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

摘要

We study the gluon propagator $D_{\mu\nu}^{ab}(x)$ in the Landau gauge inSU(3) lattice QCD at $\beta$ = 5.7, 5.8, and 6.0 at the quenched level. Theeffective gluon mass is estimated as $400 \sim 600$MeV for $r \equiv (x_\alphax_\alpha)^{1/2} = 0.5 \sim 1.0$ fm. Through the functional-form analysis of$D_{\mu\nu}^{ab}(x)$ obtained in lattice QCD, we find that the Landau-gaugegluon propagator $D_{\mu\mu}^{aa}(r)$ is well described by the Yukawa-typefunction $e^{-mr}/r$ with $m \simeq 600$MeV for $r = 0.1 \sim 1.0$ fm in thefour-dimensional Euclidean space-time. In the momentum space, the gluonpropagator $\tilde D_{\mu\mu}^{aa}(p^2)$ with $(p^2)^{1/2}= 0.5 \sim 3$ GeV isfound 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. Associatedwith the Yukawa-type gluon propagator, we derive analytical expressions for thezero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\rm eff}(t)$,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 $\sim$1fm. 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 $\omega=m$.