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 — preprints:2002:ttp02-39 [2016/03/17 11:03] (current) Line 1: Line 1: + ====== TTP02-39 The analytic value of a 3-loop sunrise graph in a particular kinematical configuration ====== + + + <​hidden TTP02-39 ​ The analytic value of a 3-loop sunrise graph in a particular kinematical configuration > 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 $x=0$. + ​ + |**P. Mastrolia, E. Remiddi** ​ | + |**  Nucl.Phys.B ​ 657 397-406 2003  **  | + | {{preprints:​2002:​ttp02-39.pdf|PDF}} {{preprints:​2002:​ttp02-39.ps|PostScript}} [[http://​arxiv.org/​abs/​hep-ph/​0211451|arXiv]] ​  | + | |