  I report on our investigations into the impact of (un)polarized transverse
momentum dependent parton distribution functions (TMD PDFs or TMDs) for gluons
at hadron colliders, especially at A Fixed Target Experiment at the LHC
(AFTER@LHC). In the context of high energy proton-proton collisions, we look at
final states with low mass (e.g. $\eta_b$) in order to investigate the
nonperturbative part of TMD PDFs. We study the factorization theorem for the
$q_T$ spectrum of $\eta_b$ produced in proton-proton collisions relying on the
effective field theory approach, defining the tools to perform phenomenological
investigations at next-to-next-to-leading log (NNLL) and next-to-leading order
(NLO) accuracy in the perturbation theory. We provide predictions for the
unpolarized cross section and comment on the possibility of extracting
nonperturbative information about the gluon content of the proton once data at
low transverse momentum are available.
