Dirac Neutrino Anapole Moment

We calculate the Dirac neutrino anapole moment (a_vl) in the context of the Standard Model (SM) making use of the Dirac form factor F_D(q²) introduced recently by J. Bernabéu, L. G. Cabral‐Rosetti, J. Papavassiliou y J. Vidal by using the Pinch Technique (PT) formalism, working in two different gauge‐fixing schemes (R_ξ guage and the electroweak BFM), at the one loop level. We show that the neutrino anapole form factor F_A(q²) and Dirac form factor F_D(q²) are related as follows: $FA(q2) = 1q2FD(q2)$⁠. Hence, the Dirac neutrino charge radius $〈rvl2〉$ and the anapole moment satisfy the simple relation $avl = 16〈rvl2〉$⁠. 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_vl is of the order 10⁻³⁴ cm².