Analytical five-loop expressions for the renormalization group QED   $\beta$-function in different renormalization schemes
  We obtain analytical five-loop results for the renormalization group $\beta$-function of Quantum Electrodynamics with the single lepton in different renormalization schemes. The theoretical consequences of the results obtained are discussed. 
A. L. Kataev and S. A. Larin
hep-ph hep-lat hep-th