CMB constraints on the simultaneous variation of the fine structure constant and the electron mass

We study constraints on time variation of the fine structure constant α from cosmic microwave background (CMB) taking into account simultaneous change in α and the electron mass mₑ which might be implied in unification theories. We obtain the constraints -0.097<Δα/α<0.034 at 95% C.L. using WMAP data only, and -0.042<Δα/α<0.026 combining with the constraint on the Hubble parameter by the HST Hubble Key Project. These are improved by 15% compared with constraints assuming only α varies. We discuss other relations between variations in α and mₑ but we do not find evidence for varying α.