Four-loop cusp anomalous dimension from obstructions
Bibliographic record
Abstract
We introduce a method for extracting the cusp anomalous dimension at $L$ loops from four-gluon amplitudes in $\mathcal{N}=4$ Yang-Mills without evaluating any integrals that depend on the kinematical invariants. We show that the anomalous dimension only receives contributions from the obstructions introduced in [F. Cachazo, M. Spradlin, and A. Volovich, J. High Energy Phys. 07 (2006) 007]. We illustrate this method by extracting the two- and three-loop anomalous dimensions analytically and the four-loop one numerically. The four-loop result was recently guessed to be ${f}^{(4)}=\ensuremath{-}(4{\ensuremath{\zeta}}_{2}^{3}+24{\ensuremath{\zeta}}_{2}{\ensuremath{\zeta}}_{4}+50{\ensuremath{\zeta}}_{6}\ensuremath{-}4(1+r){\ensuremath{\zeta}}_{3}^{2})$ with $r=\ensuremath{-}2$ using integrability and string theory arguments in [N. Beisert, B. Eden, and M. Staudacher, J. Stat. Mech. (2007) P021]. Simultaneously, ${f}^{(4)}$ was computed numerically in [Z. Bern, M. Czakon, L. J. Dixon, D. A. Kosower, and V. A. Smirnov, Phys. Rev. D 75, 085010 (2007)] from the four-loop amplitude obtaining, with best precision at the symmetric point $s=t$, $r=\ensuremath{-}2.028(36)$. Our computation is manifestly $s/t$ independent and improves the precision to $r=\ensuremath{-}2.000\text{ }02(3)$, providing strong evidence in favor of the conjecture. The improvement is possible due to a large reduction in the number of contributing terms, as well as a reduction in the number of integration variables in each term.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".