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

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 $x=0$.

9 pages, 3 figures

References in corpus (2)

• The analytic value of the sunrise self-mass with two equal masses and the external invariant equal to the third squared mass
• High-precision e-expansions of three-loop master integrals contributing to the electron g-2 in QED

Cited by in corpus (6)

• Feynman Diagrams and Differential Equations
• An analytic solution for the equal-mass banana graph
• Two-loop sunset diagrams with three massive lines
• On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order
• Three-loop on-shell Feynman integrals with two masses
• The analytic value of a 4-loop sunrise graph in a particular kinematical configuration