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

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>T</a:mi> <a:mo>=</a:mo> <a:mn>0</a:mn> </a:math> to temperatures <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>T</c:mi> <c:mo>></c:mo> <c:msub> <c:mi>T</c:mi> <c:mi>c</c:mi> </c:msub> </c:math> 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.