CP violating dark photon kinetic mixing and Type-III Seesaw.

Dark photon physics has attracted significant theoretical and experimental attention. A dark photon from a $U(1)_X$ gauge group can have renormalizable kinetic mixing with the $U(1)_Y$ gauge boson of the SM $SU(3)_C\times SU(2)_L\times U(1)_Y$ gauge group. It only permits CP conserving mixing. When a $SU(2)_L$ triplet scalar with a non-zero vacuum expectation value is introduced, a dimension 5 operator can be constructed to generate a CP violating kinetic mixing. To further realize a renormalizable model for CP violating kinetic mixing, new ingredients are needed. We construct for the first time such a model. We find that the triplet leptons in type-III seesaw model can play the crucial role in building such a renormalizable model. This natural connection of dark photon and neutrino physics may have important implications about how new physics might emerge. The CP violating kinetic mixing induced electron electric dipole moment (EDM) can be as large as current experimental bounds. The model can be further tested by improved measurement of electron EDM.