Considering 2 → 2 gauge-theory scattering with general colour in the highenergy limit, we compute the Regge-cut contribution to three loops through next-to-nextto-leading high-energy logarithms (NNLL) in the signature-odd sector. Our formalism is based on using the non-linear Balitsky-JIMWLK rapidity evolution equation to derive an effective Hamiltonian acting on states with a fixed number of Reggeized gluons. A new effect occurring first at NNLL is mixing between states with k and k + 2 Reggeized gluons due non-diagonal terms in this Hamiltonian. Our results are consistent with a recent determination of the infrared structure of scattering amplitudes at three loops, as well as a computation of 2 → 2 gluon scattering in N = 4 super Yang-Mills theory. Combining the latter with our Regge-cut calculation we extract the three-loop Regge trajectory in this theory. Our results open the way to predict high-energy logarithms through NNLL at higher-loop orders.
Threshold logarithms become dominant in partonic cross sections when the selected final state forces gluon radiation to be soft or collinear. Such radiation factorizes at the level of scattering amplitudes, and this leads to the resummation of threshold logarithms which appear at leading power in the threshold variable. In this paper, we consider the extension of this factorization to include effects suppressed by a single power of the threshold variable. Building upon the Low-Burnett-Kroll-Del Duca (LBKD) theorem, we propose a decomposition of radiative amplitudes into universal building blocks, which contain all effects ultimately responsible for next-to-leading-power (NLP) threshold logarithms in hadronic cross sections for electroweak annihilation processes. In particular, we provide a NLO evaluation of the radiative jet function, responsible for the interference of next-to-soft and collinear effects in these cross sections. As a test, using our expression for the amplitude, we reproduce all abelian-like NLP threshold logarithms in the NNLO Drell-Yan cross section, including the interplay of real and virtual emissions. Our results are a significant step towards developing a generally applicable resummation formalism for NLP threshold effects, and illustrate the breakdown of next-to-soft theorems for gauge theory amplitudes at loop level.
Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a nonabelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.
We resum the leading logarithms α n s ln 2n−1 (1 − z), n = 1, 2, . . . near the kinematic threshold z = Q 2 /ŝ → 1 of the Drell-Yan process at next-to-leading power in the expansion in (1 − z). The derivation of this result employs soft-collinear effective theory in position space and the anomalous dimensions of subleading-power soft functions, which are computed. Expansion of the resummed result leads to the leading logarithms at fixed loop order, in agreement with exact results at NLO and NNLO and predictions from the physical evolution kernel at N 3 LO and N 4 LO, and to new results at the five-loop order and beyond.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.