Practical guide to loop integration

Practical guide to loop integration is a short block course I have developed for the University of Durham in 2022 and extended for the University of Bern in 2024.

Contact: Yannick Ulrich

Please report mistakes as issues or per email.

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 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. Next, I will discuss the method of regions to reduce the number of scales of the integrals. Finally, I will discuss the method of differential equations and in particular Auxilary Mass Flow to actually calculate 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 will take place every Tuesday from 16 April 2024 to 28 May 2024 at 14:00 CEST -- 16:00 CEST.

Course material from 2022

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