Where do the tedious products of zetas come from?

Details Where do the tedious products of zetas come from? Where do the tedious products of zetas come from?

2002-11-13

arxiv.org/abs/hep-ph/0211194v1

Nucl.Phys.Proc.Suppl. 116 (2003) 432-436

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1016/S0920-5632(03)80214-1

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.

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