New Formulation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi><mml:mi>Z</mml:mi></mml:math>Box Corrections to the Weak Charge of the Proton
Bibliographic record
Abstract
We present a new formulation of one of the major radiative corrections to the weak charge of the proton---that arising from the axial-vector hadron part of the $\ensuremath{\gamma}Z$ box diagram, $\ensuremath{\mathfrak{R}}\mathrm{e}{\ensuremath{\square}}_{\ensuremath{\gamma}Z}^{\mathrm{A}}$. This formulation, based on dispersion relations, relates the $\ensuremath{\gamma}Z$ contributions to moments of the ${F}_{3}^{\ensuremath{\gamma}Z}$ interference structure function. It has a clear connection to the pioneering work of Marciano and Sirlin, and enables a systematic approach to improved numerical precision. Using currently available data, the total correction from all intermediate states is $\ensuremath{\mathfrak{R}}\mathrm{e}{\ensuremath{\square}}_{\ensuremath{\gamma}Z}^{\mathrm{A}}=0.004\text{ }4(4)$ at zero energy, which shifts the theoretical estimate of the proton weak charge from 0.071 3(8) to 0.070 5(8). The energy dependence of this result, which is vital for interpreting the ${Q}_{\mathrm{weak}}$ experiment, is also determined.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.017 | 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".