Advanced pinch technique: Still one loop - Cornwall, John M.; Papavassiliou, Joannis; Binosi, Daniele (The Pinch Technique and Its Applications to Non-Abelian Gauge Theories, 2010)
In this chapter, we study several more advanced aspects of the pinch technique (PT), still sticking to one-loop processes, mostly in perturbation theory but with some discussion of one-dressed-loop effects related to gluon mass generation. One of these applications of the pinch technique also has nonperturbative consequences, coming from the invocation of a gauge-field condensate; it allows us to conclude, as we show in this chapter, that the dynamical gauge-boson mass in QCD vanishes like q−2, modulo logarithms, at large momentum. Finally, we introduce one of the main themes of the rest of the book: the pinch technique is realized to all orders by calculating conventional Feynman graphs in the background-field Feynman gauge. The subjects covered include the following:The pinch technique and the operator product expansion (OPE) at one loop, where we see how only gauge-invariant condensates such as 〈Tr GµνGµν〉 arise in PT Green's functions and how this condensate governs the vanishing at large momentum of dynamically generated gauge-boson mass in QCD.Uses of the pinch technique in studying gauge-boson mass generation, both dynamic in QCD (no symmetry breaking, whether by Higgs–Kibble fields or other mechanisms) and with spontaneous symmetry breaking.The background field method and the effective action.The one-loop equivalence between the pinch technique and the background field method in the Feynman gauge.The pinch technique and the operator product expansion: Running mass and condensatesAs mentioned more than once, the pinch technique is essential to unveiling the nonperturbative effects that are vital in understanding confinement in QCD.