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

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.