[Paper Review] Quantum field theory and the electroweak Standard Model

Gustavo Burdman|arXiv (Cornell University)|Oct 12, 2024

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper provides a comprehensive introduction to the electroweak Standard Model (EWSM) within the framework of quantum field theory, covering abelian and non-abelian gauge theories, spontaneous symmetry breaking via the Higgs mechanism, and renormalization. It emphasizes electroweak precision tests as a key tool for probing new physics, highlighting the Higgs boson's role in mass generation and the need for future experiments like Higgs factories to map the Higgs potential and test composite Higgs models.

ABSTRACT

In these lectures we give an introduction and overview of the electroweak standard model (EWSM) of particle physics. We first introduce the basic concepts of quantum field theory necessary to build the EWSM: abelian and non-abelian gauge theories, spontaneous symmetry breaking and the Higgs mechanism. We also introduce some basic concepts of renormalization, so as to be able to understand the full power of electroweak precision tests and their impact on our understanding the EWSM and its possible extensions. We discuss the current status of experimental tests and conclude by pointing the problems still existing in particle physics not solved by the EWSM and how these impact the future of the field.

Motivation & Objective

• To provide a pedagogical introduction to the electroweak Standard Model (EWSM) for advanced students and researchers.
• To explain the foundational role of quantum field theory, particularly gauge theories and spontaneous symmetry breaking, in constructing the EWSM.
• To analyze electroweak precision tests as a powerful probe of new physics beyond the Standard Model.
• To identify open questions in particle physics—such as the origin of the Higgs sector and dark matter—that motivate future theoretical and experimental research.
• To discuss the potential of future facilities, including Higgs factories and gravitational wave detectors, in testing the EWSM and its extensions.

Proposed method

• Uses canonical quantization and path integral formalism to derive Lorentz-invariant amplitudes in quantum field theory.
• Applies the Higgs mechanism to spontaneously break the electroweak gauge symmetry, generating masses for the W and Z bosons and the Higgs boson.
• Employs renormalization techniques to ensure predictive power in quantum field theories, particularly in the context of electroweak precision observables.
• Analyzes gauge boson self-couplings and Higgs couplings as key observables for testing the EWSM and detecting deviations from the Standard Model.
• Considers effective field theory approaches to include higher-dimensional operators and probe new physics beyond the renormalizable EWSM Lagrangian.
• Evaluates the potential of future experiments—such as HL-LHC and Higgs factories—to measure triple Higgs couplings and test composite Higgs models.

Figure 1: Emission, propagation and absorption of a particle.

Experimental results

Research questions

• RQ1 How does the Higgs mechanism generate masses for the W and Z bosons while preserving gauge invariance?
• RQ2 What are the implications of electroweak precision measurements for new physics beyond the Standard Model?
• RQ3 Can precise measurements of Higgs boson couplings at the HL-LHC or future Higgs factories distinguish between a fundamental Higgs and a composite state?
• RQ4 What observable signatures would arise from a composite Higgs sector, particularly in deviations of Higgs couplings from Standard Model predictions?
• RQ5 How can gravitational wave signals from the electroweak phase transition serve as a probe of new physics in the Higgs potential?

Key findings

• The electroweak Standard Model successfully explains the origin of mass via the Higgs mechanism, with the Higgs boson discovered at the LHC confirming the mechanism.
• Electroweak precision tests, particularly of fermion couplings and gauge boson self-couplings, are highly sensitive to new physics, with current data consistent with the SM at the 1% level.
• The triple Higgs coupling $ g_{h^3} $ is a critical observable for mapping the Higgs potential; precise measurement requires significant data beyond the HL-LHC, possibly necessitating a Higgs factory.
• Composite Higgs models predict deviations in Higgs couplings—potentially momentum-dependent—offering a testable signature for new physics at future colliders.
• The absence of signals from new resonances at the LHC suggests that any new physics associated with the Higgs sector may manifest only through subtle deviations in couplings or vacuum stability.
• Future experiments, including LISA and CMB measurements of $ N_{\text{eff}} $, may detect new relativistic degrees of freedom or gravitational wave signals from a first-order electroweak phase transition, indicating physics beyond the EWSM.

Figure 2: Emission, propagation and absorption of a charged particle. Consistency with either temporal order is restored by having anti-particles. Emission of a negatively charged particle at $y$ followed by absorption at $x$ is equivalent to emission of the positively-charged anti-particle at $x$ ,