The Massless Higher-Loop Two-Point Function |
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Authors: | Francis Brown |
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Institution: | (1) Institut de Mathematiques de Jussieu, UMR 7586, Université Pierre et Marie Curie-Paris 6, F-75005 Paris, France |
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Abstract: | We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method
yields a criterion for a primitive Feynman graph G to evaluate to multiple zeta values. The criterion depends only on the topology of G, and can be checked algorithmically. As a corollary, we reprove the result, due to Bierenbaum and Weinzierl, that the massless
2-loop 2-point function is expressible in terms of multiple zeta values, and generalize this to the 3, 4, and 5-loop cases.
We find that the coefficients in the Taylor expansion of planar graphs in this range evaluate to multiple zeta values, but
the non-planar graphs with crossing number 1 may evaluate to multiple sums with 6th roots of unity. Our method fails for the five loop graphs with crossing number 2 obtained by breaking open the bipartite
graph K
3,4 at one edge.
CNRS. |
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Keywords: | |
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