Results of the Five - Loop Calculation

In this chapter, we summarize the results of the five-loop calculations for the power series expansions of the renormalization constants governing the relations between bare and renormalized parameters. These expansions were first calculated more than 15 years ago [1]. Several errors were corrected in a more recent recalculation [2]. An essential error had occurred in diagram No.116 (see page 434) fro which the R * operation was explained in detail on page 223. The renormalization constants receive contributions from the quadratically and logarithmically divergent 1PI-diagrams without tadpole parts, to be collectively called G 2 and G 4 for two-and four-point functions. Each diagram contributes a polynomial in 1/ε, multiplied by a weight factor W and a symmetry factor S. The renormalized coupling constant in these expansions is ¯ g whose normalization was specified in Eq. (13.24). The loop expansions are: