# Linearly polarized gluons at next-to-next-to leading order and the Higgs transverse momentum distribution

## TL;DR

This paper computes the NNLO correction for linearly polarized gluon TMDs, completing the theoretical framework for precise Higgs transverse momentum distribution predictions within TMD factorization.

## Contribution

It provides the first NNLO calculation of the small-b matching for linearly polarized gluons, enabling complete NNLO predictions for Higgs spectra in TMD factorization.

## Key findings

- NNLO correction significantly impacts Higgs qT distribution.
- Correction affects the positivity bound for gluon polarization.
- Numerical results refine theoretical predictions for Higgs production.

## Abstract

We calculate the small-b (or large-qT) matching of transverse momentum dependent (TMD) distribution for linearly polarized gluons to the integrated gluon distributions at the next-to-next-to-leading order (NNLO). This is the last missing part for the complete NNLO prediction of the Higgs spectrum within TMD factorization. We discuss the numerical impact of the correction so derived to the qT-differential cross-section for Higgs boson production and to the positivity bound for linearly polarized gluon transverse momentum distribution.