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The renormalization of softly broken SQED is related to the one ofsupersymmetric QED by using the construction with a local gauge supercouplingand by taking into account softly broken anomalous axial U(1) symmetry. Fromthis extended model one obtains the non-renormalization theorems of SQED andthe counterterms of the soft breaking parameters as functions of thesupersymmetric counterterms. Due to the Adler-Bardeen anomaly of the axialcurrent an invariant regularization scheme does not exist, and therefore the$\beta$-functions of soft breaking parameters are derived from an algebraicconstruction of the Callan-Symanzik equation and of the renormalization groupequation. We obtain the soft $\beta$-functions in terms of the gauge$\beta$-function and of the anomalous dimension of the supersymmetric mattermass. In particular, we find that the X-term of the scalar mass$\beta$-function as well as the gauge $\beta$-function in $l\geq 2$ are due tothe Adler-Bardeen anomaly of the axial symmetry.Comment: 28 page

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Nonrenormalization theorems in softly broken supersymmetric QED and the soft<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>functions

Nonrenormalization theorems in softly broken supersymmetric QED and the softβfunctions