Soft-Gluon Resummation in Heavy Quarkonium Physics

TL;DR

This work addresses large soft-gluon threshold corrections in heavy quarkonium hadroproduction by implementing NLL soft-gluon resummation within the NRQCD factorization framework. Using Mellin-space techniques and the Minimal Prescription, the authors derive a resummed cross section that augments the NLO result and reduces scale sensitivity when renormalization and factorization scales are tied. Numerical results show sizable increases over NLO predictions and improved stability for equal-scale choices, with independent scale variations revealing more limited gains. Open questions identify the role of the NRQCD factorization scale and the need for careful treatment of higher-order and P-wave subtleties, indicating a path toward more complete phenomenological predictions.

Abstract

Soft-gluon resummation within the framework of heavy quarkonium hadroproduction is considered. A few selected cases are studied in detail. A sizeable increase of the cross sections with respect to the next-to-leading order predictions with central factorization/renormalization scale choice can generally be observed. Improvements in the dependence of the cross sections on the two scales, especially when they are kept equal, are also found.

Figures (6)

• Figure 1: The cross section for production, in $pp$ collisions via the gluon-gluon channel, of a fictitious ${}^1S_0^{[1]}$ quarkonium state made up of 50 GeV quarks, at 200 and 500 GeV centre-of-mass energy.
• Figure 2: The cross section for production, in $pp$ collisions via the $q\bar{q}$ channel, of a ${}^3S_1^{[8]}$ state with 50 GeV quarks.
• Figure 3: Cross section as in fig. \ref{['fig:m50']}, but with independent variation of the renormalization (left plot) and factorization (right plot) scales. Top plots are for $\sqrt{S} = 200$ GeV, bottom ones for $\sqrt{S} = 500$ GeV.
• Figure 4: The cross sections for production of the bottomonium state ${}^1S_0^{[1]}$ via the gluon--gluon channel, at 20 and 50 GeV centre-of-mass energy, as functions of the renormalization/factorization scales.
• Figure 5: The cross sections for production, in $pp$ collisions via the $q\bar{q}$ channel, of a ${}^3S_1^{[8]}$ bottomonium state.