Fourth Generation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>Violation Effects on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:mi>K</mml:mi><mml:mi>π</mml:mi></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>φ</mml:mi><mml:mi>K</mml:mi></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi><mml:mi>K</mml:mi></mml:math>in Next-to-Leading-Order Perturbative QCD
Bibliographic record
Abstract
We study the effect from a sequential fourth generation quark on penguin-dominated two-body nonleptonic $B$ meson decays in the next-to-leading order perturbative QCD formalism. With an enhancement of the color-suppressed tree amplitude and possibility of a new $CP$ phase in the electroweak penguin amplitude, we can account better for ${A}_{CP}({B}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})\ensuremath{-}{A}_{CP}({B}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{0})$. Taking $|{V}_{{t}^{\ensuremath{'}}s}{V}_{{t}^{\ensuremath{'}}b}|\ensuremath{\sim}0.02$ with a phase just below 90\ifmmode^\circ\else\textdegree\fi{}, which is consistent with the $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ rate and the ${B}_{s}$ mixing parameter $\ensuremath{\Delta}{m}_{{B}_{s}}$, we find a downward shift in the mixing-induced $CP$ asymmetries of ${B}^{0}\ensuremath{\rightarrow}{K}_{S}{\ensuremath{\pi}}^{0}$ and $\ensuremath{\phi}{K}_{S}$. The predicted behavior for ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{K}_{S}$ is opposite.
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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 | 0.006 | 0.004 |
| Meta-epidemiology (narrow) | 0.005 | 0.008 |
| Meta-epidemiology (broad) | 0.003 | 0.008 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.007 | 0.006 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.007 | 0.007 |
| Research integrity | 0.005 | 0.008 |
| Insufficient payload (model declined to judge) | 0.004 | 0.013 |
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; both teacher heads agree on what is shown here.
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".