Can one distinguish τ-neutrinos from antineutrinos in neutral-current pion production processes?

A potential way to distinguish τ-neutrinos from antineutrinos, below the τ-production threshold, but above the pion production one, is presented. It is based on the different behavior of the neutral-current pion production off the nucleon, depending on whether it is induced by neutrinos or antineutrinos. This procedure for distinguishing τ-neutrinos from antineutrinos neither relies on any nuclear model, nor it is affected by any nuclear effect (distortion of the outgoing nucleon waves, etc.). We show that neutrino-antineutrino asymmetries occur both in the totally integrated cross sections and in the pion azimuthal differential distributions. To define the asymmetries for the latter distributions we just rely on Lorentz-invariance. All these asymmetries are independent of the lepton family and can be experimentally measured by using electron or muon neutrinos, due to the lepton family universality of the neutral-current neutrino interaction. Nevertheless and to estimate their size, we have also used the chiral model of [E. Hernández, J. Nieves, M. Valverde, hep-ph/0701149] at intermediate energies. Results are really significant since the differences between neutrino and antineutrino induced reactions are always large in all physical channels.