Unitary mixing scalar-vector in $\xi$ gauge

We study the effect of unitary mixing of scalar and vector fields in general $\xi$ gauge. This effect takes place for non-conserved vector currents and $\xi$ gauge generates some additional problems with unphysical scalar field. We obtained solutions of Dyson-Schwinger equations and perfomed the renormalization of full propagators. The key feature of renormalization is the usage of Ward identity, which relates some different Green functions. We found that using Ward identity leads to disappearing of $\xi$-dependence in renormalized matrix element.