Yang-Mills theory in the maximal Abelian gauge in presence of scalar matter fields

We address the issue of the all order multiplicative renormalizability of SU(2) Yang-Mills theories quantized in the maximal Abelian gauge in presence of scalar matter fields. The nonlinear character of the maximal Abelian gauge requires the introduction of quartic interaction terms in the Faddeev-Popov ghosts, a well-known feature of this gauge. We show that, when scalar matter fields are introduced, a second quartic interaction term between scalar fields and Faddeev-Popov ghosts naturally arises. A Becchi-Rouet-Stora-Tyutin invariant action accounting for those quartic interaction terms is identified and proven to be multiplicative renormalizable to all orders by means of the algebraic renormalization procedure.