Do we need Feynman diagrams for higher orders perturbation theory?
  We compute the two and three loop corrections to the beta function for Yang-Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one loop effective potential into zero and positive modes and are entirely analytical. No two or three loop Feynman diagrams are considered in the process. 
Renata Jora
hep-ph hep-th