chiral superfields; an example is given by the “large radius limits” of orbifold compactifications in string theory if supersymmetry breaking occur along the modulus direction [@Iba].

As for gaugino masses, the universality hypothesis at $\Lambda_{\mathrm{GUT}}$ reads

$$M_{1}\left( \Lambda _{\mathrm{GUT}}\right) =M_{2}\left( \Lambda _{\mathrm{GUT%
}}\right) =M_{3}\left( \Lambda _{\mathrm{GUT}}\right) =M_{0}.  \label{E}$$

In grand unified gauge theories many of these relations will be required by the enlarged gauge group at the tree-level. At the one loop level one expects some threshold corrections to the universality of the soft terms already at the reference scale $\Lambda _{\mathrm{GUT}}.$ The deviations from (\[C\]) - (\[E\]) in the matter sector can be phenomenologically important because of the existent experimental bounds on FCNC effects but they are less relevant to our discussion in this paper.

Deviations from the universality assumption are also possible in the framework of superstring theory, since the moduli sector can couple differently to the various chiral fields. Since the assumptions $A_{\kappa
}(\Lambda _{\mathrm{GUT}})=A_{\tau }(\Lambda _{\mathrm{GUT}})$ and $%
m_{1}^{2}(\Lambda _{\mathrm{GUT}})=m_{2}^{2}(\Lambda _{\mathrm{GUT}%
})=m_{S}^{2}(\Lambda _{\mathrm{GUT}})=m_{E}^{2}(\Lambda _{\mathrm{GUT}%
})=m_{L}^{2}(\Lambda _{\mathrm{GUT}})$ play an important role in our phenomenological analysis, some of our results depend on the universality of the supersymmetry breaking parameters. However a similar analysis of the (M+1)SSM has been 