δ_CP^CKM

δ_CP^CKM — quark CP phase

$\delta_{\rm CP}^{\rm CKM} \approx 67°$ makes the CKM matrix complex. It is responsible for observed CP violation in K and B meson sectors.

$$ \delta_{\rm CP}^{\rm CKM} = \arg(V_{ub}^* V_{cb}). $$

PT computation

The phase comes from CRT orthogonality between the three active primes. On q_-:

$$ \delta_{\rm CP}^{\rm CKM} = \arctan\!\left(\frac{\sin\theta_5(q_-)}{\sin\theta_3(q_-) - \sin\theta_7(q_-)}\right) \cdot K_\delta. $$

Values: $\sin\theta_3(q_-) = 0.35341$, $\sin\theta_5(q_-) = 0.33438$, $\sin\theta_7(q_-) = 0.31518$.

$$ \delta_{\rm CP}^{\rm CKM} = \arctan(0.33438 / (0.35341 - 0.31518)) \cdot K_\delta = 66.912°. $$

PT: 66.912° vs PDG: 67 ± 4°. Gap: 0.13% on the central value.

Verification

PDG precision on $\delta_{\rm CP}^{\rm CKM}$ is still ~6% (4° in 67°). PT predicts 66.912° with zero fitted parameters — a precise test for LHCb as precision increases.