Lectures on LHC Physics

Abstract

With the discovery of the Higgs boson the LHC experiments have closed the most important gap in our understanding of fundamental interactions. We now know that the interactions between elementary particles can be described by quantum field theory, more specifically by a renormalizable gauge theory. This theory is valid to arbitrarily high energy scales and do not require an ultraviolet completion. In these notes I cover three aspects to help understand LHC results in the Higgs sector and in searches for physics beyond the Standard Model: many facets of Higgs physics, QCD as it is relevant for LHC measurements, and standard phenomenological background knowledge. The lectures should put young graduate students into a position to really follow advanced writeups and first research papers. In that sense they can serve as a starting point for a research project in LHC physics. With this new, significantly expanded version I am confident that also some more senior colleagues will find them useful and interesting.

The Higgs legacy of the LHC Run I

“…Note that this does not have to be the case based on first principles: if all uncertainties were flat in the rates, the resulting profile likelihood would keep its box shape, and the errors would be added linearly [91,94]. The central limit theorem does not guarantee a Gaussian distribution, because the profile likelihood does not involve a convolution.…”

“…The main differences between the frequentist RFit treatment and Gaussian theoretical uncertainties are not related to the shape of the final distribution, but to the size of the combined theoretical uncertainties. First, combining two flat theoretical uncertainties, for example from unknown higher orders and the parton densities, will lead to a linear combination of the two error bars in the frequentist RFit scheme [91,94,[97][98][99][100]. In the Gaussian approach they are added in quadrature.…”

Mass effects in the Higgs-gluon coupling: boosted vs. off-shell production

“…One example of new physics which can generate sizable perturbative corrections to the Higgs-gluon coupling are light supersymmetric top squarks [62][63][64][65][66][67][68]. Because of the non-decoupling structure of the Standard Model with Yukawa couplings we can integrate out the top quark in the low-energy limit, which describes the interactions between gluons and any Higgs bosons in a simple effective Lagrangian [39][40][41][42]. For the top quark this effective Lagrangian provides a very good prediction of the inclusive Higgs production rate with at most O(10%) deviations in typical inclusive distributions for gg → H production [43][44][45][46][47][48].…”

Scaling patterns for QCD jets

“…Numerically, we can combine the QCD parton shower with hard matrix element calculations, to predict jet radiation patterns over wide phase space regions ( [16][17][18]; for a pedagogical introduction see e.g. [19]). Analytically, Sudakov factors and generating functionals can be used to describe QCD jet radiation [20,21].…”