Proof of NRQCD Factorization at All Order in Coupling Constant in Heavy Quarkonium Production

TL;DR

This paper proves the all-order factorization in heavy quarkonium production within the NRQCD color octet mechanism using a path integral approach, extending previous NNLO results to all orders in coupling constant.

Contribution

It provides a rigorous all-order proof of factorization in heavy quarkonium production in NRQCD, emphasizing the necessity of gauge-completed non-perturbative matrix elements.

Findings

Factorization holds at all orders in coupling constant.

Gauge invariance requires gauge-completed NRQCD matrix elements.

The proof extends previous NNLO results to all orders.

Abstract

Recently the proof of factorization in heavy quarkonium production in NRQCD color octet mechanism is given at next-to-next-to-leading order (NNLO) in coupling constant by using diagrammatic method of QCD. In this paper we prove factorization in heavy quarkonium production in NRQCD color octet mechanism at all order in coupling constant by using path integral method of QCD. Our proof is valid to all powers in the heavy quark relative velocity. We find that the gauge invariance and the factorization at all order in coupling constant require gauge-completed non-perturbative NRQCD matrix elements that were introduced previously to prove factorization at NNLO.