Neutrino Magnetic Moment Behaviour in a

We have shown in [1] that a neutrino magnetic moment form factor µ ν (q 2) could be considerably amplified at low momentum transfer, q 2 ≤ m 2 N , at the cost of introducing an extra light neutral fermion N with mass m N and nonzero magnetic moment. It was assumed that the magnetic moment of N would originate in a renormalizable way at a heavy scale M. While the enhancement of the neutrino magnetic moment was unam-biguous, we stressed that in this effective Lagrangian approach an uncertainty persisted about the behaviour of µ ν (q 2) in the interval m 2 N ≪ q 2 ≪ M 2. This is not unexpected in presence of a nonrenormalizable effective theory (a particle with bare magnetic moment). We show in a simple renormalizable model for the magnetic moment of particle N how a 2 loop calculation solves the ambiguity. In the domain m 2 N ≪ q 2 ≪ M 2 we confirm the result obtained in [1] using a sharp cutoff . It is amusing that the correct results are given, as expected, through dimensional regularization in the full theory, but NOT in the effective lagrangian approach.