The Hamiltonian Mean Field model: anomalous or normal diffusion?

We consider the out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model, by focusing in particular on the properties of single-particle diffusion. As we shall here demonstrate analytically, if the autocorrelation of momenta in the so-called quasi-stationary states can be fitted by a q-exponential, then diffusion ought to be normal for q<2, at variance with the interpretation of the numerical experiments proposed in Refs. A. Pluchino, A. Rapisarda, Progress in Theoretical Physics Supplement 162, 18 (2006); A. Pluchino, V. Latora, A. Rapisarda, Physica A 338, 60 (2004); A. Rapisarda, A. Pluchino, Europhysics News 36, 202 (2005).