An effective field theory approach to quarkonium at small transverse momentum

TL;DR

This paper develops an effective field theory framework for analyzing quarkonium production and decay at small transverse momentum, enabling systematic resummation of large logarithms in TMD-sensitive observables.

Contribution

It introduces a novel EFT-based factorization theorem involving TMD fragmentation and shape functions for quarkonium, with derived RG equations for resummation.

Findings

Derived a factorization theorem for quarkonium TMD observables.

Established RG equations for rapidity and virtuality evolution.

Provides a systematic approach for TMD-sensitive quarkonium processes.

Abstract

In this work we apply effective field theory (EFT) to observables in quarkonium production and decay that are sensitive to soft gluon radiation, in particular measurements that are sensitive to small transverse momentum. Within the EFT framework we study $\chi_Q$ decay to light quarks followed by the fragmentation of those quarks to light hadrons. We derive a factorization theorem that involves transverse momentum distribution (TMD) fragmentation functions and new quarkonium TMD shape functions. We derive renormalization group equations, both in rapidity and virtuality, which are used to evolve the different terms in the factorization theorem to resum large logarithms. This theoretical framework will provide a systematic treatment of quarkonium production and decay processes in TMD sensitive measurements.