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We compute one-loop and two-loop beta-functions for vacuum expectation values(VEVs) in gauge theories. In R_xi gauge the VEVs renormalize differently fromthe respective scalar fields. We focus particularly on the origin and behaviorof this difference and show that it can be interpreted as the anomalousdimension of a certain scalar background field, leading to simple directcomputation and qualitative understanding. The results are given for generic aswell as supersymmetric gauge theories. These complement the set of well-knowngamma- and beta-functions of Machacek/Vaughn. As an application, we compute thebeta-functions for VEVs and tan(beta) in the MSSM, NMSSM and E6SSM.

Renormalization of vacuum expectation values in spontaneously broken gauge theories