  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.
