Proof of Color Octet NRQCD Factorization of P-Wave Heavy Quarkonium Production at All Orders in Coupling Constant

TL;DR

This paper extends the proof of color octet NRQCD factorization from S-wave to P-wave heavy quarkonium production at all orders, revealing differences in gauge-link structures within the non-perturbative matrix elements.

Contribution

It provides a rigorous proof of NRQCD factorization for P-wave quarkonium production at all orders, expanding previous work on S-wave states.

Findings

Color octet NRQCD P-wave matrix element contains four gauge-links in the fundamental representation.

The proof applies to high energy colliders at all orders in coupling constant.

Differences in gauge-link structures between S-wave and P-wave states are identified.

Abstract

Recently we have proved color octet NRQCD factorization of S-wave heavy quarkonium production at all orders in coupling constant at high energy colliders in Eur. Phys. J. C76 (2016) 448. In this paper we extend this to prove color octet NRQCD factorization of P-wave heavy quarkonium production at all orders in coupling constant at high energy colliders. We find that while the color octet NRQCD S-wave non-perturbative matrix element contains two gauge-links in the adjoint representation of SU(3), the color octet NRQCD P-wave non-perturbative matrix element contains four gauge-links in the fundamental representation of SU(3).