Gauge independence in ordinary Yang-Mills theories

Gauge dependence of effective action and renormalization group functions

“…Notice that it requires a renormalization which independent from the renormalizations needed for the effective action Γ. In the literature [32,33,6], different approaches have been used to define [−∂ ξ α Ψ] Q based on the Wilson expansion or on the extended BRST technique [6]. All of these approaches amount to obtain the equation (9) where K ′ α can be studied algebraically.…”

“…By adapting the extended BRST technique of [6] to the present context, one can show (see appendix) that there exist local functionals K [αβ] such that…”

“…An algebraic approach to the problem, independent of the renormalization scheme, has been proposed in [6]. On the assumption of the existence of an invariant renormalization scheme, extensions to generic, not necessarily power counting renormalizable theories have been considered in [7,8,9,10] and more recently in [11,12].…”

Gauge dependence and renormalization of tan β in the minimal supersymmetric standard model

“…On the other hand, presumingS(Γ reg ) = 0 at some loop order, there is a very simple necessary condition forS(Γ) = 0 at this order, yielding a simple check whether a given set of renormalization conditions is compatible withS(Γ) = 0. As shown in [10,12], the counterterms in gauge theories can be generally classified into gaugedependent total BRS variations and gauge-independent non-BRS variations. Independent of the presence of spontaneous symmetry breaking, the non-BRS variations correspond to the symmetric parameters of the theory, whereas the vacuum expectation values as well as field renormalization constants are related to total BRS variations.…”

“…In the following, we will show that in fact both schemes lead to a gauge dependence of tan β already at the one-loop level. The tool we use to determine the gauge dependence is an extended Slavnov-Taylor identity introduced in [9,10]…”