Precision Determination of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:msub><mml:mi>Λ</mml:mi><mml:mover accent="true"><mml:mi>MS</mml:mi><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:msub></mml:math>from the QCD Static Energy
Bibliographic record
Abstract
We use the recently obtained theoretical expression for the complete QCD static energy at next-to-next-to-next-to leading-logarithmic accuracy to determine ${r}_{0}{\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}$ by comparison with available lattice data, where ${r}_{0}$ is the lattice scale and ${\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}$ is the QCD scale. We obtain ${r}_{0}{\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}={0.622}_{\ensuremath{-}0.015}^{+0.019}$ for the zero-flavor case. The procedure we describe can be directly used to obtain ${r}_{0}{\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}$ in the unquenched case, when unquenched lattice data for the static energy at short distances becomes available. Using the value of the strong coupling ${\ensuremath{\alpha}}_{s}$ as an input, the unquenched result would provide a determination of the lattice scale ${r}_{0}$.
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.011 | 0.007 |
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".