On the phenomenological implications of a Pati-Salam model spontaneously broken by Higgs fields in fundamental representations

TL;DR

This paper introduces a supersymmetric Pati-Salam model with small Higgs representations, addressing neutrino masses, proton decay, and mass hierarchy issues, while maintaining near-conformal behavior and avoiding Landau poles up to the Planck scale.

Contribution

The model uniquely combines small Higgs representations, supersymmetric symmetries, and discrete symmetries to address key GUT challenges and is compatible with string theory constructions.

Findings

One-loop beta coefficient of SU(4)_C is zero, near-conformal in UV.

Landau poles are avoided up to the Planck scale.

Proton decay is suppressed beyond current experimental bounds.

Abstract

We present a supersymmetric Pati-Salam model with small representations as a potential candidate for physics beyond the Standard Model. The model features a Higgs sector with bifundamental fields $H_R+\bar H_R=(4,1,2)+(\bar 4,1,2)$, $H_L+\bar H_L=(4,2,1)+(\bar 4,2,1)$ as well as a pair of bi-doublet fields $h_a=(1,2,2)$ where $ a=1,2$, with three families of fermions accommodated in $ (4,2,1)+(\bar 4,1,2)$ as usual. The matter spectrum is augmented with three copies of neutral singlets that mix with ordinary neutrinos to realize the seesaw mechanism. The model introduces supersymmetric R-symmetry and a global discrete $\mathbb{Z}_n$ symmetry ($n > 2$) that prevents disastrous superpotential couplings, while its spontaneous breaking implies the existence of domain walls that are successfully addressed. Interestingly, the one-loop beta coefficient of the $SU(4)_C$ gauge coupling is zero in the minimal $\mathbb{Z}_3$ model, rendering the corresponding gauge coupling near-conformal in the UV. Meanwhile, Landau poles are avoided up to the Planck scale and proton decay is suppressed, resulting in a proton lifetime beyond current experimental bounds. By virtue of the extended Higgs sector, the key advantage of this PS model is its ability to disentangle quark and lepton masses through higher-dimensional effective operators, addressing a common limitation in GUT models with small Higgs representations. This makes the model more economical and easier to be constructed from string theory, particularly in several heterotic and F-theory models where Higgses in the adjoint representation are absent.