$q_T$-slicing with multiple jets

TL;DR

This paper introduces two new $q_T$-based slicing methods for jet processes, enabling high-precision NNLO calculations and simplifying the soft function, with potential extensions to hadron fragmentation.

Contribution

It proposes novel $q_T$-slicing generalizations for jet final states, demonstrating their effectiveness at NLO and NNLO, and simplifying the soft function for planar processes.

Findings

Developed two $q_T$-slicing generalizations for jets.

Demonstrated NNLO slicing for $e^+e^- \to 2$ jets.

Simplified soft function for planar processes.

Abstract

Modern collider phenomenology requires unprecedented precision for the theoretical predictions, for which slicing techniques provide an essential tool at next-to-next-to-leading order (NNLO) in the strong coupling. The most popular slicing variable is based on the transverse momentum $q_T$ of a color-singlet final state, but its generalization to final states with jets is known to be very difficult. Here we propose two generalizations of $q_T$ that can be used for jet processes, providing proof of concept with an NLO slicing for $pp \to 2$ jets. We present factorization formulae that enable our approach to NNLO, calculate the NNLO collinear-soft function and demonstrate slicing at this order for $e^+e^- \to 2$ jets. One of these generalizations of $q_T$ only applies to planar Born processes, such as $pp \to 2$ jets, but offers a dramatic simplification of the soft function. We also discuss how our approach can directly be extended to obtain predictions for the fragmentation of hadrons. This presents a promising path for high-precision QCD calculations with multi-jet final states.