The effective gluon mass and the gluon propagator form in the Landau gauge in SU(3) lattice QCD

We study the gluon propagator in the Landau gauge in SU(3) lattice QCD with $\beta = 5.7, 5.8$ and $6.0$ at the quenched level in the region of $r = 0.1 \sim 1.0$ fm, which is relevant to quark-hadron physics. First, we evaluate the effective gluon mass in lattice QCD, since gluons have been conjectured to acquire large effective mass due to non-perturbative effects of QCD. The effective gluon mass is estimated to be about $400 \sim 600$ MeV in the Landau gauge in an infrared region of $r = 0.5 \sim 1.0$ fm. Next, we investigate the functional form of the gluon propagator in the Landau gauge. As a remarkable fact, the gluon propagator is found to be well reproduced by the simple Yukawa-type function $e^{-mr}/r$ in the whole region of $r = 0.1 \sim 1.0$ fm in the four-dimensional Euclidean space-time. Note that this Yukawa-type propagator in four-dimensional space-time corresponds to a new-type propagator of $(p^2+m^2)^{-3/2}$ in the momentum space. Based on the Yukawa-type gluon propagator obtained from lattice QCD, we also discuss a possible construction of the infrared effective theory such as a Nambu-Jona-Lasinio-type theory from QCD.