The charge of an electron is -e in energy scales well into the atomic scale. At infinitesimal scales it becomes infinite. This relation must be continuous for re-normalization to work, thus the intermediate value theorem asserts that it attains all values between at some energy level. I want to determine the scale at which the charge is observed to be -2e. This should only involve a few highest order terms. Where can I find the highest order perturbation terms for the charge of an electron as the energy scale increases/length scale decreases?