Curing the unphysical behaviour of NLO quarkonium production at the LHC and its relevance to constrain the gluon PDF at low scales

We address the unphysical energy dependence of quarkonium-hadroproduction cross sections at Next-toLeading Order (NLO) in as which we attribute to an oversubtraction in the factorisation of the collinear singularities inside the PDFs in the MS scheme. Such over- or undersubtractions have a limited phenomenological relevance in most of the scattering processes in particle physics. On the contrary, it is particularly harmful for P-T-integrated charmonium hadroproduction which renders a wide class of NLO results essentially unusable. Indeed, in such processes, as is not so small, the PDFs are not evolved much and can be rather flat for the corresponding momentum fractions and, finally, some process-dependent NLO pieces are either too small or too large. We propose a scale-fixing criterion which avoids such an over-subtraction. We demonstrate its efficiency for eta(c, b) but also for a fictitious light elementary scalar boson. Having provided stable NLO predictions for eta(c,b) PT integrated cross sections, sigma(NLO)(eta Q), and discussed the options to study.b hadroproduction, we argue that their measurement at the LHC can help better determine the gluon PDF at low scales and tell whether the local minimum in conventional NLO gluon PDFs around x = 0.001 at scales below 2 GeV is physical or not.

Automated summary

This study addresses the unphysical energy dependence of quarkonium-hadroproduction cross sections at Next-to-Leading Order, attributing it to an oversubtraction in the factorisation of collinear singularities in the PDFs in the MS scheme. A proposed scale-fixing criterion is demonstrated to effectively avoid this issue and stabilize NLO predictions for eta(c,b) PT-integrated cross sections. The measurement of these processes at the LHC can help determine the gluon PDF at low scales and assess the physical significance of local minima in conventional NLO gluon PDFs.