Electron self-energy in QED at two loops revisited

Abstract

We reconsider the two-loop electron self-energy in quantum electrodynamics. We present a modern calculation, where all relevant two-loop integrals are expressed in terms of iterated integrals of modular forms. As boundary points of the iterated integrals, we consider the four cases p2=0, p2=m2, p2=9m2 and p2=∞. The iterated integrals have q-expansions, which can be used for the numerical evaluation. We show that a truncation of the q-series to order O(q30) gives numerically, for the finite part of the self-energy, a relative precision better than 10-20 for all real values p2/m2.