Gauge dependence and renormalization of $\tan \beta$ in the MSSM

Abstract

Well-known and newly developed renormalization schemes for $\tan \beta$ are analyzed in view of three desirable properties: gauge independence, process independence, and numerical stability in perturbation theory. Arguments are provided that no scheme can meet all three requirements, and as an illustration, a ``No-Go-Theorem'' for the renormalization of $\tan \beta$ is established. Nevertheless, two particularly attractive schemes emerge. A discussion about which scheme might be the best compromise in practice is given.

Comments: 20 pages, improved version that was published in PRD D66 (2002)