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

S. Laporta·P. Mastrolia·E. Remiddi
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Abstract

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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S. Laporta, P. Mastrolia, E. Remiddi. 2004-05-05. The analytic value of a 4-loop sunrise graph in a particular kinematical configuration. https://doi.org/10.1016/j.nuclphysb.2004.03.029

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