Some approximate renormalization group invariants for supersymmetric extensions of the Standard Model and the Yukawa unification

TL;DR

The paper constructs approximate renormalization group invariants involving Yukawa couplings in supersymmetric Standard Model extensions, analyzing their implications for Yukawa unification and potential underlying symmetries.

Contribution

It introduces new approximate invariants for Yukawa couplings and explores their use in understanding unification and underlying gauge symmetries.

Findings

Yukawa invariants depend weakly on scale, making them useful for unification analysis.

Proposes two relations for Yukawa couplings at the unification scale and tests their compatibility with experimental data.

Adding exotic superfields can achieve Yukawa unification consistent with these invariants, suggesting an underlying E6 symmetry.

Abstract

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.