New strategy for the lattice evaluation of the leading order hadronic contribution to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">(</mml:mo><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>μ</mml:mi></mml:msub></mml:math>
Bibliographic record
Abstract
A reliable evaluation of the integral giving the hadronic vacuum polarization contribution to the muon anomalous magnetic moment should be possible using a simple trapezoid rule integration of lattice data for the subtracted electromagnetic current polarization function in the Euclidean momentum interval ${Q}^{2}>{Q}_{\mathrm{min}}^{2}$, coupled with an $N$-parameter Pad\'e or other representation of the polarization in the interval $0<{Q}^{2}<{Q}_{\mathrm{min}}^{2}$, for sufficiently high ${Q}_{\mathrm{min}}^{2}$ and sufficiently large $N$. Using a physically motivated model for the $I=1$ polarization, and the covariance matrix from a recent lattice simulation to generate associated fake ``lattice data,'' we show that systematic errors associated with the choices of ${Q}_{\mathrm{min}}^{2}$ and $N$ can be reduced to well below the 1% level for ${Q}_{\mathrm{min}}^{2}$ as low as $0.1\text{ }\text{ }{\mathrm{GeV}}^{2}$ and rather small $N$. For such low ${Q}_{\mathrm{min}}^{2}$, both a next-to-next-to-leading-order (NNLO) chiral representation with one additional NNNLO term and a low-order polynomial expansion employing a conformally transformed variable also provide representations sufficiently accurate to reach this precision for the low-${Q}^{2}$ contribution. Combined with standard techniques for reducing other sources of error on the lattice determination, this hybrid strategy thus looks to provide a promising approach to reaching the goal of a subpercent-precision determination of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment on the lattice.
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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 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.014 | 0.006 |
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".