Gauge-invariant self-energies and vertex parts of the standard model in the pinch technique framework

Abstract

The pinch technique (PT) is applied to obtain one-loop gauge-invariant self-energies, vertex and box diagrams in the electroweak sector of the standard model. Describing the interaction of vector bosons with fermions in terms of current correlation functions, we propose to directly identify the pinch parts with the contributions of equal-time commutators in the relevant Ward identities. We argue that this procedure isolates the parts of vertex and box diagrams that are independent of strong interaction dynamics. The formalism promptly leads us to very simple gauge-invariant transverse self-energies, as well as vertex and box diagrams relevant to four-fermion processes mediated by charged and neutral currents. They automatically possess very desirable theoretical properties. We then apply the PT to ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{W}^{+}{W}^{\ensuremath{-}}$ and explicitly demonstrate that the propagatorlike pinch parts are absorbed in the same self-energies encountered in the four-fermion case. The PT self-energies and vertex corrections are compared with those obtained in other formulations. A number of applications are discussed, including the possibility of a gauge-invariant on-shell definition of the vector-boson mass.