Some approximate renormalization group invariants for supersymmetric extensions of the Standard Model and the Yukawa unification
For supersymmetric extensions of the Standard Model we construct some expressions that include Yukawa couplings for the third and second generations and receive relatively small quantum corrections. This implies that they slightly depend on scale and are therefore approximate renormalization group invariants. Using these invariants we try to analyse possible relations between the Yukawa couplings at the unification scale $M_X$ as well as the predictions for values of $\mbox{tg}\,\beta$ and $\alpha(M_X)$. In particular, we suggest two variants of such relations and investigate whether they agree with the experimental values of elementary particle masses. It is demonstrated that the Yukawa unification for the third and second generations consistent with them can be achieved by adding exotic superfields forming 3 representations $5+\bar{5}$ of the group $SU(5)$ to the MSSM field content. We argue that this may indicate the possible underlying $E_6$ gauge symmetry.