Vector-scalar mixing to all orders for an arbitrary gauge model in the generic linear gauge

I give explicit formulae for full propagators of vector and scalar fields in a generic spin-1 gauge model quantized in an arbitrary linear covariant gauge. The propagators, expressed in terms of all-order one-particle-irreducible correlation functions, have a remarkably simple form because of constr...

Full description

Bibliographic Details
Main Author: Adrian Lewandowski
Format: Article
Language:English
Published: Elsevier 2019-06-01
Series:Nuclear Physics B
Online Access:http://www.sciencedirect.com/science/article/pii/S0550321319301026
Description
Summary:I give explicit formulae for full propagators of vector and scalar fields in a generic spin-1 gauge model quantized in an arbitrary linear covariant gauge. The propagators, expressed in terms of all-order one-particle-irreducible correlation functions, have a remarkably simple form because of constraints originating from Slavnov-Taylor identities of Becchi-Rouet-Stora symmetry. I also determine the behavior of the propagators in the neighborhood of the poles, and give a simple prescription for the coefficients that generalize (to the case with an arbitrary vector-scalar mixing) the standard Z factors of Lehmann, Symanzik and Zimmermann. So obtained generalized Z factors, are indispensable to the correct extraction of physical amplitudes from the amputated correlation functions in the presence of mixing.The standard Rξ gauges form a particularly important subclass of gauges considered in this paper. While the tree-level vector-scalar mixing is, by construction, absent in Rξ gauges, it unavoidably reappears at higher orders. Therefore the prescription for the generalized Z factors given in this paper is directly relevant for the extraction of amplitudes in Rξ gauges.
ISSN:0550-3213