First evidence for $\\cos 2\\beta>0$ and resolution of the CKM Unitarity Triangle ambiguity by a time-dependent Dalitz plot analysis of $B^{0} \\to D^{(*)} h^{0}$ with $D \\to K_{S}^{0} \\pi^{+} \\pi^{-}$ decays
Bibliographic record
Abstract
We present first evidence that the cosine of the CP-violating weak phase $2\\beta$ is positive, and hence exclude trigonometric multifold solutions of the CKM Unitarity Triangle using a time-dependent Dalitz plot analysis of $B^{0} \\to D^{(*)} h^{0}$ with $D \\to K_{S}^{0} \\pi^{+} \\pi^{-}$ decays, where $h^{0} \\in \\{\\pi^{0}, \\eta, \\omega \\}$ denotes a light unflavored and neutral hadron. The measurement is performed combining the final data sets of the BaBar and Belle experiments collected at the $\\Upsilon(4S)$ resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. The data samples contain $( 471 \\pm 3 )\\times 10^6\\, B\\bar{B}$ pairs recorded by the BaBar detector and $( 772 \\pm 11 )\\times 10^6\\, B\\bar{B}$ pairs recorded by the Belle detector. The results of the measurement are $\\sin{2\\beta} = 0.80 \\pm 0.14 \\,(\\rm{stat.}) \\pm 0.06 \\,(\\rm{syst.}) \\pm 0.03 \\,(\\rm{model})$ and $\\cos{2\\beta} = 0.91 \\pm 0.22 \\,(\\rm{stat.}) \\pm 0.09 \\,(\\rm{syst.}) \\pm 0.07 \\,(\\rm{model})$. The result for the direct measurement of the angle $\\beta$ of the CKM Unitarity Triangle is $\\beta = \\left( 22.5 \\pm 4.4 \\,(\\rm{stat.}) \\pm 1.2 \\,(\\rm{syst.}) \\pm 0.6 \\,(\\rm{model}) \\right)^{\\circ}$. The quoted model uncertainties are due to the composition of the $D^{0} \\to K_{S}^{0} \\pi^{+} \\pi^{-}$ decay amplitude model, which is newly established by performing a Dalitz plot amplitude analysis using a high-statistics $e^{+}e^{-} \\to c\\bar{c}$ data sample. CP violation is observed in $B^{0} \\to D^{(*)} h^{0}$ decays at the level of $5.1$ standard deviations. The significance for $\\cos{2\\beta}>0$ is $3.7$ standard deviations. The trigonometric multifold solution $\\pi/2 - \\beta = (68.1 \\pm 0.7)^{\\circ}$ is excluded at the level of $7.3$ standard deviations. The measurement resolves an ambiguity in the determination of the apex of the CKM Unitarity Triangle.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".