Naturally Large Tan $β$

Abstract

We show that if there are only two Higgs doublets in the supersymmetric standard model, large $\tanβ$ requires a fine tuning in the parameters of the Lagrangian of order ($1/\tanβ$), which cannot be explained by any approximate symmetry. With an extended Higgs sector, large $\tanβ$ can be natural. We give an explicit example with four doublets in which it is possible to achieve large $\tanβ$ as a result of an approximate symmetry, without any light superpartners. The approximate symmetry can be extended to explain all the hierarchies in the quark mass matrix.