Question for SU(5) x SU(5) string unification

Abstract

Here we ask if it is possible to have string unification in $\mathsf{SU}(5)\times \mathsf{SU}(5)$ gauge group. We specifically investigate the weakly coupled heterotic string unification for the four couplings in this framework. We show that only a limited versions of $\mathsf{SU}(5)\times \mathsf{SU}(5)$ with adjoint representation components at intermediated scales, between $M_Z$ and $\Lambda$ (unification), are allowed. This is essentially due to the limitation in the parameter space to the gauge coupling constant ${\alpha }_1^{-1}$ related to hypercharge. Indeed, only the vanishing hypercharge decompositions of $\mathsf{SU}(5{)}_{\mathsf{L}}$ subgroup can help to this unification, namely, the fermion and boson triplets, ${\Sigma }_3\sim (1,3{)}_0$, and the fermion and boson octets, ${\Sigma }_8\sim (8,1{)}_0$. Thus, these intermediate particles are compatible with the so-called Adjoint $\mathsf{SU}(5)$. The triplets must live in TeV region and could be accessible at colliders while the octets must alive in very high energy scales. We also show that the non-SUSY unification scenario requires the introduction of an additional $\mathsf{SU}(2{)}_{\mathsf{L}}$ scalar color triplet, $\eta \sim (3,3{)}_{-1/3}$, at relatively low energies ($\sim 10^{5-11}$GeV), and it may induce the proton decay.

13 pages, 9 figures. References updated and typos corrected

References in corpus (9)

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