Mass and coupling constant limits from convergence conditions on the effective charge in QED

The massless fermion limit of QED is discussed. For on-shell renormalizatio n the high energy behavior fixes no lower limit on the mass of the lightest fermion if the fine structure constant a is allowed to vary. The choice of an arbitrary (spacelike) subtraction point does, however, fix a lower limi t on the mass of the lightest fermion, for any subtraction scale mu, if the effective charge alpha(eff)(mu) respects both quantum mechanical superposi tion and renormalization scale invariance. Limits on the values of a. Or th e electron mass are obtained within the Standard Electroweak Model by requi ring convergence of alpha(eff)(M-Z).