Practical approximation scheme for the pion dynamics in the three-nucleon system
Bibliographic record
Abstract
We discuss a working approximation scheme to a recently developed formulation of the coupled $\ensuremath{\pi}\mathrm{NNN}\ensuremath{-}\mathrm{NNN}$ problem. The approximation scheme is based on the physical assumption that, at low energies, the 2N-subsystem dynamics in the elastic channel is conveniently described by the usual 2N-potential approach, while the explicit pion dynamics describes small, correction-type effects. Using the standard separable-expansion method, we obtain a dynamical equation of the Alt-Grassberger-Sandhas (AGS) type. This is an important result, because the computational techniques used for solving the normal AGS equation can also be used to describe the pion dynamics in the 3N system once the matrix dimension is increased by one component. We have also shown that this approximation scheme treats the conventional 3N problem once the pion degrees of freedom are projected out. Then, the 3N system is described with an extended AGS-type equation where the spin-off of the pion dynamics (beyond the 2N potential) is taken into account in additional contributions to the driving term. These new terms are shown to reproduce the diagrams leading to modern 3N-force models. We also recover two sets of irreducible diagrams that are commonly neglected in 3N-force discussions, and conclude that these sets should be further investigated.
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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".