Gluon distribution at very small x from C-even quarkonia production at the LHC

TL;DR

This paper proposes using C-even quarkonia production at the LHC to measure the gluon distribution function in nucleons across a very broad range of Bjorken x, from 10^(-2) down to 10^(-6).

Contribution

It introduces a method to determine the gluon distribution at very small x using quarkonia production data, with detailed scale evaluations at NLO.

Findings

Gluon distribution can be probed down to x~10^(-6).

Estimated production cross sections are up to tens of nanobarns for charmonia.

The gluon distribution scale varies from ~2.5 GeV^2 to ~20 GeV^2.

Abstract

C-parity-even quarkonia eta_b,c and chi_b,c with spin 0 and 2 are produced via two-gluon fusion. The expected cross section of the inclusive production of the quarkonia at the LHC, times the branching ratios of convenient decays, is up to tens of nanobarn per unit rapidity in the case of charmonia and around one nanobarn for the bottomonia. Measuring the quarkonia production as function of rapidity will allow to determine the gluon distribution function in nucleons in a very broad range of the Bjorken x from x~10^(-2) where it is already known, down to x~10^(-6) where it is totally unknown. The scale of the gluon distribution found from such measurements turns out to be rather low, Q^2 ~ 2.5 - 3 GeV^2, for charmonia and rather large, Q^2 ~ 20 GeV^2$, for bottomonia. We evaluate the scale by studying the next-to-leading-order production cross sections.