Dirac Neutrino Anapole Moment

Abstract

We calculate the Dirac neutrino anapole moment (a_{\nu_l}) in the context of the Standard Model (SM) making use of the Dirac form factor F_D(q^2) introduced recently by J. Bernabeu, L. G. Cabral-Rosetti, J. Papavassiliou y J. Vidal by using the Pinch Technique (PT) formalism, working in two different gauge-fixing schemes (R_\xi guage and the electroweak BFM), at the one loop level. We show that the neutrino anapole form factor F_A(q^2) and Dirac form factor F_D(q^2) are related as follows: F_A(q^2) = \frac{1}{q^2} F_D(q^2). Hence, the Dirac neutrino charge radius < r^2_{\nu_l} > and the anapole moment satisfy the simple relation a_{\nu_l} = {1/6} < r^2_{\nu_l} >. Therefore, we show that the anapole moment (as the charge radius) of the neutrino is a physical quantity, which only gets contribution from the proper neutrino electromagnetic vertex (in electroweak BFM), and that a_{\nu_l} is of the order 10^{-34} cm^2.