Lattice QCD Analysis for Gluons

Abstract

Nonperturbative properties of gluons are studied in SU(3) lattice QCD at the quenched level. The first subject is a functional-form analysis of the gluon propagator $D_{\mu \nu }^{ab}(x)$ in the Landau gauge. We find that the gluon propagator $D_{\mu \mu }^{aa}(r)$ obtained in lattice QCD is well described by the four-dimensional (4D) Yukawa-type function $e^{-mr}/r$ with $m\simeq 600$MeV for the Euclidean 4D distance $r=0.1\sim 1.0$ fm. In momentum space, the gluon propagator ${\tilde{D}}_{\mu \mu }^{aa}(p^2)$ ($p=0.5\sim 3$ GeV) is found to be well approximated with a new-type propagator of $(p^2+m^2{)}^{-3/2}$, which corresponds to 4D Fourier image of the Yukawa-type function. Associated with the Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\mathrm{eff}}(t)$, and the spectral function $\rho (\omega )$ of the gluon field. The mass parameter $m$ turns out to be the infrared effective mass of gluons. The obtained gluon spectral function $\rho (\omega )$ is almost negative-definite for $\omega >m$, except for a positive $\delta$-functional peak at $\omega =m$. The second subject is a lattice-QCD determination of the relevant gluonic momentum-component for color confinement. As a remarkable fact, the string tension is found to be almost unchanged even after cutting off the high-momentum gluon component above 1.5 GeV in the Landau gauge. In fact, the relevant gluonic scale for color confinement is concluded to be below 1.5 GeV.

Comments: Invited talk at International Workshop on QCD Green's Functions, Confinement, and Phenomenology - QCD-TNT09, September 07 - 11 2009, ECT Trento, Italy