[Paper Review] Electric and magnetic Landau-gauge gluon propagators in finite-temperature SU(2) gauge theory

Attilio Cucchieri, Tereza Mendes|arXiv (Cornell University)|May 1, 2011

Quantum Chromodynamics and Particle Interactions4 references3 citations

TL;DR

This lattice study investigates electric and magnetic gluon propagators in finite-temperature SU(2) Yang-Mills theory using the largest lattices to date. It finds that the longitudinal propagator $D_L(p)$ reaches an infrared plateau with a finite peak near $0.9T_c$, while finite-$N_t$ effects around $T_c$ distort earlier results; after correcting for these, $D_L(0)$ at $T_c$ is reduced by ~50% and matches the value at $0.5T_c$, indicating no sharp transition. The transverse propagator $D_T(p)$ shows infrared suppression and violation of spectral positivity, consistent with dimensional reduction.

ABSTRACT

We perform lattice simulations in pure-SU(2) Yang-Mills theory to investigate how the infrared behavior of electric and magnetic gluon propagators in Landau gauge is affected by temperature. We consider the largest lattices to date, in an attempt to keep systematic errors under control. Electric and magnetic screening masses are calculated through an Ansatz from the zero-temperature case, based on complex-conjugate poles for the momentum-space propagators. As recently reported in [1], we find good fits to the proposed form at all temperatures considered, with different ratios of real to imaginary part of the pole masses for the longitudinal (electric) and transverse (magnetic) propagators. The behavior of the magnetic propagator D_T(p) is in agreement with the dimensional-reduction picture, showing infrared suppression (with a turnover in momentum) and violation of spectral positivity at all nonzero temperatures considered. The longitudinal propagator D_L(p) appears to reach a plateau at small momenta and is subject to severe finite-Nt effects around the critical temperature Tc. As a consequence, only lattices with temporal extent Nt > 8 seem to be free from systematic errors. After these errors are removed, the infrared-plateau value is considerably reduced around the transition and the sharp peak observed previously for this quantity at Tc is no longer present. The resulting infrared behavior for D_L(p) at Tc is essentially the same as for 0.5Tc . An investigation of the temperature range between 0.5Tc and Tc reveals that a less pronounced (finite) peak may occur at smaller temperatures, e.g. T ~ 0.9Tc.

Motivation & Objective

• To investigate the infrared behavior of electric and magnetic gluon propagators in Landau gauge at finite temperature in pure SU(2) Yang-Mills theory.
• To assess the impact of finite-size effects, particularly on $N_t$ and aspect ratio, on the longitudinal propagator near $T_c$.
• To determine whether the sharp peak in $D_L(0)$ at $T_c$ observed in prior studies is a finite-volume artifact or a physical feature.
• To test the applicability of the Gribov-Stingl form with complex-conjugate poles to both longitudinal and transverse propagators across the temperature range.
• To examine the behavior of screening masses and spectral positivity violations in real and momentum space.

Proposed method

• Lattice simulations of pure SU(2) Yang-Mills theory on large spatial lattices with $N_t > 8$ to minimize finite-size effects.
• Use of the Gribov-Stingl ansatz to fit momentum-space propagators, assuming complex-conjugate poles for both longitudinal and transverse components.
• Calculation of electric and magnetic screening masses from the inverse of the infrared plateau value $D_L(0)^{-1/2}$ and from pole positions.
• Analysis of real-space propagators to test reflection positivity and detect oscillatory behavior indicative of complex-mass poles.
• Systematic comparison of data across different $N_t$ and $N_s$ values to isolate finite-$N_t$ artifacts, especially near $T_c$.
• Use of symmetric lattices ($N_t = N_s$) as reference for zero-temperature behavior and to identify systematic errors.

Experimental results

Research questions

• RQ1 Does the sharp peak in the infrared plateau of the longitudinal gluon propagator $D_L(0)$ at $T_c$ persist when finite-size effects are properly controlled?
• RQ2 How do the electric and magnetic screening masses, derived from the propagators, behave across the deconfinement transition?
• RQ3 To what extent do the longitudinal and transverse propagators exhibit violation of spectral positivity and oscillatory real-space behavior?
• RQ4 Is the Gribov-Stingl form with complex-conjugate poles a valid description of the infrared behavior of both propagators at finite temperature?
• RQ5 What is the true temperature dependence of $D_L(0)$ in the range $0.5T_c$ to $T_c$, after removing finite-$N_t$ artifacts?

Key findings

• The infrared plateau value of the longitudinal propagator $D_L(0)$ is reduced by approximately 50% after removing finite-$N_t$ systematic errors, particularly for $N_t eq 8$.
• The sharp peak in $D_L(0)$ previously observed at $T_c$ is an artifact of small $N_t$ lattices; the true maximum occurs at $T \approx 0.9T_c$ and is finite, not divergent.
• After correction, the infrared behavior of $D_L(p)$ at $T_c$ is essentially indistinguishable from that at $0.5T_c$, indicating no discontinuity in the infrared limit.
• The transverse propagator $D_T(p)$ exhibits infrared suppression, a momentum-space turnover, and violation of spectral positivity at all nonzero temperatures, consistent with the dimensional-reduction picture.
• Both longitudinal and transverse propagators show oscillatory real-space behavior, indicating complex-mass poles, and the Gribov-Stingl form provides good fits to the data across all temperatures.
• Reflection positivity is violated in the transverse propagator at all temperatures and in the longitudinal propagator only at zero temperature and near $T_c$ due to finite-size effects.