2009/08/31 by Takumi Iritani, Hideo Suganuma, Hideaki Iida
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-lat
paper · pdf · doi:10.1103/physrevd.80.114505
published as Phys.Rev.D80:114505,2009 · 20 pages, 15 figures
arxiv created 2009/12/10 · openalex publication_date 2009/12/18 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the gluon propagator D_\ensuremathμ\ensuremathνab(x) in the Landau gauge in SU(3) lattice QCD at \ensuremathβ=5.7, 5.8, and 6.0 at the quenched level. The effective gluon mass is estimated as 400--600 MeV for r\ensuremath≡(x_\ensuremathαx_\ensuremathα)1/2=0.5--1.0 fm. Through the functional-form analysis of D_\ensuremathμ\ensuremathνab(x) obtained in lattice QCD, we find that the Landau-gauge gluon propagator D_\ensuremathμ\ensuremathμaa(r) is well described by the Yukawa-type function e^\ensuremath-mr/r with m\ensuremath≃600 MeV for r=0.1--1.0 fm in the four-dimensional Euclidean space-time. In the momentum space, the gluon propagator \stackrel\texttildelowD_\ensuremathμ\ensuremathμaa(p2) with (p2)1/2=0.5--3 GeV is found to be well approximated with a new-type propagator of (p2+m2)^\ensuremath-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 \ensuremathρ(\ensuremathω) of the gluon field. The mass parameter m turns out to be the effective gluon mass in the infrared region of \ensuremath∼1 fm. As a remarkable fact, the obtained gluon spectral function \ensuremathρ(\ensuremathω) is almost negative definite for \ensuremathω>m, except for a positive \ensuremathδ-functional peak at \ensuremathω=m.