Lattice Calculation of the Proton Charge Radius
Bibliographic record
Abstract
The charge radius of the proton has been measured in scattering and spectroscopy experiments using both electronic and muonic probes. The electronic and muonic measurements are discrepant at $5\sigma$, giving rise to what is known as the proton radius puzzle. With the goal of resolving this, we introduce a novel method of using lattice QCD to determine the isovector charge radius -- defined as the slope of the electric form factor at zero four-momentum transfer -- by introducing a mass splitting between the up and down quarks. This allows us to access timelike four-momentum transfers as well as spacelike ones, leading to potentially higher accuracy in determining the form factor slope at $Q^2 = 0$ by interpolation. In this preliminary study, we find a Dirac isovector radius squared of $0.320 \pm 0.074$ fm$^2$ at quark masses corresponding to $m_\pi = 450$ MeV. We compare the feasibility of this method with other approaches of determining the proton charge radius from lattice QCD.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".