Parity violation in CMB vs EFT of Standard Model

The recent analysis of the cosmic microwave background (CMB) indicates a rotation of the polarization plane of the CMB photons from the last scattering surface, called cosmic birefringence. A standard explanation for this effect is a parity-odd scalar field coupled to photons, whose coherent motion, if exists, breaks parity in the photon sector along the propagation for a cosmological distance. To examine the degree of validity of this premise, we explore whether or not the Standard Model (SM) particles can generate a sufficient level of cosmic birefringence. Our systematic study utilizing the SM effective field theory (SMEFT) reveals that indeed none of the operators in SMEFT would be able to give the reported birefringence angle. Should this observational result be confirmed, therefore, the existence of a new particle beyond SMEFT that is much lighter than the electroweak scale would be an inevitable conclusion.