The problems of unification-mismatch and low $α_3$: A solution with light vector-like matter

The commonly accepted notion of a weak unified coupling $\alpha_X \approx 0.04$, based on the assumption of the MSSM--spectrum, is questioned. It is suggested that the four--dimensional unified string coupling should very likely have an intermediate value $(\sim 0.2-0.3$, say) so that it may be large enough to stabilize the dilaton but not so large as to disturb the coupling--unification relations. Bearing this in mind, as well as the smallness of the MSSM unification scale $M_X$ compared to the string scale, the consequences of a previously suggested extension of the MSSM spectrum are explored. The extension contains two vector--like families of quarks and leptons with relatively light masses of order 1 TeV, having the quantum numbers of ${\bf 16}+{\bf \overline{16}}$ of $SO(10)$. It is observed that such an extension provides certain unique advantages. These include: (a) removing the stated mismatch between MSSM and string unifications with regard to $\alpha_X$ and to some extent $M_X$ as well, (b) achieving coupling unification with a relatively low value of $\alpha_3(m_Z)$, in accord with its world average value, and (c) following earlier works, providing a simple explanation of the observed inter--family mass--hierarchy. The extension provides scope for exciting new discoveries, beyond those of SUSY and Higgs particles, at future colliders, including the LHC and the NLC.