scalars

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