The two-loop sunrise graph with arbitrary masses
Abstract
We discuss the analytical solution of the two-loop sunrise graph with arbitrary non-zero masses in two space-time dimensions. The analytical result is obtained by solving a second-order differential equation. The solution involves elliptic integrals and in particular the solutions of the corresponding homogeneous differential equation are given by periods of an elliptic curve.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- May 2013
- DOI:
- 10.1063/1.4804996
- arXiv:
- arXiv:1302.7004
- Bibcode:
- 2013JMP....54e2303A
- Keywords:
-
- 02.10.Ox;
- 02.30.Rz;
- 02.30.Hq;
- Combinatorics;
- graph theory;
- Integral equations;
- Ordinary differential equations;
- High Energy Physics - Phenomenology
- E-Print:
- 24 pages