Effective string theory constraints on the long distance behavior of the subleading potentials

Abstract

The dynamics of heavy quarkonium systems in the strong coupling regime reduces to a quantum mechanical problem with a number of potentials which may be organized in powers of 1/m, m being the heavy quark mass. The potentials must be calculated non-perturbatively, for instance in lattice QCD. It is well known that the long distance behavior of the static (1/m^0) potential is well reproduced by an effective string theory. We show that this effective string theory, if correct, should also reproduce the long distance behavior of all 1/m suppressed potentials. We demonstrate the practical usefulness of this result by finding a suitable parameterization of the recently calculated 1/m potential. We also calculate the 1/m^2 velocity dependent and spin dependent potentials. Once Poincaré invariance is implemented, the shapes of most of the spin independent potentials are fully predicted in terms of the string tension, and the shapes of the spin dependent ones in terms of a single parameter.

5 pages, 1 figure, reference and explanations added. Journal version

References in corpus (7)

• Effective field theories for heavy quarkonium
• The Nf=0 heavy quark potential from short to intermediate distances
• Quark confinement and the bosonic string
• Nonperturbative determination of the QCD potential at O(1/m)
• Spin-dependent potentials from lattice QCD
• Poincare' invariance and the heavy-quark potential
• Spectroscopy, leptonic decays and the nature of heavy quarkonia

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