One-loop analytic structure of the deep-infrared Landau-gauge gluon propagator at finite temperature

TL;DR

The paper analyzes the finite-temperature deep-infrared structure of the Landau-gauge gluon propagator using a one-loop screened massive expansion in both pure Yang–Mills theory and full QCD. It employs two parameter strategies (gauge-invariant vacuum optimization and lattice-fitted finite-temperature parameters) to compute zero-momentum gluon poles and the generalized spectral function, finding persistent complex-conjugate poles on the principal sheet and a positivity-violating, non-sharp spectral function across temperatures up to several hundred MeV. In full QCD, quark-mass thresholds further enrich the spectral structure, but no sharp finite-temperature gluon quasi-particle peak emerges; the results show linear-in-temperature pole behavior at high $T$, with no crossing of real and imaginary parts within the studied ranges. The study concludes that, within this framework, there is no clear deconfinement signature in the infrared gluon propagator, highlighting the need for higher-order corrections, HTL effects, or gauge-invariant analyses to robustly connect propagator analyticity to deconfinement observables.

Abstract

With the aim of looking for signatures of deconfinement, the poles and the spectral function of the Landau-gauge gluon propagator are investigated at one loop, vanishing spatial momentum and finite temperature within the framework of the screened massive expansion of pure Yang-Mills theory and of full QCD. When computed using both temperature-independent parameters optimized by principles of gauge invariance and temperature-dependent parameters obtained by fitting lattice data at zero Matsubara frequency, the propagator is found to have a pair of complex-conjugate poles in its squared complexified frequency variable throughout the considered temperature interval, ranging from $T=0$ to temperatures $T>T_{c}$ of interest to quark-gluon plasma phenomenology. The spectral function is found to violate positivity and not to develop sharp peaks over said temperature interval. In full QCD, a simple model is used for mass generation in the infrared quark sector; the dependence of our results on the quark masses is discussed.

Figures (14)

• Figure 1: 1PI diagrams with no more than three vertices used to compute the one-loop gluon polarization in the screened massive expansion of pure Yang-Mills theory. Top: tree-level gluon mass counterterm. Bottom: loop diagrams. A diagram specular to (3b) with one mass counterterm in the lower internal gluon line is not displayed explicitly, but included in (3b) itself.
• Figure 2: Full-QCD one-loop quark polarization diagram.
• Figure 3: Integration contour used to derive the generalized spectral representation of the finite-temperature gluon propagator as a function of the spectral frequency $\omega$. The red crosses and wiggly line represent the singularities of the propagator: a finite number of complex poles in its principal Riemann sheet and a branch cut on the imaginary axis. The radius of the contour is sent to infinity.
• Figure 4: Real and imaginary part of one of the four symmetric, complex-conjugate poles $z(T)=i[\varepsilon_{0}(T)+i\gamma_{0}(T)]$ of the Euclidean Landau-gauge pure-Yang-Mills gluon propagator at zero spatial momentum $|{\bf p}|=0$, as functions of the temperature $T$. Computed for $m=0.656$ GeV, $\pi_{0}=-0.876$.
• Figure 5: Zero-momentum ($|{\bf p}|=0$) spectral function of the Landau-gauge pure-Yang-Mills gluon propagator as a function of the spectral frequency $\omega$, for different values of the temperature $T$. The dashed vertical lines mark the $m$ and $2m$ mass thresholds. Computed for $m=0.656$ GeV, $\pi_{0}=-0.876$.