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 χQ 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.
Highlights
Refs. [12,13,14,15,16,17,18,19,20] for processes involving jets)
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
Quarkonia are studied within the framework of NRQCD factorization [22,23,24,25,26,27,28] where the cross section is written as a sum of products of short distance matching coefficients and the corresponding long distance matrix elements (LDMEs)
Summary
SCET and vNRQCD are effective field theories that describe the degrees of freedom of QCD in the soft and collinear, and non-relativistic limits, respectively. Both theories are well established and address a wide spectrum of physical phenomena. We aim to study a TMD dependent observable in χJ decaying to light quarks followed by their fragmentation to light hadrons. VNRQCD is needed for the heavy quarkonium in the initial state and SCET is needed for the energetic hadrons as well as soft radiation in the final state. Our aim is not to give a comprehensive review of those EFTs but rather to introduce the elements and notation necessary for the analysis we pursue
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