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I give explicit fromulae for full propagators of vector and scalar fields ina generic spin-1 gauge model quantized in an arbitrary linear covariant gauge.The propagators, expressed in terms of all-order one-particle-irreduciblecorrelation functions, have a remarkably simple form because of constraintsoriginating from Slavnov-Taylor identities of Becchi-Rouet-Stora symmetry. Ialso determine the behavior of the propagators in the neighborhood of thepoles, and give a simple prescription for the coefficients that generalize (tothe case with an arbitrary vector-scalar mixing) the standard$\sqrt{\mathcal{Z}}$ factors of Lehmann, Symanzik and Zimmermann. So obtainedgeneralized $\sqrt{\mathcal{Z}}$ factors, are indispensable to the correctextraction of physical amplitudes from the amputated correlation functions inthe presence of mixing. The standard $R_\xi$ guauges form a particularlyimportant subclass of gauges considered in this paper. While the tree-levelvector-scalar mixing is, by construction, absent in $R_\xi$ gauges, itunavoidably reappears at higher orders. Therefore the prescription for thegeneralized $\sqrt{\mathcal{Z}}$ factors given in this paper is directlyrelevant for the extraction of amplitudes in $R_\xi$ gauges.

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