The analytic value of a 4-loop sunrise graph in a particular kinematical configuration

Details The analytic value of a 4-loop sunrise graph in a particular kinematical configuration The analytic value of a 4-loop sunrise graph in a particular kinematical configuration

2003-11-20

arxiv.org/abs/hep-ph/0311255v3

Nucl.Phys. B688 (2004) 165-188

Physics

High Energy Physics

High Energy Physics - Phenomenology

18 pages, 3 figures; minor changes into the Introduction; references added; accepted by Nucl. Phys. B

Scientific paper

10.1016/j.nuclphysb.2004.03.029

The 4-loop sunrise graph with two massless lines, two lines of equal mass M and a line of mass m, for external invariant timelike and equal to m^2 is considered. We write differential equations in x=m/M for the Master Integrals of the problem, which we Laurent-expand in the regularizing continuous dimension d around d=4, and then solve exactly in x up to order (d-4)^3 included; the result is expressed in terms of Harmonic PolyLogarithms of argument x and maximum weight 7. As a by product, we obtain the x=1 value, expected to be relevant in QED 4-loop static quantities like the electron (g-2). The analytic results were checked by an independent precise numerical calculation

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