Strong CP Problem and Symmetric Mass Solution

Abstract

We propose a novel solution to the Strong CP problem -- to explain why SU(3) strong force has a nearly zero theta angle $\bar\theta_3 \simeq 0$ 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 $\bar\theta_3$. 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 $\mathbb{Z}_2^{\rm PR}$ symmetry at high energy, so the $\bar\theta_3 = 0$. 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.