Lectures on LHC Physics

TL;DR

These notes provide a structured, graduate-level roadmap through Higgs physics and its QCD context in LHC phenomenology. They connect electroweak symmetry breaking to the observable Higgs sector, detailing production mechanisms (gluon fusion, vector boson fusion, associated production), decay channels, and coupling measurements, while integrating QCD tools such as DGLAP, PDFs, and phase-space methods. The text also surveys beyond-Standard Model ideas (technicolor, little Higgs, Higgs inflation) and discusses theoretical constraints (unitarity, RG running, Coleman–Weinberg) and precision tests (S,T, ρ). Together, the lectures serve as both a theoretical foundation and a practical guide for interpreting LHC Higgs results and planning future explorations. The material emphasizes EFT approaches, collider signatures, and the interplay between theory and experiment in high-energy 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.

Figures (30)

• Figure 1: Allowed range of Higgs masses in the Standard Model after taking into account electroweak precision data, most notably the $\rho$ parameter contribution from the Higgs itself, Eq.\ref{['eq:rho_higgs']}. Figure from the LEP electroweak working group, with updates available under http://lepewwg.web.cern.ch/LEPEWWG.
• Figure 2: Mexican hat form of the Higgs potential, figure from the University of Edinburgh website.
• Figure 3: Triviality or Landau pole (upper) and stability bounds (lower) for the Standard Model Higgs boson in the $m_H - Q$ plane. Similar arguments first appeared in Ref. Cabibbo:1979ay, the actual scale dependence can be seen in Refs. christofLindner:1985uk.
• Figure 4: Masses of all supersymmetric Higgs states as a function of the pseudoscalar Higgs mass, computed with FeynHiggs. Figures of this kind can be found for example in Ref. Hahn:2009zz.
• Figure 5: Branching ratios of the Standard-Model Higgs boson as a function of its mass, computed with HDECAY. Off--shell effects in the decays to $WW$ and $ZZ$ are taken into account. Figure found for example in Refs.Spira:1997dgDjouadi:2005gi.