Cancellation of Infrared Divergence in Inclusive Production of Heavy Quarkonia

TL;DR

This paper proposes a scheme to cancel infrared divergences in the inclusive production of heavy quarkonia, improving the theoretical foundation of NRQCD factorization by defining quarkonia as resonance states and accounting for soft gluon exchanges.

Contribution

It introduces a novel scheme to cancel topologically unfactorized infrared divergences in heavy quarkonia production, redefining quarkonia as resonance states and including decay product reconstruction.

Findings

Infrared divergences are canceled in the new scheme.

Heavy quarkonia are defined as resonance states, not just color singlet pairs.

Soft gluon exchanges and state transitions are incorporated.

Abstract

A scheme is presented here to cancel out the topologically unfactorized infrared divergences in the inclusive production of heavy quarkonia, which affect the NRQCD factorization of these processes. The heavy quarkonia are defined as resonance states of QCD instead of color singlet heavy quark pair. Thus the final heavy quark pair is nor necessarily to be color singlet. In addition, the heavy quarkonia are reconstructed by their decay products. As the result, transition between states containing containing heavy quarks caused by exchanges of soft gluons are also taken into account here. Such cancellation is crucial for the NRQCD factorization of these processes.