It is one of the biggest challenge in particle physics and cosmology to determine the mass of neutrinos. Current neutrinoless double beta decay experiment show that the total neutrino mass is smaller than 1–6 eV.
In recent years, precise CMB data make it possible to constrain neutrino masses cosmologically. It says that the total neutrino mass is smaller than 2 eV in standard ACDM model.1 But if there are other physical processes which affects the CMB anisotropies, such constraint may be changed. A primordial magnetic field (PMF) is one of such physical processes. In this work, we constrain the total neutrino mass from CMB anisotropies with the PMF effect.