Naturally Large Tan ${\hat{I}}^2$

Abstract

We show that if there are only two Higgs doublets in the supersymmetric standard model, large $\tan {\hat{I}}^2$ requires a fine tuning in the parameters of the Lagrangian of order ($1/\tan {\hat{I}}^2$), which cannot be explained by any approximate symmetry. With an extended Higgs sector, large $\tan {\hat{I}}^2$ can be natural. We give an explicit example with four doublets in which it is possible to achieve large $\tan {\hat{I}}^2$ 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.

8 pages (uses harvmac), UCSD/PTH 93-24, MIT-CTP-2230