# Transverse momentum dependent distributions in $e^+e^-$ and semi-inclusive deep-inelastic scattering using jets

## TL;DR

This paper develops a method to extract transverse momentum dependent distributions using jets instead of hadrons, providing a new approach that simplifies the analysis and enhances sensitivity to proton structure.

## Contribution

It introduces the calculation of TMD jet functions at one loop and demonstrates their application to phenomenology in $e^+e^-$ and SIDIS processes, achieving high perturbative accuracy.

## Key findings

- Large jet radius limit accurately describes full R results
- Two-loop jet function extracted using Event2
- Predictions show good perturbative convergence

## Abstract

The extraction of transverse momentum dependent distributions (TMDs) in semi-inclusive deep inelastic scattering (SIDIS) is complicated by the presence of both initial- and final-state nonperturbative physics. We recently proposed measuring jets (instead of hadrons) as a solution, showing that for the Winner-Take-All jet axis the same factorization formulae valid for hadrons applied to jets of arbitrary size. This amounts to simply replacing TMD fragmentation functions by our TMD jet functions. In this paper we present the calculation of these jet functions at one loop. We obtain phenomenological results for $e^+e^- \to$ dijet (Belle II, LEP) and SIDIS (HERA, EIC) with a jet, building on the arTeMiDe code. Surprisingly, we find that the limit of large jet radius describes the full $R$ results extremely well, and we extract the two-loop jet function in this limit using Event2, allowing us to achieve N$^3$LL accuracy. We demonstrate the perturbative convergence of our predictions and explore the kinematic dependence of the cross section. Finally, we investigate the sensitivity to nonperturbative physics, demonstrating that jets are a promising probe of proton structure.