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 nonperturbatively, for instance, in lattice QCD. It is well known that the long-distance behavior of the static (1/m0) 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/m2 velocity-dependent and spin-dependent potentials. Once Poincare 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.