TeV Scale Quark-Lepton Unification

Abstract

We propose a quark-lepton symmetric Pati-Salam (PS) model based on the gauge group $SU(2)_L \times SU(2)_R \times SU(4)_C$ with an $E_6$-inspired particle spectrum which naturally accommodates a multi-TeV leptoquark gauge boson $X_\mu(3,1,\frac{2}{3})$. A softly broken $Z_2$ symmetry plays a crucial role in realizing this scenario, under which the Standard Model (SM) fermions are even, while new vector-like fermions present in the model are odd. A notable feature of this model is that the PS gauge boson $X_\mu$ itself is $Z_2$-odd, causing it to couple exclusively between SM fermions and the vector-like fermions, except in the right-handed down-quark sector, where mixing is induced by the soft breaking of $Z_2$. This structure leads to helicity suppression of tree-level meson decays mediated by $X_\mu$, with helicity-unsuppressed contributions arising only via one-loop diagrams. We show that $X_\mu$ can be as light as 1.1 TeV while being compatible with all flavor-violating constraints. However, mass relations among the $(W'^\pm_\mu, Z'_\mu, X_\mu)$ gauge bosons push the $X_\mu$ mass limit up to 4.3 TeV from the stringent LHC bounds on the $Z^\prime$ mass. This comparatively low PS-breaking scale opens up promising collider opportunities for probing the leptoquark gauge boson, as well as the distinctive signature of vector-like down-type quarks carrying an unusual baryon number of $2/3$. The model can be further tested via lepton flavor-violating processes induced by the leptoquark gauge boson, such as $\mu \to e \gamma$, $\mu \to e e e$, and $\mu$-$e$ conversion in nuclei. Neutrino masses arise in the model through dimension-seven operators at tree-level, as well as from dimension-five operators via one-loop diagrams.