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

Abstract

We address the unphysical energy dependence of quarkonium-hadroproduction cross sections at Next-to-Leading Order (NLO) in α s 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, α s 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 η c,b but also for a fictitious light elementary scalar boson. Having provided stable NLO predictions for η c,b P Tintegrated cross sections, σ NLO η Q , and discussed the options to study η 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.

Revisiting NLO QCD corrections to total inclusive J/psi and Upsilon photoproduction cross sections in lepton-proton collisions

“…One reason for such a cut is probably the difficulty to obtain numerically stable NLO results when they appeared [24,25] 2 . In fact, as we will discuss, these were probably due to the appearance of large negative NLO contributions which we will address here along the same lines as our recent study on η c production [27].…”

“…In two cases, the NLO cross section becomes negative as s γp increases. As for Υ(1S ), the cross section remains positive in the considered energy range for any realistic scale choice, like for η b hadroproduction up to 100 TeV [27]. Let us now discuss the origin of such an unphysical behaviour for J/ψ photoproduction and propose a solution to it.…”

“…( 6). Already at this stage, we can note then that, at large ŝ, the NLO cross section will be proportional to ln(M 2 Q /µ 2 F ) and a process-dependent coefficient, c (1) γi ( ŝ → ∞, m 2 Q ), which only comes on the real-emission contributions, like for η Q hadroproduction [27].…”

“…Unless µ F is sufficiently smaller than M Q in order to compensate A γi , lim ŝ→∞ σNLO γi is negative, like for η Q [27] and it is another clear case of oversubtraction by the AP-CT. Indeed, in this limit, the virtual contributions are suppressed; only the real emissions contribute via their square.…”

“…Indeed, A γg and A γq are process-dependent, while the DGLAP equations are process-independent, which necessarily makes the compensation imperfect. A solution to this problem is [27] to force the partonic cross section to vanish in this limit, whose contribution should in principle be damped down by the PDFs.…”