QCD resummation for hadronic final states

TL;DR

This topical review surveys all-order QCD resummation for hadronic final states, focusing on soft and collinear factorization and its implications for collider observables such as event shapes and jet substructure. It develops generating-functional and coherent-branching formalisms in QED and QCD, and presents practical frameworks (e.g., Caesar) for automated resummation to NLL and NNLL accuracy, including extensions to hadron collisions and non-global observables. Key contributions include the detailed treatment of thrust resummation, non-global logarithms via the BMS equation and Caron-Huot's color-density formalism, and the analysis of jet masses and grooming algorithms with associated resummation. The work highlights both the power and limitations of factorization in high-precision QCD predictions and outlines emerging techniques that enhance predictive control for LHC phenomenology.

Abstract

We review the basic concepts of all-order calculations in Quantum Chromodynamics (QCD) and their application to collider phenomenology. We start by discussing the factorization properties of QCD amplitudes and cross-sections in the soft and collinear limits and their resulting all-order exponentiation. We then discuss several applications of this formalism to observables which are of great interest at particle colliders. In this context, we describe the all-order resummation of event-shape distributions, as well as observables that probe the internal structure of hadronic jets.

Figures (11)

• Figure 1: Feynman diagrams contributing to the cross-section of $e^{+}e^{-}\to q\bar{q}g$.
• Figure 2: Schematic representation of soft emissions in QED and QCD. On the left independent emission from different external legs in QED. On the right angular ordered emissions along an external leg in QED (top) and in QCD (bottom).
• Figure 3: Typical thrust values for back-to-back two-jet configurations (left) and three-jet final states (right).
• Figure 4: The distribution of the thrust event shape at NNLL matched to NNLO, in red, compared to the fixed-order (NNLO) result, in green. The bands indicate the theoretical uncertainty. Plot taken from Ref. Monni:2011gb.
• Figure 5: The emission phase-space in the ($\eta, \ln k_t/Q$) plane, as parametrized by the Caesar formula Eq. (\ref{['caesar-obs']}.) We note that, in the soft and collinear limit, emissions are uniformly distributed in this plane. Figure taken from Ref. Banfi:2004yd.