SU(2) lattice gluon propagators at finite temperatures in the deep infrared region and Gribov copy effects

TL;DR

This paper investigates SU(2) gluon propagators at finite temperatures, focusing on Gribov copy effects and infrared behavior, revealing non-zero zero-momentum transverse propagator and introducing magnetic and electric mass scales.

Contribution

It provides a detailed numerical analysis of gluon propagators at finite temperature, highlighting Gribov copy effects and proposing new definitions for infrared mass scales.

Findings

Gribov copy effects are strong for transverse propagator in IR

D_T(0) remains non-zero in the infinite volume limit

Infrared region D_T(p) does not fit pole-type formulas

Abstract

We study numerically the SU(2) Landau gauge transverse and longitudinal gluon propagators at non-zero temperatures T both in confinement and deconfinement phases. The special attention is paid to the Gribov copy effects in the IR-region. Applying powerful gauge fixing algorithm we find that the Gribov copy effects for the transverse propagator D_T(p) are very strong in the infrared, while the longitudinal propagator D_L(p) shows very weak (if any) Gribov copy dependence. The value D_T(0) tends to decrease with growing lattice size; however, D_T(0) is non-zero in the infinite volume limit, in disagreement with the suggestion made in [1]. We show that in the infrared region D_T(p) is not consistent with the pole-type formula not only in the deconfinement phase but also for T < T_c. We introduce new definition of the magnetic infrared mass scale ('magnetic screening mass') m_M. The electric mass m_E has been determined from the momentum space longitudinal gluon propagator. We study also the (finite) volume and temperature dependence of the propagators as well as discretization errors.