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Non-renormalization theorems in softly broken SQED and the soft -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
-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 -functions in terms of the gauge
-function and of the anomalous dimension of the supersymmetric matter
mass. In particular, we find that the X-term of the scalar mass
-function as well as the gauge -function in are due to
the Adler-Bardeen anomaly of the axial symmetry.Comment: 28 page