On the neutrino vector and axial vector charge radius

A Majorana neutrino is characterized by just one flavor diagonal electromagnetic form factor: the anapole moment, that in the static limit corresponds to the axial vector charge radius <r^2_A>. As is the case for the vector charge radius of a Dirac neutrino, proving that this is a well defined physical quantity is non trivial. I will first describe briefly the origin of the long standing controversy about the physical or non physical nature of the neutrino charge radius. Then I will argue that, in contrast to Dirac neutrino electromagnetic form factors, for Majorana neutrinos cosmological and astrophysical arguments do not provide useful informations on <r^2_A>, and therefore this quantity has to be studied by means of terrestrial experiment. Finally, I will discuss the constraints that can be derived on <r^2_A> for the tau neutrino from a comprehensive analysis of the data on single photon production off Z-resonance, and I will conclude with a few comments on $\nu_\mu$ scattering data from the NuTeV, E734, CCFR and CHARM-II collaborations and on the limits implied for <r^2_A> for the muon neutrino.