Nonrenormalization theorems in softly broken supersymmetric QED and the soft beta functions - art. no. 115012

The renormalization of softly broken supersymmetric QED (SQED) is related t o supersymmetric QED by using the construction with a local gauge supercoup ling and by taking into account softly broken anomalous axial U(1) symmetry . From this extended model one obtains the nonrenormalization theorems of s calar QED and the counterterms of the soft breaking parameters as functions of the supersymmetric counterterms. Because of the Adler-Bardeen anomaly o f the axial vector current an invariant regularization scheme does not exis t, and therefore the beta functions of soft breaking parameters are derived from an algebraic construction of the Callan-Symanzik equation and of the renormalization-group equation. We obtain the soft beta functions in terms of the gauge beta function and of the anomalous dimension of the supersymme tric matter mass. In particular, we find that the X term of the scalar mass beta function as well as the gauge beta function in l greater than or equa l to2 are due to the Adler-Bardeen anomaly of the axial symmetry.