Heavy Quarkonium Production at Low Pt in NRQCD with Soft Gluon Resummation

TL;DR

This paper enhances NRQCD predictions for low transverse momentum heavy quarkonium production by incorporating all-order soft gluon resummation, improving agreement with experimental data and refining non-perturbative form factors.

Contribution

It introduces a comprehensive soft gluon resummation within NRQCD for quarkonium production, challenging previous assumptions about the non-perturbative Sudakov form factor.

Findings

Resummed predictions align better with experimental data.

The gluon distribution's Sudakov form factor differs from previous models.

Implications for determining color-octet matrix elements are discussed.

Abstract

We extend the non-relativistic QCD (NRQCD) prediction for the production of heavy quarkonium with low transverse momentum in hadronic collisions by taking into account effects from all order soft gluon resummation. Following the Collins-Soper-Sterman formalism, we resum the most singular terms in the partonic subprocesses. The theoretical predictions of $J/\psi$ and $\Upsilon$ productions are compared to the experimental data from the fixed target experiments (E866) and the collider experiments (RHIC, Tevatron, LHC). The associated non-perturbative Sudakov form factor for the gluon distributions is found to be different from the previous assumption of rescaling the quark form factor by the ratio of color factors. This conclusion should be further checked by future experiments on Higgs boson and/or di-photon production in $pp$ collisions. We also comment on the implication of our results on determining the color-octet matrix elements associated with the $J/\psi$ and $\Upsilon$ productions in the NRQCD factorization formalism.