Vacuum magnetic birefringence experiment as a probe of the dark sector

Vacuum magnetic birefringence (VMB) is a nonlinear electromagnetic effect predicted by quantum electrodynamics (QED). In addition to seeing the effect from QED, it is also possible for the measurement to probe the dark sector. VMB as predicted by QED is parity conservative, but the effect from the dark sector can be parity violative. To pursue this possibility, we calculated the effect from the dark sector with the generalized Heisenberg-Euler effective Lagrangian that is applicable to parity-violating theories in the weak and homogeneous field limit. The contribution of the dark sector neutrinos in a dark sector model to the VMB experiment is studied. The contribution comes from the mixing of the photon with the dark sector Z boson and induces a parity-violating electromagnetic interaction. Polarization change of a laser beam in an external magnetic field is studied, where the angle between the initial polarization and the magnetic field is 45 degrees or -45 degrees. The contribution from the dark sector modifies the magnitude of the polarization change, so it can be detected by measuring the magnitude precisely. In addition to the change in the magnitude, the dark sector also induces parity-violating effects. We also propose a new scheme to measure the effect of parity violation directly. By measuring the change of polarization of a laser polarized in parallel with or perpendicular to the applied magnetic field with a ring Fabry-Perot resonator, one can search for the effect directly. If a signal appears in this scheme, it would be evidence of parity violation from beyond standard model theories.