Integration by parts: The algorithm to calculate β-functions in 4 loops

  title={Integration by parts: The algorithm to calculate $\beta$-functions in 4 loops},
  author={K. Chetyrkin and F. Tkachov},
  journal={Nuclear Physics},
Abstract The following statement is proved: the counterterm for an arbitrary 4-loop Feynman diagram in an arbitrary model is calculable within the minimal subtraction scheme in terms of rational numbers and the Riemann ζ-function in a finite number of steps via a systematic “algebraic” procedure involving neither integration of elementary, special, or any other functions, nor expansions in and summation of infinite series of any kind. The number of steps is a rapidly increasing function of the… Expand
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