Gauge parameter dependence in the background field gauge and the construction of an invariant charge

By using the enlarged BRS transformations we control the gauge parameter de pendence of Green functions in the background field gauge. We show that it is unavoidable - also if we consider the local Ward identity - to introduce the normalization value xi(0) of the gauge parameter xi. The dependence of Green functions on xi(0) is governed by a partial differential equation in a similar manner as the dependence on the normalization point kappa is gov erned by the RG equation. By modifying the Ward identity we are able to con struct in 1-loop order a gauge parameter independent combination of 2-point vector and background vector functions. By explicit construction of the ne xt orders we show that this combination can be used to construct a gauge pa rameter independent RG-invariant charge. However, it is seen that this RG-i nvariant charge does not satisfy the differential equation of the normaliza tion value xi(0) of the gauge parameter, and, hence, is not xi(0)-independe nt as required. (C) 1999 Published by Elsevier Science B.V.