Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-04-06
Phys.Lett. B434 (1998) 115-125
Physics
High Energy Physics
High Energy Physics - Phenomenology
14 pages, LaTeX, 2 figures included via epsf.sty; Two references and some clarifications added
Scientific paper
10.1016/S0370-2693(98)00741-2
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 $\bar{\rm MS}$ quark mass. We anticipate that threshold calculations expressed in terms of the scheme introduced here exhibit improved convergence properties.
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