# Associated production of $\chi_c$ pairs with a gluon in the collinear-factorization approach

## TL;DR

This paper calculates the production cross section of $$ pairs in proton-proton collisions, comparing collinear and $k_T$-factorization approaches, and highlights the importance of next-to-leading order contributions with associated jets.

## Contribution

It provides the first detailed comparison between collinear and $k_T$-factorization approaches for $$ pair production, emphasizing the role of higher-order jet emissions.

## Key findings

- Next-to-leading order contributions dominate over the basic $2 o 2$ process.
- Associated jet emissions significantly increase the cross section.
- Production at large rapidity differences is enhanced by central gluon emissions.

## Abstract

We calculate cross section for production of $\chi_c$ pairs in proton-proton collisions. The cross section for the $g g \to \chi_{c J_1} \chi_{c J_2}$ is considerably smaller (especially for $\chi_{c 1} \chi_{c 1}$ final state) than that obtained recently in the $k_T$-factorization approach. We calculate therefore next-to-leading order contributions with $\chi_c$ pair and one extra associated (mini-)jet. We find these contributions to be much larger than those for the $2 \to 2$ contribution. Especially the emission of a leading gluon (carrying a large momentum fraction of one of the incoming gluons) are important. These emissions in the $k_T$-factorization approach are absorbed into the initial state unintegrated gluon distributions. A smaller contribution to the cross section comes from the production of central gluons emitted with rapidities between the $\chi_c$-mesons. They do lead, however, to an enhancement of the $\chi_c$-pair production at large rapidity distance between the mesons. Our present study explains the size of the cross section for the $\chi_c$ pair production obtained previously in the $k_T$-factorization approach. Several differential distributions are presented.