A quark mass definition adequate for threshold problems

Recent calculations of heavy quark cross sections near threshold at next-to-next-to-leading order have found second-order corrections as large as first-order ones. We analyse long-distance contributions to the heavy quark potential in momentum and coordinate space and demonstrate that long-distance contributions in momentum space are suppressed as Lambda(QCD)(2)/q(2). We then show that the long-distance sensitivity of order Lambda(QCD)r introduced by the Fourier transform to coordinate space cancels to all orders in perturbation theory with long-distance contributions to the heavy quark pole mass. This leads us to define a subtraction scheme - the 'potential subtraction scheme' - in which large corrections to the heavy quark potential and the potential-subtracted' quark mass are absent. We compute the two-loop relation of the potential-subtracted quark mass to the MS quark mass. We anticipate that threshold calculations expressed in terms of the scheme introduced here exhibit improved convergence properties. (C) 1998 Elsevier Science B.V. All rights reserved.