Bounds on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msubsup><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">HVP</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">LO</mml:mi></mml:mrow></mml:msubsup></mml:math> using Hölder's inequalities and finite-energy QCD sum rules
Bibliographic record
Abstract
This study establishes bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon ( a μ HVP , LO , a μ = ( g − 2 ) μ / 2 ) by using Hölder's inequality and related inequalities in Finite-Energy QCD sum rules. Considering contributions from light quarks ( u , d , s ) up to five-loop order in perturbation theory within the chiral limit, leading-order light-quark mass corrections, next-to-leading order for dimension-four QCD condensates, and leading-order for dimension-six QCD condensates, the study finds QCD lower and upper bounds as ( 657.0 ± 34.8 ) × 10 − 10 ≤ a μ HVP , LO ≤ ( 788.4 ± 41.8 ) × 10 − 10 .
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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 | 0.005 | 0.020 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.021 | 0.005 |
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".