A New Stability Equation for the Abelian Higgs-Kibble Model with a Dim.6 Derivative Operator

We show that the dynamics of the scalar Higgs field in the Abelian Higgs-Kibble model, supplemented with a dimension 6 derivative operator, can be constrained at the quantum level by a certain stability equation. The latter holds true in the Landau gauge and is derived within the recently proposed extended field formalism where the physical scalar is described by a gauge-invariant field variable. Physical implications of the stability equation are discussed.