Gluon-propagator functional form in the Landau gauge in SU(3) lattice QCD: Yukawa-type gluon propagator and anomalous gluon spectral function

We study the gluon propagator D_μνᵃᵇ(x) in the Landau gauge in SU(3) lattice QCD at β=5.7, 5.8, and 6.0 at the quenched level. The effective gluon mass is estimated as 400--600 MeV for r≡(x_αx_α)1/2=0.5--1.0 fm. Through the functional-form analysis of D_μνᵃᵇ(x) obtained in lattice QCD, we find that the Landau-gauge gluon propagator D_μμᵃᵃ(r) is well described by the Yukawa-type function e^-mr/r with m600 MeV for r=0.1--1.0 fm in the four-dimensional Euclidean space-time. In the momentum space, the gluon propagator D_μμᵃᵃ(p²) with (p²)1/2=0.5--3 GeV is found to be well approximated with a new-type propagator of (p²+m²)^-3/2, which corresponds to the four-dimensional Yukawa-type propagator. Associated with the Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator D₀(t), the effective mass Meff(t), and the spectral function ρ(ω) of the gluon field. The mass parameter m turns out to be the effective gluon mass in the infrared region of ~1 fm. As a remarkable fact, the obtained gluon spectral function ρ(ω) is almost negative definite for ω>m, except for a positive δ-functional peak at ω=m.