Pade-Summation Approach to QCD -Function Infrared Properties
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Bibliographic record
Abstract
In view of the successful asymptotic Padé-approximant predictions for higher-loop terms within QCD and massive scalar field theory, we address whether Padé-summations of the MS QCD β-function for a given number of flavours exhibit an infrared-stable fixed point, or alternatively, an infrared attractor of a double valued couplant as noted by Kogan and Shifman for the case of supersymmetric gluodynamics. Below an approximant-dependent flavour threshold (6 ≤ nf ≤ 8), we find that Padé-summation β-functions incorporating [2|1], [1|2], [2|2], [1|3], and [3|1] approximants whose Maclaurin expansions match known higher-than-one-loop contributions to the β-function series always exhibit a positive pole prior to the occurrence of their first positive zero, precluding any identification of this first positive zero as an infrared-stable fixed point of the β-function. This result is shown to be true regardless of the magnitude of the presently-unknown five-loop β-function contribution explicitly appearing within Padé-summation β-functions incorporating [2|2], [1|3] and [3|1] approximants. Moreover, the pole in question suggests the occurrence of dynamics in which both a strong and an asymptotically-free phase share a common infrared attractor. We briefly discuss the possible relevance of infrared-attractor dynamics to the success of recent calculations of the glueball mass spectra in QCD with Nc → ∞ via supergravity. As nf increases above an approximant-dependent flavour threshold, Padé-summation β-functions incorporating [2|2], [1|3] and [3|1] approximants exhibit dynamics controlled by an infrared-stable fixed point over a widening domain of the five-loop MS β-function parameter (β4/β0). Subsequent to the above-mentioned flavour threshold, all approximants considered exhibit infrared-stable fixed points that decrease in magnitude with increasing flavour number.
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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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it