Constraints on $\tan{\beta}$ in SUSY SU(5) GUT

Abstract

On the evaluation of $\tan{\beta}$ is revisited by the method of the renormalization group with the criteria of the bottom-tau unification in the SUSY SU(5) GUT model. Among the conventional supersymmetric theories, an energy-scale constant $M_{SUSY}$ is introduced by-hand to decouple the lower energy-scale region from the effects of the supersymmetric particles. Provided that $M_{SUSY}$ really exists, only small $\tan{\beta} \simeq 2$ is allowed theoretically. While, medium value as $\tan{\beta} = 6 \sim 25$ is also supported if $M_{SUSY}$ is vanished away from the model.