Neutrino Magnetic Moments Meet Precision $N_{\mathrm{e}\mathrm{f}\mathrm{f}}$ Measurements

In the early universe, Dirac neutrino magnetic moments due to their chirality-flipping nature could lead to thermal production of right-handed neutrinos, which would make a significant contribution to the effective neutrino number, $N_{\mathrm{e}\mathrm{f}\mathrm{f}}$. We present in this paper a dedicated computation of the neutrino chirality-flipping rate in the thermal plasma. With a careful and consistent treatment of soft scattering and the plasmon effect in finite temperature field theories, we find that neutrino magnetic moments above $2.7\times {10}^{-12}{\mu }_B$ have been excluded by current CMB and BBN measurements of $N_{\mathrm{e}\mathrm{f}\mathrm{f}}$, assuming flavor-universal and diagonal magnetic moments for all three generation of neutrinos. This limit is stronger than the latest bounds from XENONnT and LUX-ZEPLIN experiments, and comparable with those from stellar cooling considerations.