Abstract
The generic two-loop diagram of massless scalar field theory ind dimensions, with propagators raised to powers {α i |i=1,5} is shown to have a symmetry groupZ 2×S 6 corresponding to reflection and permutation of six linear combinations of the six parameters. The expansion about α i =d/4=1 is given to the level required for six-loop renormalization. All but five of the coefficients are obtained from products of one-loop diagrams. All but one are expressed in terms of the Riemann zeta function.
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Barfoot, D.T., Broadhurst, D.J. Z 2×S 6 symmetry of the two-loop diagram. Z. Phys. C - Particles and Fields 41, 81–85 (1988). https://doi.org/10.1007/BF01412581
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DOI: https://doi.org/10.1007/BF01412581