Stars as Laboratories for Fundamental Physics - MPP Theory Group

Nonstandard Neutrinos 273
Fig. 7.8. Important processes involving direct neutrino electromagnetic couplings,
notably magnetic dipole moments and magnetic or electric transition
moments.
Because an anomalous neutrino charge radius causes a contact interaction
it would manifest itself by the modification C V → C V +
1
3√
2 πα⟨r 2 ⟩/G F , i.e. there would be a small correction to the overall
cross section. A dipole moment, on the other side, modifies the energy
spectrum of the recoil electrons, notably at low energies, because of its
forward-peaked nature from the Coulomb divergence.
If neutrinos had electric dipole moments, or electric or magnetic
transition moments, these quantities would also contribute to the scattering
cross section. Therefore, the quantity measured in electron recoil
experiments involving relativistic neutrinos is (e.g. Raffelt 1989)
µ 2 ν = ∑
j=ν e,ν µ,ν τ
|µ ij − ϵ ij | 2 , (7.25)
where i refers to the initial-state neutrino flavor. Therefore, in principle
there is a possibility of destructive interference between the magnetic
and electric transition moments of Dirac neutrinos. (Majorana neutrinos
have only magnetic or electric transition moments, but not both if
CP is conserved.)