Non-renormalization theorems in softly broken SQED and the soft β-functions

The renormalization of softly broken SQED is related to the one of supersymmetric QED by using the construction with a local gauge supercoupling and by taking into account softly broken anomalous axial U(1) symmetry. From this extended model one obtains the non-renormalization theorems of SQED and the counterterms of the soft breaking parameters as functions of the supersymmetric counterterms. Due to the Adler–Bardeen anomaly of the axial current an invariant regularization scheme does not exist, and therefore the β-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 β-functions in terms of the gauge β-function and of the anomalous dimension of the supersymmetric matter mass. In particular, we find that the X-term of the scalar mass β-function as well as the gauge β-function in l ≥ 2 are due to the Adler–Bardeen anomaly of the axial symmetry. ∗E-mail addresses: [email protected], [email protected].