Where do the tedious products of zetas come from?

Abstract

Lamentably, the full analytical content of the epsilon-expansion of the master two-loop two-point function, with arbitrary self-energy insertions in 4-2epsilon dimensions, is still unknown. Here we show that multiple zeta values (MZVs) of weights up to 12 suffice through O(epsilon^9). Products of primitive MZVs are generated by a processes of "pseudo-exponentiation"" whose combinatorics faithfully accord with expectations based on Kreimer's modified shuffle product and on the Drinfeld-Deligne conjecture. The existence of such a mechanism, relating thousands of complicated rational numbers, enables us to identify precise and simple combinations of MZVs specific to quantum field theories in even numbers of spacetime dimensions.

arXiv comment5 pages, LaTeX, uses npb.sty, talk given at "RadCor 2002 - Loops and Legs 2002", Kloster Banz, Germany, Sep 8-13, 2002

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