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

TL;DR

This paper investigates how effective string theory constrains the long-distance behavior of subleading potentials in heavy quarkonium, providing predictions for their shapes and parameterizations based on non-perturbative calculations.

Contribution

It demonstrates that effective string theory predictions extend beyond static potentials to all 1/m suppressed potentials, including spin-dependent and velocity-dependent terms.

Findings

Effective string theory reproduces long-distance behavior of subleading potentials.

Parameterization of the 1/m potential based on lattice QCD data.

Predicted shapes of most spin-independent potentials in terms of string tension.

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 Poincar\'e 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.