Resummation of threshold double logarithms in inclusive production of heavy quarkonium

TL;DR

This paper develops a resummation technique for threshold double logarithms in heavy quarkonium production, fixing issues with negative cross sections in fixed-order calculations and improving agreement with experimental data.

Contribution

It introduces an all-orders resummation method for threshold double logarithms in heavy quarkonium production within nonrelativistic QCD.

Findings

Resummation fixes negative cross section problem at high transverse momentum.

Improves theoretical predictions for $J/\psi$ production rates.

Threshold logarithms are crucial for accurate heavy quarkonium cross sections.

Abstract

We resum threshold double logarithms in inclusive production of heavy quarkonium that arise from singularities near the boundary of phase space. This resolves the catastrophic failure in the conventional approach based on fixed-order perturbation theory calculations in nonrelativistic QCD, where quarkonium cross sections at large transverse momentum can turn negative. We identify the root cause of this negative cross section problem as the appearance of threshold logarithms in radiative corrections, and resum them to all orders in perturbation theory at the leading double logarithmic level. We find that resummation of threshold logarithms is imperative for describing measured $J/\psi$ production rates at large transverse momentum.