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We address the issue of the all order multiplicative renormalizability ofSU(2) Yang-Mills theories quantized in the maximal Abelian gauge in presence ofscalar matter fields. The non-linear character of the maximal Abelian gaugerequires the introduction of quartic interaction terms in the Faddeev-Popovghosts, a well known feature of this gauge. We show that, when scalar matterfields are introduced, a second quartic interaction term between scalar fieldsand Faddeev-Popov ghosts naturally arises. A BRST invariant action accountingfor those quartic interaction terms is identified and proven to bemultiplicative renormalizable to all orders by means of the algebraicrenormalization procedure.

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