Can we explain cosmic birefringence without a new light field beyond Standard Model?

The recent analysis of the Planck 2018 polarization data shows a nonzero isotropic cosmic birefringence (ICB) that is not explained within the $\Lambda$CDM paradigm. We then explore the question of whether the nonzero ICB is interpreted by the framework of the Standard Model Effective Field Theory (SMEFT), or at the energy scales of the cosmic microwave background, the low-energy EFT (LEFT) whose dynamical degrees of freedom are five SM quarks and all neutral and charged leptons. Our systematic study reveals that any operator in the EFT on a cosmological background would not give the reported ICB angle, which is observationally consistent with frequency independence. In particular, we estimate the size of the ICB angle generated by the effect that the cosmic microwave background photons travel through the medium of the cosmic neutrino background with parity-violating neutrino-photon interactions and find that it would be too small to explain the data. If the reported ICB angle should be confirmed, then our result would indicate the existence of a new particle that is lighter than the electroweak scale and feebly interacting with the SM particles.