The strong coupling from $e^+e^-\to$~hadrons
Bibliographic record
Abstract
We use a new compilation of the hadronic R <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>R</mml:mi> </mml:math> -ratio from available data for the process e^+e^-\to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <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>→</mml:mo> </mml:mrow> </mml:math> hadrons below the charm mass to determine the strong coupling \alpha_s <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> , using finite-energy sum rules. Quoting our results at the \tau <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>τ</mml:mi> </mml:math> mass to facilitate comparison to the results obtained from similar analyses of hadronic \tau <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>τ</mml:mi> </mml:math> -decay data, we find \alpha_s(m_\tau^2)=0.298\pm 0.016\pm 0.006 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>τ</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0.298</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.016</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.006</mml:mn> </mml:mrow> </mml:math> in fixed-order perturbation theory, and \alpha_s(m_\tau^2)=0.304\pm 0.018\pm 0.006 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>τ</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0.304</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.018</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.006</mml:mn> </mml:mrow> </mml:math> in contour-improved perturbation theory, where the first error is statistical, and the second error combines various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic \tau <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>τ</mml:mi> </mml:math> decays. We briefly compare the R(s) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>s</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> -based analysis with the \tau <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>τ</mml:mi> </mml:math> -based analysis.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.041 | 0.015 |
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".