Toward multi-differential cross sections: measuring two angularities on a single jet
Bibliographic record
Abstract
The analytic study of differential cross sections in QCD has typically focused on individual observables, such as mass or thrust, to great success. Here, we present a first study of double differential jet cross sections considering two recoil-free angularities measured on a single jet. By analyzing the phase space defined by the two angularities and using methods from soft-collinear effective theory, we prove that the double differential cross section factorizes at the boundaries of the phase space. We also show that the cross section in the bulk of the phase space cannot be factorized using only soft and collinear modes, excluding the possibility of a global factorization theorem in soft-collinear effective theory. Nevertheless, we are able to define a simple interpolation procedure that smoothly connects the factorization theorem at one boundary to the other. We present an explicit example of this at next-to-leading logarithmic accuracy and show that the interpolation is unique up to α 4 order in the exponent of the cross section, under reasonable assumptions. This is evidence that the interpolation is sufficiently robust to account for all logarithms in the bulk of phase space to the accuracy of the boundary factorization theorem. We compare our analytic calculation of the double differential cross section to Monte Carlo simulation and find qualitative agreement. Because our arguments rely on general structures of the phase space, we expect that much of our analysis would be relevant for the study of phenomenologically well-motivated observables, such as N -subjettiness, energy correlation functions, and planar flow.
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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".