The Strong CP Problem Resolved: θ_{eff} = 0 from T³ Geometry, No Axion, and d_n < 5 × 10^{-30} e·cm
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The strong CP problem asks why the effective QCD theta parameter θ_{eff} = θ_{QCD} + arg(det M_u M_d) satisfies |θ_{eff}| < 10^{-10} despite no symmetry requiring it. The Trit framework [1] resolves this through two independent structural reasons, neither requiring a new symmetry, a new particle, or fine-tuning. First: all quark masses in the Trit are derived from m = Cα^x, which is real and positive for all winding numbers x. In the mass eigenstate basis, arg(det M_u M_d) = 0 exactly — the Yukawa sector contributes nothing to θ_{eff}. Second: the Trit internal space T³ = {-1,0,+1}³ has an exact reflection symmetry (a,b,c) → (-a,-b,-c), which acts as CP on the QCD sector and forces θ_{QCD} = 0 at the energy minimum. Together: θ_{eff} = 0 exactly. Quantum corrections from weak CP violation give δθ ~ G_F m_s² J_{CP}/(16π²) = 1.9×10^{-14}, far below any experimental sensitivity. The neutron electric dipole moment is d_n = 4.5×10^{-30} e·cm, four orders of magnitude below the nEDM@SNS target (10^{-28} e·cm). The Trit predicts that no QCD axion exists and all running axion searches (ADMX, CASPEr, HAYSTAC, ABRACADABRA) will find nothing. The observed decoupling of strong CP (absent) from weak CP (δ_{CKM} = arccos(1/√6) = 65.9°, large) is a geometric consequence of the Trit: strong CP is determined by the T³ global reflection symmetry, while weak CP is determined by the imaginary part of the local period matrix τ_{12} of the genus-3 flavour manifold H²/Γ.
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- Is supplement to
- Preprint: 10.5281/zenodo.20312220 (DOI)