Potential NRQCD and Heavy-Quarkonium Spectrum at Next-to-Next-to-Next-to-Leading Order

Abstract

The next-to-next-to-next-to-leading order (N^3LO) Hamiltonian of potential nonrelativistic QCD is derived. The complete matching of the Hamiltonian and the contribution from the ultrasoft dynamical gluons relevant for perturbative bound-state calculations is performed including one-, two-, and three-loop contributions. The threshold expansion is used to disentangle and match contributions of different scales in the effective-theory calculations. As a physical application, the heavy-quarkonium spectrum is obtained at N^3LO for the case of vanishing QCD beta function. Our results set the stage for a full N^3LO analysis of the heavy-quarkonium system.

29 pages (Latex), 4 figures (Axodraw)

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• The Threshold t-tbar Cross Section at NNLL Order
• The Running Coulomb Potential and Lamb Shift in QCD
• RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function
• Top Quark Threshold Production at a gamma-gamma Collider at Next-to-Next-to-Leading Order

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