Three-loop effective potential for softly broken supersymmetry

Abstract

The effective potential has been previously calculated through three-loop order, in Landau gauge, for a general renormalizable theory using dimensional regularization. However, dimensional regularization is not appropriate for softly broken supersymmetric gauge theories, because it explicitly violates supersymmetry. In this paper, I obtain the three-loop effective potential using a supersymmetric regulator based on dimensional reduction. Checks follow from the vanishing of the effective potential in examples with supersymmetric vacua, and from renormalization scale invariance in examples for which supersymmetry is broken, either spontaneously or explicitly by soft terms. As byproducts, I obtain the three-loop Landau gauge anomalous dimension for the scalar component of a chiral supermultiplet, and the beta function for the field-independent vacuum energy.