Effective string theory and the long-range relativistic corrections to the quark-antiquark potential

The complete expression of the heavy quark-antiquark potential up to order $1/m^2$ is known from QCD in terms of Wilson loop expectation values. We use that expression and a mapping, assumed to be valid at large distances, between Wilson loop expectation values and correlators evaluated in the effective string theory, to compute the potential. We obtain previously unknown results for the spin and momentum-independent parts of the potential. These are linearly rising with the distance and may be interpreted as relativistic corrections to the string tension. We confirm known results for the other parts of the potential. Finally, we compute the discrete spectrum of a heavy quark-antiquark pair whose interaction is just given by the obtained potential.