TeV scale quark-lepton unification

A bstract We propose a quark-lepton symmetric Pati-Salam (PS) model based on the gauge group SU(2) L × SU(2) R × SU(4) C with an E 6 -inspired particle spectrum which naturally accommodates a multi-TeV leptoquark gauge boson $$ {X}_{\mu}\left(3,1,\frac{2}{3}\right) $$ X μ 3 1 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 μ 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 μ , with Z 2 -unsuppressed contributions arising only via one-loop diagrams. We show that X μ can be as light as 1.1 TeV while being compatible with all flavor-violating constraints. However, mass relations among the $$ \left({W}_{\mu}^{\prime \pm },{Z}_{\mu}^{\prime },{X}_{\mu}\right) $$ W μ ′ ± Z μ ′ X μ gauge bosons push the X μ mass limit up to 4.3 TeV from the stringent LHC bounds on the Z ′ 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 μ → eγ , μ → eee , and μ - 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.