Non-renormalization theorems in softly broken SQED and the soft $\beta$-functions

Abstract

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 $\beta$-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 supersymmetric matter mass. In particular, we find that the X-term of the scalar mass $\beta$-function as well as the gauge $\beta$-function in $l\ge 2$ are due to the Adler-Bardeen anomaly of the axial symmetry.

28 pages

Cited by in corpus (5)

• Renormalization of the Minimal Supersymmetric Standard Model
• Supersymmetric Yang-Mills theories with local coupling: The supersymmetric gauge
• Calculating the anomalous supersymmetry breaking in Super-Yang-Mills theories with local coupling
• N=1 SYM Action and BRST Cohomology
• Softly broken supersymmetric Yang-Mills theories: Renormalization and non-renormalization theorems