A Pati-Salam realization of the Nelson-Barr mechanism

We present a UV completion of the Standard Model in which quarks and leptons are unified under color SU(4). A single fermionic representation, the real antisymmetric, provides the building blocks to address the strong CP problem via the Nelson-Barr mechanism, while simultaneously correcting the charged-lepton and down-quark mass relations predicted by Pati-Salam theories for the two heaviest generations. We show that the characteristic scales of the theory are strongly constrained by its phenomenology. The interplay between the quality of the Nelson-Barr mechanism and the non-observation of baryon-number-violating processes determines the scale of spontaneous CP violation and the mass of the new vector-like down quark, while the mass of the Standard Model down quark and the upper bound on neutrino masses fix the quark-lepton unification scale. The theory predicts a distinctive baryon-number-violating decay mode of the neutron, $n \to K^+ \ell^-$ (with $\ell = e,\mu$), which lies within the projected sensitivity of upcoming nucleon-decay experiments such as Hyper-Kamiokande and DUNE.