Hands-on ONE-LOOP Calculations from start to finish

Lecturer: Prof Mike Seymour

Title: Hands-on one-loop calculations from start to finish

Time: Wednesdays 05/11/25 - 17/12/25 15:00 (except 10/12 15:30)

Place: Soton, B46 Room 5005 + Teams

Abstract: This practical course will start with an overview of the NLO calculational landscape, but will focus primarily on students performing a one-loop calculation for themselves from start to finish, including the effect of a suitably-defined observable. If time and interest allow, it could end with an extension to parton shower matching and/or resummation of large logarithms. The course will include a weekly one-hour session with Prof. Seymour, but the expectation is that students will work on their calculations and associated reading between sessions - it is not just a lecture course! It will last seven weeks.

Lectures 1 and 2a give an overview of the modern tools available for one-loop calculations, and overview of the rest of the course, while each of the remaining lectures are divided into two halves: the second half setting goals for the following week's self-study, and the first half of the next lecture wrapping it up.

Lecture 1: the need for NLO calculations; the tools available to do NLO calculations for you; the value of doing a one-loop calculation for yourself; is NLO enough?

Lecture 2a: the anatomy of an NLO calculation; one-loop matrix elements; dimensional regularisation; real emission matrix elements; phase space integration; collinear singularities/PDFs.
Lecture 2b: getting started with our own calculation: the LO cross section for pp->l+l-.

Lecture 3a: wrapping up lecture 2b.
Lecture 3b: the one-loop correction to the qqbar->l+l- matrix element; dimensional regularisation, Feynman parametrisation; Wick rotation; pole extraction.

Lecture 4a: wrapping up lecture 3b.
Lecture 4b: the real-emission matrix elements qqbar->l+l-g and qg->l+l-g: phase space integration; singularities; universality.

Lecture 5a: wrapping up lecture 4b.
Lecture 5b: subtraction of universal poles, a diversion into l+l- -> jets: the dipole subtraction algorithm; the importance of an infrared-safe observable.

Lecture 6a: wrapping up lecture 5b.
Lecture 6b: back to pp->l+l-, why are initial-state singularities different? PDF definition at NLO; scale dependence; our complete NLO calculation.

Lecture 7a: wrapping up lecture 6b.
Lecture 7b: a brief look at pp->l+l- + jets, what is new? Renormalisation and running coupling; more about infrared-safe observables.

Optional lecture 8 if time and interest: parton showers and matching or resummation of large logarithms or one-loop top quark cross sections and the top mass definition, at the audience's request.