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

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

2002-11-28

arxiv.org/abs/hep-ph/0211451v1

Nucl.Phys. B657 (2003) 397-406

Physics

High Energy Physics

High Energy Physics - Phenomenology

9 pages, 3 figures

Scientific paper

10.1016/S0550-3213(03)00144-5

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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