{ 1{ Quark Masses A. Introduction

This note discusses some of the theoretical issues involved in the determination of quark masses. Unlike the leptons, quarks are connned inside hadrons and are not observed as physical particles. Quark masses cannot be measured directly, but must be determined indirectly through their innuence on hadron properties. As a result, the values of the quark masses depend on precisely how they are deened; there is no one deenition that is the obvious choice. Though one often speaks loosely of quark masses as one would of the electron or muon mass, any careful statement of a quark mass value must make reference to a particular computational scheme that is used to extract the mass from observations. It is important to keep this scheme dependence in mind when using the quark mass values tabulated in the data listings. The simplest way to deene the mass of a quark is by making a t of the hadron mass spectrum to a nonrelativistic quark model. The quark masses are deened as the values obtained from the t. The resulting masses only make sense in the limited context of a particular quark model. They depend on the phenomenological potential used, and on how relativistic eeects are modelled. The quark masses used in potential models also cannot be connected with the quark mass parameters in the QCD Lagrangian. Fortunately, there exist other deenitions of the quark mass that have a more general signiicance, though they also depend on the method of calculation. The purpose of this review is to explain the most important such deenitions and their interrelations.