Abstract
We argue that the Nelson–Barr solution to the Strong CP Problem can be naturally realized in an E_6 grand-unified theory. The chiral SM fermions reside in three generations of E_6 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 E_6 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.
Highlights
One of the most puzzling aspects of the Standard Model (SM) is the absence of CP violation in strong interactions, as measured by the topological angle θ = θQCD − θF, (1.1)where θQCD denotes the coefficient of αs2/8π GGand θF = arg det Mu Md
We argue that the Nelson–Barr solution to the Strong CP Problem can be naturally realized in an E6 grandunified theory
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
Summary
We address the issue of predictivity by embedding the Nelson–Barr mechanism into an E6 grandunified framework This allows to connect the phases in the neutrino sector to the CKM phase, and in particular to predict the Dirac CP phase that will be measured in the near future. Spontaneous CP breaking will induce a mixing between these vectorlike fields with the chiral fermions, and complex phases will enter low-energy quark, charged lepton and neutrino masses in a correlated manner. In our model the Nelson–Barr mechanism becomes predictive in the neutrino sector because of the E6 GUT structure, which in turn is phenomenologically viable because of the mixing with the heavy fermions needed to generate the CKM phase.
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