Next-to-next-to-leading power corrections to unpolarized Semi-Inclusive Deep Inelastic Scattering

TL;DR

This paper extends the theoretical framework for Semi-Inclusive Deep Inelastic Scattering by deriving and analyzing next-to-next-to-leading power corrections, crucial for high-precision data interpretation and future experimental predictions.

Contribution

The work develops analytic expressions for NNLP corrections in SIDIS, including convolutions of distributions and fragmentation functions, expanding previous approaches from Drell-Yan to SIDIS.

Findings

Derived NNLP corrections for unpolarized structure functions.

Compared predictions with HERMES and COMPASS data.

Provided forecasts for Jefferson Lab and Electron-Ion Collider.

Abstract

Semi-Inclusive Deep Inelastic Scattering (SIDIS) is a key tool for exploring the three-dimensional structure of the nucleon through Transverse Momentum Dependent parton distributions and fragmentation functions. While leading-power contributions to the SIDIS cross-section are well established, next-to-leading (NLP) of order $1/Q$ and next-to-next-to-leading power (NNLP) corrections of order $1/Q^2$ to the hadronic tensor have only recently begun to be systematically investigated. These corrections are essential for the reliable phenomenology and interpretation of modern high-precision data. In recent papers by one of the authors, NNLP corrections to Drell-Yan process were derived using rapidity factorization formalism. In the present work we extend this approach to SIDIS and obtain analytic expressions for the unpolarized structure functions. We derive NNLP corrections that include convolutions of unpolarized distributions, $f_1$, with unpolarized fragmentation functions, $D_1$, and Boer-Mulders functions, $h_1^\perp$, with Collins fragmentation functions, $H_1^\perp$. We compare our results with previous formulations, provide numerical studies, confront our predictions with HERMES and COMPASS measurements, and present predictions for future experiments at Jefferson Lab and the Electron-Ion Collider.