Neutrinos with Magnetic Moment: Depolarization Rate in Plasma

Neutrinos with a magnetic moment $\mu$ change their helicity when interacting with an electromagnetic field. Various aspects of this effect have been described as spin precession, spin-flip scattering, and magnetic Cherenkov radiation. These perspectives are unified in an expression for the $\nu_L\to\nu_R$ transition rate which involves the correlators of the electromagnetic field distribution. Our general formula corrects a previous result and generalizes it to the case where the fields cannot be viewed as classical and where the momentum transfers need not be small. We evaluate our result explicitly for a relativistic QED plasma and determine the depolarization rate to leading order in the fine structure constant. Assuming that big-bang nucleosynthesis constraints do not allow a right-handed neutrino in equilibrium we derive the limit $\mu<6.2\EE{-11}\mu_B$ on the neutrino magnetic moment. Bounds on $\mu$ from a possible large scale magnetic fields are found to be more stringent even for very weak fields.