TeV-scale vector leptoquark from Pati-Salam unification with vectorlike families

In this paper, we show an explicit way to realize a TeV-scale vector leptoquark from the Pati-Salam unification with extra vectorlike families. The leptoquark mass is constrained to be heavier than PeV scale by the measurement of a flavor violating kaon decay, KL → μe, in conventional models. This strong constraint can be avoided by introducing vectorlike families consistently with the quark and lepton masses and Cabbibo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata matrices. In this model, the vector leptoquark can be sufficiently light to explain the recent b → sμμ anomaly, while the b → cτν anomaly is difficult to be explained due to the strong constraints from the Z′ boson and vectorlike quark searches at the LHC. When the b → sμμ anomaly is explained, we show that O(0.2)% tuning is required in the fermion matrix, the future experiments in μ → eγ and μ−e conversions will cover most available parameter space, and sizable neutral meson mixings, induced by the extra Higgs doublets, are unavoidable.