Transverse Momentum Measurements with Jets at Next-to-Leading Power

TL;DR

This paper develops a framework for calculating next-to-leading power corrections in transverse momentum measurements involving jets, providing new jet functions and demonstrating divergence cancellation, with applications to future collider experiments.

Contribution

It introduces a factorized expression involving twist-2 and twist-3 operators, calculates new jet functions at order αs, and shows divergence cancellation in jet-based observables.

Findings

Derived a factorized cross section including twist-2 and twist-3 operators.

Calculated jet functions at order αs for recoil-free schemes.

Showed divergence cancellation in sub-leading-power jet factorization.

Abstract

In view of the increasing precision of theoretical calculations and experimental measurements, power corrections to transverse-momentum-dependent observables are highly important. We study the next-to-leading power corrections for transverse momentum measurements in $e^+ e^- \rightarrow 2$ jets. We obtain a factorized expression for the cross section, which involve twist-2 and twist-3 operators, and identify the new jet functions that appear in it. We calculate these jet functions at order {\alpha}s for a family of recoil-free schemes, and provide the corresponding anomalous dimensions at leading order. Additionally, we show that the (endpoint) divergences that typically arise in sub-leading-power factorization can be subtracted and cancel for our case. By working with jets, everything is perturbatively calculable and there are substantial simplifications compared to the general next-to-leading power framework. Importantly, our analysis with jets can be extended to semi-inclusive deep-inelastic scattering, with the future Electron-Ion Collider as key application.