Measurement of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math> cross section using initial-state radiation at <i>BABAR</i>
Bibliographic record
Abstract
The process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}2{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$ is investigated by means of the initial-state radiation technique, where a photon is emitted from the incoming electron or positron. Using $454.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected around a center-of-mass energy of $\sqrt{s}=10.58\text{ }\text{ }\mathrm{GeV}$ by the BABAR experiment at SLAC, approximately 150000 signal events are obtained. The corresponding nonradiative cross section is measured with a relative uncertainty of 3.6% in the energy region around 1.5 GeV, surpassing all existing measurements in precision. Using this new result, the channel's contribution to the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon is calculated as $({g}_{\ensuremath{\mu}}^{{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}2{\ensuremath{\pi}}^{0}}\ensuremath{-}2)/2=(17.9\ifmmode\pm\else\textpm\fi{}{0.1}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.6}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ in the energy range $0.85\text{ }\text{ }\mathrm{GeV}<{E}_{\mathrm{CM}}<1.8\text{ }\text{ }\mathrm{GeV}$. In the same energy range, the impact on the running of the fine-structure constant at the ${Z}^{0}$-pole is determined as $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}^{{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}2{\ensuremath{\pi}}^{0}}({M}_{\mathrm{Z}}^{2})=(4.44\ifmmode\pm\else\textpm\fi{}{0.02}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}{0.14}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. Furthermore, intermediate resonances are studied and especially the cross section of the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}2{\ensuremath{\pi}}^{0}$ is measured.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.096 | 0.051 |
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".