Universal Seesaw Pati-Salam Model with P for Strong CP

TL;DR

The paper develops a universal seesaw realization of the Pati-Salam model with spontaneous parity breaking to address the strong CP problem without an axion. It employs a minimal Higgs sector and vector-like fermions to generate all fermion masses, while ensuring the determinants of the quark mass matrices are real, enabling a parity-based solution to $\bar{\theta}$. Neutrinos are massless at tree level and acquire small Majorana masses radiatively, consistent with oscillation data. Although new loops involving color-octet/sextet fermions and leptoquarks contribute to $\bar{\theta}$, these effects are strongly suppressed by mass ratios or by $\kappa_L^2/\kappa_R^2$, making the strong CP problem effectively resolved within phenomenologically viable parameter spaces; the parity-restoration scale is inferred to be $\mu_P \approx 5.2 \times 10^{13}$ GeV. The model also predicts rare baryon-number-violating processes with lifetimes far beyond current reach and provides explicit benchmark points that realize realistic fermion masses and mixings.

Abstract

We develop a universal seesaw version of the Pati-Salam model wherein quarks and leptons of each family are unified into common multiplets transforming as $ψ_L(2,1,4))+ ψ_R((1,2,4)$ under the $SU(2)_L \times SU(2)_R \times SU(4)_c$ gauge symmetry. Parity symmetry is spontaneously broken in the model, which helps in solving the strong CP problem without the axion. The Higgs sector of the model is very simple, consisting of a single pair of $H_L(2,1,4)+ H_R(1,2,4)$ fields. Fermion masses arise through mixing of the chiral fermions with vector-like quarks and leptons contained in $(1,1,15)$ as well as $(1,1,10)_L+(1,1,10)_R$ multiplets via a universal seesaw mechanism. Consistency of such a spectrum with the observed quark and lepton masses is established. The parity solution to the strong CP problem is shown to be effective in this framework, although there are new loop contributions to $\overlineθ$, compared to the analogous left-right symmetric model, arising from color sextet and octet fermions, as well as from diagrams mediated by leptoquark bosons. We also find that, in this setup, although lepton number is broken, neutrino masses remain zero at the tree-level. Small and finite Majorana neutrino masses are induced via one-loop diagrams, which we analyze and show to be compatible with oscillation experiments.

Figures (9)

• Figure 1: Running masses of the quarks and leptons $m_f(\mu)$ as a function of the renormalization scale $\mu$. The dashed vertical line represents the parity–restoration scale $\mu_P=5.2\times 10^{13}\,\mathrm{GeV}$. The numerical values of the running masses at $\mu_P$ are listed in Table \ref{['tab:mf-muP']}.
• Figure 2: One–loop radiative corrections to the down–quark and charged–lepton masses induced by the $Y_{15}$ coupling. The diagrams involve the exchange of $\chi^d_{L,R}$ leptoquark scalars together with the neutral fermion $N_L$, the color octet $\mathcal{O}_L$, and the up–type quarks and generate new flavor structures in $M_d$ and $M_e$ beyond the tree–level contribution.
• Figure 3: One–loop radiative corrections to the down–quark and charged–lepton masses induced by the $Y_{10}$ coupling. The diagrams involve the exchange of $\chi^u_{L,R}$ leptoquark scalars, leptoquark and neutral gauge bosons together with the charged lepton, the color sextet, and the down–type quarks.
• Figure 4: Radiative neutrino mass generation through one-loop correction
• Figure 5: One-loop radiative diagrams contributions to the down-quark mass matrix through leptoquark gauge bosons and leptoquark scalars.