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Mechanism for the strong CP problem (θQCD ≈ 0) within the framework

Develop a mechanism within the E6^L × E6^R and exceptional Jordan algebra framework that explains why the QCD vacuum angle θQCD is approximately zero.

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Background

The proposed construction focuses on flavor kinematics and charged-fermion mass ratios and mixings; it does not address the strong CP problem. The smallness of θQCD remains a critical unsolved issue in particle physics.

The authors explicitly list the need for a mechanism for θQCD ≈ 0 as an open issue, indicating that their framework should eventually incorporate or be compatible with a solution (e.g., axion-like dynamics or other mechanisms) consistent with their exceptional-algebraic structure.

References

Open issues. (a) A UV origin of $\delta$, $\varepsilon$, and $\kappa_{23}$, ideally from the $U(1){\rm dem}$ sector of $E_6R$; (b) quantitative RG--running across sectors in the $E_6L\times E_6R$ setting; (c) leptonic absolute mass scale and Majorana phases; (d) a mechanism for $\theta{\rm QCD}\approx 0$.

— Fermion mass ratios from the exceptional Jordan algebra (2508.10131 - Singh, 13 Aug 2025) in Clarifications and limitations, Open issues paragraph