MASS AND COUPLING CONSTANT LIMITS FROM CONVERGENCE CONDITIONS ON THE EFFECTIVE CHARGE IN QED

Abstract

The massless fermion limit of QED is discussed. For on-shell renormalization the high energy behavior fixes no lower limit on the mass of the lightest fermion if the fine structure constant α is allowed to vary. The choice of an arbitrary (spacelike) subtraction point does, however, fix a lower limit on the mass of the lightest fermion, for any subtraction scale μ, if the effective charge α eff (μ) respects both quantum mechanical superposition and renormalization scale invariance. Limits on the values of α or the electron mass are obtained within the Standard Electroweak Model by requiring convergence of α eff (MZ).