Strong coupling unification and extra dimensions

Abstract

We analyze the implications of electroweak and strong coupling unification in a very general class of models extending the minimal supersymmetric standard model in $4+p$ dimensions $(p\geq 0)$. In general, electroweak precision data require the presence of large extra dimensions (low compactification scales, $M_c$) and/or low unification scale, $M_U$. In particular, the actual experimental value of the strong coupling at $M_Z$ imposes an upper bound on the compactification and unification scales. In four dimensional theories ($M_c\simeq M_U$) with canonical hypercharge assignment we find $M_U\lesssim 10^{9}$ GeV. In theories with extra dimensions ($M_c<M_U$) we find $M_c\lesssim 10^7$ GeV, for a supersymmetric spectrum at the TeV scale.