Strong CP Problem and Symmetric Mass Solution

TL;DR

This paper introduces Symmetric Mass Generation (SMG) as a novel mechanism to solve the Strong CP problem by generating symmetry-preserving mass gaps without breaking gauge symmetries, explaining the near-zero theta angle in the Standard Model.

Contribution

The paper proposes new SMG-based models that generate fermion masses without breaking symmetries, addressing the Strong CP problem and fermion doubling issues in chiral theories.

Findings

SMG can generate mass gaps without symmetry breaking.

Models predict highly interacting SM or mirror fermions.

Solutions relate to fermion doubling and parity symmetry issues.

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.