The massless higher-loop two-point function
| dc.creator | Brown, Francis | |
| dc.date | 2008-04-10 | |
| dc.date.accessioned | 2026-07-07T12:55:03Z | |
| dc.date.available | 2026-07-07T12:55:03Z | |
| dc.description | 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 $6^\mathrm{th}$ 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. | |
| dc.identifier | https://arxiv.org/abs/0804.1660 | |
| dc.identifier | http://arxiv.org/abs/0804.1660 | |
| dc.identifier | Commun.Math.Phys.287:925-958,2009 | |
| dc.identifier | doi:10.1007/s00220-009-0740-5 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224146 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | High Energy Physics - Phenomenology | |
| dc.subject | Number Theory | |
| dc.title | The massless higher-loop two-point function | |
| dc.type | text |