# Linearly polarised Transverse Momentum Dependent Parton Distribution Function at NNLO in QCD

## TL;DR

This paper computes the NNLO matching coefficients for linearly polarized TMDPDFs to the integrated gluon distribution, advancing precision in QCD predictions for Higgs and quarkonium production processes.

## Contribution

It provides the first NNLO calculation of matching coefficients for linearly polarized TMDPDFs using a novel regularization method.

## Key findings

- First NNLO computation of linearly polarized TMDPDF matching coefficients.
- Enhanced theoretical precision for Higgs and quarkonium production models.
- Application of modified δ-regulator for rapidity divergences.

## Abstract

We present for first time the computation at large $q_T$ (or small $b_T$) matching coefficients of Transverse Momentum Dependent Parton Distribution Function (TMDPDF) for linearly polarised to the integrated gluon distribution at next-to-next-to leading order (NNLO). The computation is performed using the modified $\delta$-regulator for rapidity divergences and dimensional regularization. This TMDPDF matriz element presnts phenomenological interest in two kind of processes. The factorization of the Higgs production transverse momentum ($q_T$) distribution through gluon-gluon fusion and the quarkonium production.