An Effective Field Theory for Jet Processes

TL;DR

The paper addresses large logarithms in cone-jet cross sections, including non-global logarithms, by constructing a soft-collinear effective theory that introduces a novel collinear-soft (coft) mode. It derives a complete factorization formula with a multi-Wilson-line structure that separates physics at distinct scales and enables RG-based resummation of all logarithms, including NGLs, up to all orders. Key contributions include the identification of the coft scale $Q\delta\beta$, the multi-Wilson-line factorization for cone jets, and the renormalization framework with hierarchical jet and coft mixing that mirrors parton-shower dynamics. The approach provides a principled path to higher-precision jet observables and has potential applications for hadron-collider jet physics at the LHC.

Abstract

Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom which are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the non-global logarithms.

Figures (1)

• Figure 1: Soft factorization (left) versus coft factorization (right). Collinear particles are shown in blue, soft emissions in green and the small-angle soft radiation described by the coft mode in red. The double lines indicate the direction of the associated Wilson lines.