Power Corrections and Rapidity Logarithms in Soft-collinear Effective Theory
Bibliographic record
Abstract
In this thesis a recent formulation of Soft-Collinear Effective Theory is used to study power corrections to collider observables. The techniques and concepts developed here are primarily demonstrated in the context of the Drell-Yan process, but are also broadly applicable in processes involving high-energy collimated colored particles. First, we make progress towards the resummation of power-suppressed logarithms in processes which involve the hard interaction of two jets. We identify and compute the anomalous dimensions of all the operators that contribute to two-sector processes at $O(1/q^2)$. These anomalous dimensions are necessary to resum hard processes at next-to-leading power, although an additional observable-dependent step of matching and running is necessary to complete the full resummation. We also demonstrate how the overlap subtraction prescription for loops extends to these subleading operators. Next, we study the origin of rapidity logarithms using a formulation of Soft-Collinear Effective Theory in which infrared degrees of freedom are not explicitly separated into modes. We consider the Sudakov form factor with a massive vector boson and Drell-Yan production of lepton pairs at small transverse momentum as demonstrative examples. We find that rapidity divergences introduce a scheme dependence into the effective theory and are associated with large logarithms appearing in the soft matching conditions. This scheme dependence may be used to derive corresponding rapidity renormalization group equations. Finally, we examine the Drell-Yan process at next-to-leading power, where we derive a factorization of the differential cross section in the small-$q_T$ hierarchy with $q^2\gg q_T^2\gg\Lambda_{\mathrm{QCD}}^2$. We show that the cross section may be written in terms of matrix elements of power-suppressed operator products which contribute to $O(q_T^2/q^2)$ coefficients of the usual parton distribution functions. The factorization formula allows power-suppressed logarithms in each of the relevant factors to be resummed. We discuss the cancellation of rapidity divergences and the overlap subtractions required to eliminate double counting at next-to-leading power.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".