Measurement of the<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>-violating phase<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>β</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:mi>ϕ</mml:mi></mml:mrow></mml:msubsup></mml:math>in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:mi>ϕ</mml:mi></mml:math>decays with the CDF II detector
Bibliographic record
Abstract
We present a measurement of the $CP$-violating parameter ${\ensuremath{\beta}}_{s}^{J/\ensuremath{\psi}\ensuremath{\phi}}$ using approximately 6500 ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}$ decays reconstructed with the CDF II detector in a sample of $p\overline{p}$ collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$ corresponding to $5.2\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ integrated luminosity produced by the Tevatron collider at Fermilab. We find the $CP$-violating phase to be within the range ${\ensuremath{\beta}}_{s}^{J/\ensuremath{\psi}\ensuremath{\phi}}\ensuremath{\in}[0.02,0.52]\ensuremath{\cup}[1.08,1.55]$ at 68% confidence level where the coverage property of the quoted interval is guaranteed using a frequentist statistical analysis. This result is in agreement with the standard model expectation at the level of about one Gaussian standard deviation. We consider the inclusion of a potential $S$-wave contribution to the ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+}{K}^{\ensuremath{-}}$ final state which is found to be negligible over the mass interval $1.009<m({K}^{+}{K}^{\ensuremath{-}})<1.028\text{ }\text{ }\mathrm{GeV}/{c}^{2}$. Assuming the standard model prediction for the $CP$-violating phase ${\ensuremath{\beta}}_{s}^{J/\ensuremath{\psi}\ensuremath{\phi}}$, we find the ${B}_{s}^{0}$ decay width difference to be $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}=0.075\ifmmode\pm\else\textpm\fi{}0.035(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.006(\mathrm{syst})\text{ }\text{ }{\mathrm{ps}}^{\ensuremath{-}1}$. We also present the most precise measurements of the ${B}_{s}^{0}$ mean lifetime $\ensuremath{\tau}({B}_{s}^{0})=1.529\ifmmode\pm\else\textpm\fi{}0.025(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.012(\mathrm{syst})\text{ }\text{ }\mathrm{ps}$, the polarization fractions $|{A}_{0}(0){|}^{2}=0.524\ifmmode\pm\else\textpm\fi{}0.013(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.015(\mathrm{syst})$ and $|{A}_{\ensuremath{\parallel}}(0){|}^{2}=0.231\ifmmode\pm\else\textpm\fi{}0.014(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.015(\mathrm{syst})$, as well as the strong phase ${\ensuremath{\delta}}_{\ensuremath{\perp}}=2.95\ifmmode\pm\else\textpm\fi{}0.64(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.07(\mathrm{syst})\text{ }\text{ }\mathrm{rad}$. In addition, we report an alternative Bayesian analysis that gives results consistent with the frequentist approach.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.036 | 0.016 |
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 source (direct Gemma or distilled Codex), 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".