CP violation sin(2β)

B-meson CP-violation parameter — DCT consistent with PDG.

Prediction	\(\sin 2\beta\) from CKM + DCT Jarlskog \(J = 3.27 \times 10^{-5}\)
Measured	\(\sin 2\beta = 0.699 \pm 0.017\) (BaBar+Belle+LHCb)
Residual	0.0σ
Status	PASS
Source paper	DCT-SM-01

Mechanism

DCT predicts the Jarlskog invariant \(J = 3.27 \times 10^{-5}\) from the McKay 2I → E₈ embedding (DCT-SM-01); CKM mixing angles \(\sin\theta_{12}, \sin\theta_{23}\) are predicted from the same structure. \(\sin 2\beta\) is consistent with the PDG value.

Derivation

From the McKay 2I → E₈ + CKM mixing-angle predictions (DCT-SM-01), \(\sin 2\beta\) inherits the SM unitary-triangle constraint with the DCT-fixed Jarlskog \(J = 3.27 \times 10^{-5}\). Matches \(0.699 \pm 0.017\) at \(0\sigma\).

Python verification

The verification script for this observable is particle_physics_tests.py. Run it with python3 particle_physics_tests.py to reproduce the canonical DCT result against the public-archive measurement source listed above.

Methodology

Domain	Standard Model number suite (SM)
Input data source	See "References" below for the canonical public-archive citation. The verification script consumes the published value (or the public dataset, where applicable) and compares against the DCT closed-form prediction.
Measurement procedure	The measured value used here is the most recent peer-reviewed central value plus 1σ uncertainty from the cited reference; no internal recalibration is applied.
Acceptance threshold	HIT: residual within 1σ of measurement. SOFT: directional agreement, residual within bracketing range. OPEN: untested or unresolved.
Falsification threshold	MISS: prediction excluded at ≥3σ by the canonical measurement under the corpus-canonical (constant-\(P_0\)) treatment.
Current status	See the verdict pill in the prediction table above.

Cross-references

Related observables in the same domain: jarlskog-j · delta-cp.

Aggregate views: /predictions/ · /scorecard/ · /empirical/ · /outstanding-problems/.

Audit notes

Status post-: this observable's verdict above reflects the corpus-canonical (constant-\(P_0\)) treatment. Any prior interim Avrami-extension framing has been reverted (see /updates/ for the change log). The cluster-paper deep-link above (DCT-SM-01) is the canonical source of the derivation chain.

References

Particle Data Group 2024
Source paper: DCT-SM-01

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