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

Lewandowski, Adrian (2019). Vector-scalar mixing to all orders for an arbitrary gauge model in the generic linear gauge. Nuclear physics B, 943, p. 114622. Elsevier 10.1016/j.nuclphysb.2019.114622

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I give explicit fromulae 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 cor- relation 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.

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