Electroweak pinch technique to all orders

The generalization of the pinch technique to all orders in the electroweak sector of the Standard Model within the class of the renormalizable 't Hooft gauges, is presented. In particular, both the all-order PT gauge-boson- and scalar-fermion vertices, as well as the diagonal and mixed gauge-boson and scalar self-energies are explicitly constructed. This is achieved through the generalization to the Standard Model of the procedure recently applied to the QCD case, which consists of two steps: (i) the identification of special Green's functions, which serve as a common kernel to all self-energy and vertex diagrams and (ii) the study of the (on-shell) Slavnov–Taylor identities they satisfy. It is then shown that the ghost, scalar and scalar-gauge-boson Green's functions appearing in these identities capture precisely the result of the pinching action at arbitrary order. It turns out that the aforementioned Green's functions play a crucial role, their net effect being the non-trivial modification of the ghost, scalar and scalar-gauge-boson diagrams of the gauge-boson- or scalar-fermion vertex we have started from, in such a way as to dynamically generate the characteristic ghost and scalar sector of the background field method. The pinch technique gauge-boson and scalar self-energies are also explicitly constructed by resorting to the method of the background-quantum identities.