Production of $\chi_c$ pairs in $k_T$-factorization

TL;DR

This paper calculates the production rates and distributions of $_c$ meson pairs in proton-proton collisions at 8 TeV using the $k_T$-factorization approach, focusing on gluon exchange mechanisms.

Contribution

It introduces a detailed calculation of $_c$ pair production via gluon fusion with off-shell gluons within the color-singlet model, using nonrelativistic heavy quark approximations.

Findings

Broad rapidity difference distributions observed.

Predictions made at 8 TeV collision energy.

Differential distributions analyzed for various $_c$ pair combinations.

Abstract

We calculate the production of pairs of $\chi_c(J)$ mesons with all possible combinations of $J=0,1,2$. The leading order production mechanism is the crossed-channel gluon exchange in the gluon-gluon fusion reaction. The building blocks are the vertices $g^* g^* \to \chi_c(J)$ for off shell gluons. We stick to the color-singlet model and calculate the gluon fusion vertices in the limit of heavy quarks with nonrelativistic motion in the bound state. These vertices are used to construct the $g^* g^* \to \chi_c(J_1) \chi_c(J_2)$ amplitudes. We then calculate hadron-level cross sections using the $k_T$-factorization approach. In our numerical predictions, we use the KMR-type unintegrated gluon distributions. Several differential distributions at the $pp$ center of mass energy $\sqrt{s} = 8 \, {\rm TeV}$ are shown. The salient feature of the $t$ and $u$-channel gluon exchange are the broad distributions in rapidity difference $\Delta y$ between $\chi_c$ mesons.