Nuclear structure corrections to the Lamb shift in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>μ</mml:mi><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:none/><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si103.gif" overflow="scroll"><mml:mi>μ</mml:mi><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>
Bibliographic record
Abstract
Measuring the 2S-2P Lamb shift in a hydrogen-like muonic atom allows one to extract its nuclear charge radius with a high precision that is limited by the uncertainty in the nuclear structure corrections. The charge radius of the proton thus extracted was found to be 7-sigma away from the CODATA value, in what has become the yet unsolved "proton radius puzzle". Further experiments currently aim at the isotopes of hydrogen and helium: the precise extraction of their radii may provide a hint at the solution of the puzzle. We present the first ab initio calculation of nuclear structure corrections, including the nuclear polarization correction, to the 2S-2P transition in $\mu^3$He$^+$ and $\mu^3$H, and assess solid theoretical error bars. Our predictions reduce the uncertainty in the nuclear structure corrections to the level of a few percents and will be instrumental to the on-going $\mu^3$He$^+$ experiment. We also support the mirror $\mu\,^3$H system as a candidate for further probing of the nucleon polarizabilities and shedding more light on the puzzle.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.004 |
| Meta-epidemiology (narrow) | 0.004 | 0.008 |
| Meta-epidemiology (broad) | 0.002 | 0.007 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.008 | 0.007 |
| Scholarly communication | 0.008 | 0.007 |
| Open science | 0.009 | 0.011 |
| Research integrity | 0.007 | 0.008 |
| Insufficient payload (model declined to judge) | 0.604 | 0.008 |
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; both teacher heads agree on what is shown here.
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".