NRQCD: A Critical Review

In this talk I review some recent applications of NRQCD. I first discuss the unquenched NRQCD lattice extractions of the strong coupling constant, paying particular attention to the recent advances in reducing systematic errors. I then discuss the progress made in testing the NRQCD/factorization formalism for onium production. In particular, I gather the evidence, or lack thereof, for the universality of the production matrix elements. I also discuss the interesting question of polarized production, which is a crucial test of the formalism. I address the viability of this theory for the J/ψ system as well as what needs to be done before we can reach any definitive conclusions. The study of heavy quarks is interesting from a phenomenological as well as formal standpoint. Indeed, the utility of the experiments designed to study the CKM sector of the standard model is bounded by our theoretical understanding of states containing heavy quarks. For theorists this presents a great challenge given that, in general, it is quite difficult to make predictions for strongly interacting particles from first principles. However, we do have one powerful tool at our disposal which saves us from despondency, namely effective field theories. These theories represent limits of QCD which make approximate symmetries manifest, thus greatly enhancing our predictive power. Furthermore, since the effective theory reproduces QCD in a well defined limit, it is possible to calculate corrections in a systematic fashion. The effective theory I have been charged to review is non-relativistic QCD. As the moniker implies, this is a theory which approximates full QCD when applied to a bound state containing more than one heavy quark. The quarks necessarily have small velocities in the limit mQ ≫ ΛQCD, due to asymptotic freedom. The theory is written down as a simultaneous expansion in αS(2mQ) and the relative velocity in the center of mass frame of the quarks, v. Indeed, if we wish, we may calculate corrections to arbitrary order in powers of v and αs, at the price of introducing unknown, yet universal parameters. Thus, the relevant question is not “is NRQCD correct?”, but rather, “how well do the v and αs expansions converge for the system of interest?” In this review I will discuss recent advances in the application of NRQCD. In particular, I will concentrate on applications for which we have new data. Thus, due to space limitations, I will not discuss the interesting topic of inclusive onia decays, nor will I discuss recent theoretical progress on threshold top quark production[1]. Instead, I will focus on the utilization of NRQCD to measure the strong coupling, and the predictions for onia production. 1. The Effective Field Theory The effective Lagrangian is constructed [2] by ensuring that at the matching scale, mQ, the effective field theory reproduces on shell Greens functions of QCD to some fixed order in α(2mQ) and v. The operators in the effective field theory are then classified by their “effective v dimension”[3]. That is, to each operator we may assign a power of v which is determined by some velocity power counting rules. For our purposes, we will be interested in the fermion anti-fermion sector of the theory where the lowest order Lagrangian is Heavy Flavors 8, Southampton, UK, 1999 Ira Rothstein