Glueball spectral densities from the lattice

Abstract

The propagator of a physical degree of freedom ought to obey a Källén-Lehmann spectral representation, with positive spectral density. The latter quantity is directly related to a cross section based on the optical theorem. The spectral density is a crucial ingredient of a quantum field theory with elementary and bound states, with a direct experimental connection as the masses of the excitations reflect themselves into (continuum) δ -singularities. In usual lattice simulational approaches to the QCD spectrum the spectral density itself is not accessed. The (bound state) masses are extracted from the asymptotic exponential decay of the two-point function. Given the importance of the spectral density, each nonperturbative continuum approach to QCD should be able to adequately describe it or to take into proper account. In this work, we wish to present a first trial in extracting an estimate for the scalar glueball spectral density in SU(3) gluodynamics using lattice gauge theory.

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

“…Interestingly, re-expressing the β = 2.4 groundstate and 1st excited state mass in units of string tension, we get 3.420 (32) √ σ and 6.069(56) √ σ respectively, values that compare quite well with an independent SU(2) estimate giving 3.781(23) √ σ for the ground state and 6.126 (38) √ σ for the 1st excited state 2 .…”

“…The spectral function ρ(ω) can be obtained, if the subtraction of the polynomial part can be performed. However, performing subtractions on numerical data is extremely sensitive to the choice of p and results in relative rapid variation of {a k } with the subtraction point [32].…”

Spectral densities from the lattice

“…Here we use an alternative approach, based on Tikhonov regularization with Morozov discrepancy principle. For details see our previous papers [10,11,12].…”

Many faces of the Landau gauge gluon propagator at zero and finite temperature: positivity violation spectral density and mass scales

“…Though, as the gluon Schwinger function already reveals the spectral density cannot be positive over its whole domain, the standard MEM procedure does not apply. We will rely on an alternative approach, preliminary discussed in [13,14,15] with a more complete treatment in [16]. We found inspiration in the Tikhonov approach to ill-posed problems, supplemented with the Morozov discrepancy principle.…”