A resummable β-function for massless QED

Within the set of schemes defined by generalized, manifestly gauge invariant exact renormalization groups for QED, it is argued that the β-function in the four-dimensional massless theory cannot possess any nonperturbative power corrections. Consequently, the perturbative expression for the β-function must be resummable. This argument cannot be extended to flows of the other couplings or to the anomalous dimension of the fermions and so perturbation theory does not define a unique trajectory in the critical surface of the Gaussian fixed point. Thus, resummability of the β-function is not inconsistent with the expectation that a non-trivial fixed point does not exist.