The analytical value of the electron (g − 2) at order α3 in QED

We have evaluated in closed analytical form the contribution of the three-loop non-planar “triple-cross” diagrams contributing to the electron (g−2) in QED; its value, omitting the already known infrared divergent part, is ae(3−cross)=12π2ε(3)−5512ε(5)−16135πM4+323as+1241n42+149π21n22−13ε(3)+233π21n2−479π2−11348. This completes the analytical evaluation of the (g−2) at order α3, giving ae(3−cross)=απ38372π2ε(3)−21524ε(5)+1003as+124π21n22−124π21n22−2392160π4+13918ε(3)−2989π21n2+17101810π2+282595184=απ3(1.181241456…).