Pinch Technique: Theory and Applications

By Daniele Binosi, J. Papavassiliou. 2009

317 citations recorded by the source corpus.

Abstract We review the theoretical foundations and the most important physical applications of the Pinch Technique (PT). This general method allows the construction of off-shell Green’s functions in non-Abelian gauge theories that are independent of the gauge-fixing parameter and satisfy ghost-free Ward identities. We first present the diagrammatic formulation of the technique in QCD, deriving, at one loop, the gauge independent gluon self-energy, quark–gluon vertex, and three-gluon vertex, together with their Abelian Ward identities. The generalization of the PT to theories with spontaneous symmetry breaking is carried out in detail, and the profound connection with the optical theorem and the dispersion relations are explained within the electroweak sector of the Standard Model. The equivalence between the PT and the Feynman gauge of the Background Field Method (BFM) is elaborated, and the crucial differences between the two methods are critically scrutinized. A variety of field theoretic techniques needed for the generalization of the PT to all orders are introduced, with particular emphasis on the Batalin–Vilkovisky quantization method and the general formalism of algebraic renormalization. The main conceptual and technical issues related to the extension of the technique beyond one loop are described, using the two-loop construction as a concrete example. Then the all-order generalization is thoroughly examined, making extensive use of the field theoretic machinery previously introduced; of central importance in this analysis is the demonstration that the PT-BFM correspondence persists to all orders in perturbation theory. The extension of the PT to the non-perturbative domain of the QCD Schwinger–Dyson equations is presented systematically, and the main advantages of the resulting self-consistent truncation scheme are discussed. A plethora of physical applications relying on the PT are finally reviewed, with special emphasis on the definition of gauge-independent off-shell form-factors, the construction of non-Abelian effective charges, the gauge-invariant treatment of resonant transition amplitudes and unstable particles, and finally the dynamical generation of an effective gluon mass.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/be034c5bbb0c223c8c29d557ec9e08ba21c5e201

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Citations in the corpus

The Gribov problem and QCD dynamics (2012, methodology): “It is similar in spirit to the functional renormalization-group equation [26, 48], and has also been developed in the pinch technique formalism [43, 24].”
The nonperturbative functional renormalization group and its applications (2020, unknown): “[657, 722, 725–727, 730, 735–750] and references therein.”
Nonperturbative QCD coupling and its β function from light-front holography (2010, methodology): “[1], a difference probably stemming from the different scheme choices.”
Nonperturbative properties of Yang–Mills theories (2018, methodology): “A special application of DSEs in gauge field theories is the combination of the pinch technique [75–78] with the background field method [79, 80] which is referred to as PT-BFM [81–84].”
QCD at finite temperature and chemical potential from Dyson–Schwinger equations (2018, background): “In the vacuum there is a large body of successful work available on DSEs in the background field formalism, see [302, 305] for reviews.”
The Infrared Behaviour of the Pure Yang–Mills Green Functions (2005, background): “As we shall discuss in the next section, these results were also recently confirmed [177] by studying the coupled system of ghost and gluon propagator DSE in the PT-BFM scheme [178].”
The QCD running coupling (2016, background): “2 Λ [236] (a review of the pinch technique, including its application to the SDE and the computation of αs, can be found in [285]).”
Light-front holographic QCD and emerging confinement (2014, background): “There is however evidence from lattice gauge theory [42], Dyson Schwinger equations [43, 44], and empirical effective charges [45], that the QCD β-function vanishes in the infrared.”
How to use the Standard Model effective field theory (2014, methodology): “ons Π(p2) are not generically gauge invariant. In principle, these Π(p2) functions can be promoted to gauge invariant ones Π(p2) by a “pinch technique” prescription. (For examples, see discussions in [28, 52, 53].) 49Throughout this paper, we adopt the notation c Z≡ cos θetc., with denoting the weak”