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-mu nu(ab)(x) in the Landau gauge in SU(3) lattice QCD at beta=5.7, 5.8, and 6.0 at the quenched level. The effective gluon mass is estimated as 400-600 MeV for r equivalent to(x(alpha)x(alpha))(1/2)=0.5-1.0 fm. Through the functional-form analysis of D-mu nu(ab)(x) obtained in lattice QCD, we find that the Landau-gauge gluon propagator D-mu mu(aa)(r) is well described by the Yukawa-type function e(-mr)/r with m similar or equal to 600 MeV for r=0.1-1.0 fm in the four-dimensional Euclidean space-time. In the momentum space, the gluon propagator D approximate to(aa)(mu mu)(p(2)) with (p(2))(1/2)=0.5-3 GeV is found to be well approximated with a new-type propagator of (p(2)+m(2))(-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 D-0(t), the effective mass M-eff(t), and the spectral function rho(omega) of the gluon field. The mass parameter m turns out to be the effective gluon mass in the infrared region of similar to 1 fm. As a remarkable fact, the obtained gluon spectral function rho(omega) is almost negative definite for omega > m, except for a positive delta-functional peak at omega=m.