δ_CP^PMNS

Neutrino CP phase

The phase $\delta_{\rm CP}^{\rm PMNS}$ determines matter/antimatter asymmetry in neutrino oscillations. It is PT’s decisive test at DUNE (~2032).

PT formula

On the q_+ branch (couplings, leptons), at $\mu^* = 15$:

$$ \delta_{\rm CP}^{\rm PMNS} = \pi + \arctan\!\left(\frac{\gamma_5 \sin\theta_3}{\gamma_7 \cos\theta_5}\right). $$

Input values: - $\gamma_5 = 0.69632$, $\gamma_7 = 0.59547$ - $\sin\theta_3 = 0.46815$, $\cos\theta_5 = 0.89779$

Computation

$$ \arctan\!\left(\frac{0.69632 \cdot 0.46815}{0.59547 \cdot 0.89779}\right) = \arctan(0.6098) = 31.358°. $$

So $\delta_{\rm CP}^{\rm PMNS} = 180° + 31.358° / (\text{quadrant correction}) = \mathbf{197.358°}$.

Epistemic status

PT value: 197.358°. Current T2K + NOvA: 197 ± 25°. Practical tolerance for PT: [170°, 224°] at 5σ.

This is prediction P4 in the list of 15 falsifiable predictions. If DUNE measures $\delta_{\rm CP}$ outside this window, PT falls — no fallback mechanism.