Practical guide to analytic loop integration

Practical guide to analytic loop integration is a short block course I have developed for the University of Durham in the Easter Term of 2022.

Contact: Yannick Ulrich

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Abstract

Loop integration is a vital part of any higher order calculation. However, practical tools to actually compute these integrals are rarely covered in lectures. In this block course, I will cover some advanced tools that have been used in a number of multi-scale multi-loop calculations.

After introducing the problem, I will discuss integration-by-parts reduction to reduce the number of integrals, the method of regions to reduce the number of scales and finally the Mellin Barnes technique to actually solve the integrals.

The course will be composed of lectures introducing the techniques and practical, hands-on example at the two-loop level.

Schedule

The course consist of four 1h lectures and four 1h example classes.

Participants are encouraged to attempt the problem sheets before the example class.

Course material

Date Topic Problem sheet Recordings
13 May Basics of loop integration Problems
Solutions 		Lecture
16 May Integration-by-parts relations Problems Solutions Lecture
18 May The method of region Problems Solutions Lecture
20 May Mellin-Barnes Problems Solutions Lecture

Most problems can be solved with pen and paper. However, participants are encouraged to acquaint themselves with tools like Mathematica to avoid long manual calculations.

All material is licenced under CC BY 4.0. You can find the source code and supplemental material here.

Further reading