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arXiv · hep-ph/0211451

The analytic value of a 3-loop sunrise graph in a particular kinematical configuration

P. Mastrolia·E. Remiddi
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Abstract

We consider the scalar integral associated to the 3-loop sunrise graph with a massless line, two massive lines of equal mass $M$, a fourth line of mass equal to $Mx$, and the external invariant timelike and equal to the square of the fourth mass. We write the differential equation in $x$ satisfied by the integral, expand it in the continuous dimension $d$ around $d=4$ and solve the system of the resulting chained differential equations in closed analytic form, expressing the solutions in terms of Harmonic Polylogarithms. As a byproduct, we give the limiting values of the coefficients of the $(d-4)$ expansion at $x=1$ and $x=0$.

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P. Mastrolia, E. Remiddi. 2002-11-28. The analytic value of a 3-loop sunrise graph in a particular kinematical configuration. https://doi.org/10.1016/s0550-3213(03)00144-5

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