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Bibliographic record
Abstract
We study the implications of several recent high-precision measurements of the pion form factor in the region of the $\ensuremath{\rho}\ensuremath{-}\ensuremath{\omega}$ interference shoulder for (i) the extraction of the $\ensuremath{\rho}\ensuremath{-}\ensuremath{\omega}$ mixing matrix element, ${\ensuremath{\Pi}}_{\ensuremath{\rho}\ensuremath{\omega}}({m}_{\ensuremath{\rho}}^{2})$, and (ii) the evaluation of the isospin-breaking correction needed to incorporate hadronic $\ensuremath{\tau}$ decay data into the determination of the standard model expectation for the leading order hadronic contribution, $[{a}_{\ensuremath{\mu}}{]}_{\mathrm{had}}^{\mathrm{LO}}$, to the anomalous magnetic moment of the muon, focussing, in the latter case, on the model dependence of the $\ensuremath{\rho}\ensuremath{-}\ensuremath{\omega}$ mixing component of the isospin-breaking correction. We consider a range of different models for the broad $\ensuremath{\rho}$ contribution to the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ amplitude, applying these models to each experimental data set, and find that the model dependence of the $\ensuremath{\rho}\ensuremath{-}\ensuremath{\omega}$ mixing correction is significantly larger than the uncertainty induced by experimental errors for any individual model. We also find that, for each such model, the recent data allows one to separate $\ensuremath{\rho}\ensuremath{-}\ensuremath{\omega}$ mixing and direct $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ coupling contributions to the amplitude, and hence to obtain a reasonably precise extraction of ${\ensuremath{\Pi}}_{\ensuremath{\rho}\ensuremath{\omega}}({m}_{\ensuremath{\rho}}^{2})$, uncontaminated by direct $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ coupling effects, for use in meson-exchange model calculations of charge symmetry breaking in $NN$ scattering.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.004 | 0.002 |
| Insufficient payload (model declined to judge) | 0.016 | 0.003 |
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".