Strong CP Problem and Symmetric Mass Solution

We propose a novel solution to the Strong CP problem — to explain why SU(3) strong force has a nearly zero theta angle ¯ θ 3 (cid:39) 0 for the 4d Standard Model (SM). The new ingredient is Symmetric Mass Generation (SMG): symmetry-preserving mass or energy gap can be generated without breaking any symmetry G and without any quadratic mean-ﬁeld mass deformation as long as G is all perturbative local and nonperturbative global anomaly-free. In our ﬁrst model, we propose a disordered non-mean-ﬁeld SMG gap (instead of the ordered Anderson-Higgs-induced mass gap) for the u quark (or generally a set of quarks and leptons totally anomaly-free in G ) generated by multi-fermion interactions or by dynamical disordered mass ﬁelds, absorbing ¯ θ 3 . Another variant of this ﬁrst model is the SMG gapping a hypothetical hidden full fourth family of SM fermions. In our second model, we have a chiral SM and mirror SM together to respect the Nielsen-Ninomiya fermion-doubling and a parity-reﬂection Z PR2 symmetry at high energy, so the ¯ θ 3 = 0. Then the SMG lifts only the mirror SM with a large energy gap but leaves the chiral SM at lower energy, which not only “spontaneously” breaks the parity-reﬂection symmetry maximally but also relates our solution to solve another nonperturbative chiral fermion regularization problem by removing the fermion doubling. The predictive signature of both SMG-based models is that some SM fermions or mirror fermions are highly interacting (beyond the conventional SM Higgs or SM gauge interactions) mediated through hypothetical direct multi-fermion or disordered mass-ﬁeld interactions.