The QCD potential at O(1/m^2): Complete spin-dependent and spin-independent result

Abstract

Within an effective field theory framework, we obtain an expression, with O(1/m^2) accuracy, for the energies of the gluonic excitations between heavy quarks, which holds beyond perturbation theory. For the singlet heavy quark--antiquark energy, in particular, we also obtain an expression in terms of Wilson loops. This provides, twenty years after the seminal work of Eichten and Feinberg, the first complete expression for the heavy quarkonium potential up to O(1/m^2) for pure gluodynamics. Several errors present in the previous literature (also in the work of Eichten and Feinberg) have been corrected. We also briefly discuss the power counting of NRQCD in the non-perturbative regime.

25 pages, revtex, former Eqs. (27) and (28) fixed

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• Potential NRQCD: an effective theory for heavy quarkonium
• Renormalization group scaling in nonrelativistic QCD
• The infrared behaviour of the static potential in perturbative QCD
• The QCD Potential at $O(1/m)$
• The $B_c$ mass up to order ${\alpha }_s^4$
• The QCD heavy-quark potential to order v^2: one loop matching conditions
• Effective Field Theory Approach to Pionium

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