Quark-hadron duality and the determination of $α_s$ from hadronic $τ$ decay: facts vs. myths
Bibliographic record
Abstract
Non-perturbative effects have a small but non-trivial impact on the determination of the strong coupling from hadronic $τ$ decay data. Several approaches have been proposed to take these into account, the two most important of which are the ``truncated OPE'' approach and ``DV-model'' approach. Recently, Pich and Rodríguez-Sánchez have raised a number of criticisms of the latter approach, including, most notably, claims of the existence of (i) a supposed instability with respect to variations of the model for incorporating quark-hadron duality violations, and (ii) an alleged redundancy in the fitting strategy employed in the DV-model approach. In this paper, we address these criticisms one by one, showing they fail to survive more detailed scrutiny of the mathematical or numerical arguments that underpin them. We also show that, while the redundancy claim does not apply to the DV-model approach, it does, in fact, apply to the truncated OPE approach. In particular, the $α_s$ value determined in the latter turns out to derive purely from perturbation theory, with no role played by the non-perturbative condensates determined in the rest of the analysis. This leads to the conclusion that a revision of the conventional understanding of what is learned from truncated OPE analyses is necessary and that only very limited self-consistency checks are possible within this framework. These observations raise new, non-trivial issues for the truncated OPE approach.
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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 | 0.013 | 0.029 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.021 |
| Scholarly communication | 0.005 | 0.019 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.002 | 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".