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The spin dynamics in constant electromagnetic fields is described by theBargmann-Michel-Telegdi equation which can be upgraded with anomalous magneticand electric dipole moments. The upgraded equation remains self-consistent,Lorentz-covariant and gauge-invariant. It and its different forms have beenconfirmed in numerous experiments to high degree of accuracy. We have recentlyderived the spin motion equation within the Wentzel-Kramers-Brillouinweak-field approximation which adds a pseudoscalar correction to the BMTequation. The upgraded equation is again self-consistent, Lorentz-covariant,gauge-invariant, and free of unwanted artifacts. The pseudoscalar correction isexpected to be small, and might become important in hypersensitive experiments,like the measurements of electric dipole moments which are themselves relatedto pseudoscalar quantities. It also becomes possible to explain why EDMs are sodifficult to measure, since this correction term might lead to the effectivescreening of electric dipole moments. Within the same model, it is possible toexplain the discrepancy between experimental and theoretical values of muonmagnetic anomaly under assumption that the pseudoscalar correction is thedominant source of this discrepancy.

Pseudoscalar corrections to spin motion equation, search for electric dipole moment and muon magnetic (g-2) factor