A grand-unified Nelson–Barr model

Abstract

We argue that the Nelson–Barr solution to the Strong CP Problem can be naturally realized in an E6 grand-unified theory. The chiral SM fermions reside in three generations of E6 fundamentals together with heavy vectorlike down quarks, leptons doublets and right-handed neutrinos. CP is imposed on the Lagrangian and broken only spontaneously at high scales, leading to a mixing between chiral and vectorlike fields that allows to solve the Strong CP Problem through the Nelson–Barr mechanism. The main benefit of the E6 GUT structure is the predictivity in the SM fermion sector, and a perfect fit to all SM observables can be obtained despite being over-constrained. Definite predictions are made for the neutrino sector, with a Dirac CP phase that is correlated to the CKM phase, allowing to test this model in the near future.