The analytic value of a 3-loop sunrise graph in a particular kinematical configuration
High Energy Physics - Phenomenology
2009-11-07 v1
Abstract
We consider the scalar integral associated to the 3-loop sunrise graph with a massless line, two massive lines of equal mass , a fourth line of mass equal to , and the external invariant timelike and equal to the square of the fourth mass. We write the differential equation in satisfied by the integral, expand it in the continuous dimension around 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 expansion at and .
Keywords
Cite
@article{arxiv.hep-ph/0211451,
title = {The analytic value of a 3-loop sunrise graph in a particular kinematical configuration},
author = {P. Mastrolia and E. Remiddi},
journal= {arXiv preprint arXiv:hep-ph/0211451},
year = {2009}
}
Comments
9 pages, 3 figures