Background effective action with nonlinear massive gauge fixing

We combine a recent construction of Becchi-Rouet-Stora-Tyutin (BRST)-invariant, nonlinear massive gauge fixing with the background field formalism. The resulting generating functional preserves background-field invariance as well BRST quantum manifestly. features BRST-invariant mass parameters for and ghost fields. formalism employs Nakanishi-Lautrup which is part gauge-fixing sector thus should not affect observables. verify this expectation by computing one-loop effective action beta function coupling an example. corresponding Schwinger connected correlation functions acquires additional one-particle reducible terms that vanish on shell. also study off-shell contributions in order to explore consequences scheme involving field. As application, we show our straightforwardly accommodates nonperturbative information about propagators Landau form so-called decoupling solution. Using input, find evidence formation gluon condensate sufficiently large coupling, whose scale set parameter.