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 — preprints:2000:ttp00-10 [2016/03/17 11:03] (current) Line 1: Line 1: + ====== TTP00-10 Using differential equations to compute two-loop box integrals ====== + + + <​hidden TTP00-10 ​ Using differential equations to compute two-loop box integrals > The calculation of exclusive observables beyond the one-loop level + ​requires elaborate techniques for the computation of multi-leg two-loop + ​integrals. We discuss how the large number of different integrals + ​appearing in actual two-loop calculations can be reduced to a small + ​number of master integrals. An efficient method to compute these master + ​integrals is to derive and solve differential equations in the external + ​invariants for them. As an application of the differential equation + ​method,​ we compute the ${\cal O}(\epsilon)$-term of a particular + ​combination of on-shell massless planar double box integrals, which + ​appears in the tensor reduction of $2 \to 2$ scattering amplitudes at two + ​loops. + ​ + |**T.Gehrmann,​ E.Remiddi** ​ | + |**  Nuclear Physics B (Proc. Suppl.) ​ 89 251-255 2000  **  | + | {{preprints:​2000:​ttp00-10.pdf|PDF}} {{preprints:​2000:​ttp00-10.ps|PostScript}} [[http://​arxiv.org/​abs/​hep-ph/​0005232|arXiv]] ​  | + | |