Magnetic field instability in a neutron star driven by the electroweak electron-nucleon interaction versus the chiral magnetic effect

We show that the Standard Model electroweak interaction of ultrarelativistic electrons with nucleons (the eN interaction) in a neutron star (NS) permeated by a seed large-scale helical magnetic field provides its growth up to ≳1015 G during a time comparable with the ages of young magnetars ∼104 yr. The magnetic field instability originates from the parity violation in the eN interaction entering the generalized Dirac equation for right and left massless electrons in an external uniform magnetic field. We calculate the average electric current given by the solution of the modified Dirac equation containing an extra current for right and left electrons (positrons), which turns out to be directed along the magnetic field. Such a curren