Implications of Non-universal Soft Masses on Gauge Coupling Unification

We study the gauge coupling unification of the minimal supersymmetric standard model with non-universal soft scalar and gaugino masses. The unification scale of the gauge couplings is estimated for non-universal cases. It is sensitive to the non-universality. It turns out that these cases can be combined with the assumption of string unification, which leads to a prediction of $\sin^2 θ_W(M_Z)$ and $k_1$, the normalisation of the $U(1)_Y$ generator. String unification predicts $k_1=1.3 - 1.4$. These values have non-trivial implications on string model building. Two-loop corrections are also calculated. Some of these cases exhibit a large discrepancy between experiment and string unification. We calculate string threshold corrections to explain the discrepancy.

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