Contribution of negative-energy states to the E2-M 1 polarizability of optical clocks

We investigate the contribution of negative-energy states on the E2 and M1 polarizabilities for the 1S0 and 3P0 states of the Sr clock and find that they dominate the E2-M 1 polarizability difference. Our calculated result is -7.74(3.92)x10-5 a.u., which resolves the sign inconsistency between theory and experiment. Additionally, we extend our method to other optical clocks, confirming the crucial role of negative-energy states in determining the M1 polarizability.