Probing uncertainties of nuclear structure corrections in light muonic atoms
Bibliographic record
Abstract
Recent calculations of nuclear structure corrections to the Lamb shift in light muonic atoms are based on an expansion in a parameter $\ensuremath{\eta}$, where only terms up to second order are retained. The parameter $\ensuremath{\eta}$ can be shown to be proportional to $\sqrt{{m}_{r}/{m}_{p}}$, where ${m}_{r}$ is the reduced mass of the muon-nucleus system and ${m}_{p}$ is the proton mass, so that it is small and the expansion is expected to converge. However, practical implementations show that the $\ensuremath{\eta}$ convergence may be slower than expected. In this work, we probe the uncertainties due to this expansion using a different formalism, which is based on a multipole expansion of the longitudinal and transverse response functions. We refer to this alternative expansion as the $\ensuremath{\eta}$-less formalism. We generalize this formalism to account for the cancellation of elastic terms such as the third Zemach moment (or Friar moment) and embed it in a computationally efficient framework. We implement and test this approach in the case of muonic deuterium. The comparison of results in the point nucleon limit for both methods achieve subpercent agreement. When nucleon form factors are introduced, we find $4%$ and $2%$ differences in the third Zemach moment and nuclear polarizability, respectively, compared to the $\ensuremath{\eta}$-less expansion, indicating that the nucleon form factor approximations by Ji et al. [J. Phys. G 45, 093002 (2018)] should be improved. However, we find that the sum of these terms removes this dependence and the uncertainty due to the $\ensuremath{\eta}$ expansion and the related second-order approximation in the nucleon form factors amounts only to $0.2%$ and thus is fully justified in muonic deuterium. This computationally efficient framework paves the way for further studies in light muonic systems with more than two nucleons, where controlling and reducing uncertainties in nuclear structure corrections is key to the experimental efforts of the CREMA Collaboration.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".