Lectures on multiloop calculations

Details Lectures on multiloop calculations Lectures on multiloop calculations

2003-07-23

arxiv.org/abs/hep-ph/0307297v4

Int.J.Mod.Phys.A19:473-520,2004

Physics

High Energy Physics

High Energy Physics - Phenomenology

52 pages, 49 figures. Lectures at Calc-03 school, Dubna, 14--20 June 2003. v2: 2 references added, minor typos corrected. v3:

Scientific paper

10.1142/S0217751X04016775

I discuss methods of calculation of propagator diagrams (massless, those of Heavy Quark Effective Theory, and massive on-shell diagrams) up to 3 loops. Integration-by-parts recurrence relations are used to reduce them to linear combinations of basis integrals. Non-trivial basis integrals have to be calculated by some other method, e.g., using Gegenbauer polynomial technique. Many of them are expressed via hypergeometric functions; in the massless and HQET cases, their indices tend to integers at $\epsilon\to0$. I discuss the algorithm of their expansion in $\epsilon$, in terms of multiple $\zeta$ values. These lectures were given at Calc-03 school, Dubna, 14--20 June 2003.

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