# Differences

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+ | ====== TTP02-39 The analytic value of a 3-loop sunrise graph in a particular kinematical configuration ====== | ||

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+ | <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 $x=0$. | ||

+ | </hidden> | ||

+ | |**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]] | | ||

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