High-quality grand unified theories with three generations

Abstract

We extend the unitary groups beyond the $\mathrm{SU}(5)$ and $\mathrm{SU}(6)$ to look for possible grand unified theories that give rise to three-generational Standard Model fermions without the simple repetition. By demanding asymptotic free theories at short distances, we find gauge groups of $\mathrm{SU}(7)$, $\mathrm{SU}(8)$ and $\mathrm{SU}(9)$ together with their anomaly-free irreducible representations are such candidates. Two additional gauge groups of $\mathrm{SU}(10)$ and $\mathrm{SU}(11)$ can also achieve the generational structure without asymptotic freedom. We also find these models can solve the Peccei-Quinn (PQ) quality problem which is intrinsic in the axion models, with the leading PQ-breaking operators determined from the symmetry requirement.

arXiv comment20 pages, 6 tables, matches the published version

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• The global $B-L$ symmetry in the flavor-unified $\mathrm{SU}(N)$ theories
• Bottom quark and tau lepton masses in a toy $\mathrm{SU}(6)$