Differential equations and high-energy expansion of two-loop diagrams in D dimensions

• DOI: 10.1016/j.nuclphysb.2005.10.024
• Publication Date: 2005-11-12T12:11:13Z
• Authors: A.V. Bogdan; R.N. Lee
• Keywords: High Energy Physics - Phenomenology; High Energy Physics - Phenomenology (hep-ph); 0103 physical sciences; FOS: Physical sciences; 01 natural sciences

13 pages,8 figures, uses elsart.cls. Misprints corrected<br/>New method of calculation of master integrals using differential equations and asymptotical expansion is presented. This method leads to the results exact in space-time dimension $D$ having the form of the convergent power series. As an application of this method, we calculate the two--loop master integral for "crossed--triangle" topology which was previously known only up to $O(\ep)$ order. The case when a topology contains several master integrals is also considered. We present an algorithm of the term-by-term calculation of the asymptotical expansion in this case and analyze in detail the "crossed--box" topology with three master integrals.<br/>