Glossary

6.5 Spontaneous symmetry breaking and the Higgs mechanism

5 min read•august 14, 2024

Gauge theories in particle physics faced a challenge: how to explain massive particles without breaking symmetry. Enter and the . These concepts provide a solution by introducing a field that gives particles mass while preserving gauge invariance.

The Higgs mechanism is crucial to the Standard Model. It explains how get mass, while photons stay massless. The discovery of the in 2012 confirmed this theory, cementing its place in our understanding of fundamental physics.

Spontaneous Symmetry Breaking

Concept and Relevance to Gauge Theories

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  • Spontaneous symmetry breaking happens when a system's ground state or vacuum state fails to respect the symmetries of the system's or equations of motion
  • In quantum field theory, spontaneous symmetry breaking can result in the emergence of massless Nambu-, which are linked to the broken symmetry generators
  • Gauge theories, like the Standard Model, necessitate massless gauge bosons to preserve the gauge symmetry, but experimental observations reveal that some gauge bosons, such as the W and Z bosons, have non-zero masses
  • Spontaneous symmetry breaking can generate masses for gauge bosons while maintaining the gauge invariance of the theory at a fundamental level

Higgs Mechanism as a Specific Case

  • The Higgs mechanism is a particular instance of spontaneous symmetry breaking used in the Standard Model to give masses to the W and Z bosons
  • It introduces a new scalar field, the Higgs field, which has a non-zero (VEV) throughout spacetime
  • The Higgs field couples to the gauge bosons and fermions in the theory, and its non-zero VEV causes the spontaneous breaking of the gauge symmetry
  • The coupling between the Higgs field and the gauge bosons generates mass terms for the gauge bosons in the Lagrangian while preserving the gauge invariance of the theory

Higgs Mechanism and Gauge Boson Masses

Generating Masses for Gauge Bosons

  • The Higgs mechanism explains why the W and Z bosons have non-zero masses, while the photon remains massless
    • The Higgs field couples differently to the weak gauge bosons (W and Z) and the electromagnetic gauge boson (photon), resulting in the observed mass differences
  • The coupling between the Higgs field and the gauge bosons generates mass terms for the gauge bosons in the Lagrangian, while preserving the gauge invariance of the theory
  • The strength of the coupling determines the masses of the gauge bosons, with stronger couplings leading to heavier gauge bosons (W and Z bosons)

Higgs Boson as a Result of the Mechanism

  • The Higgs boson is a massive scalar particle that emerges as a result of the Higgs mechanism and corresponds to excitations of the Higgs field around its VEV
  • It is a crucial prediction of the Higgs mechanism and plays a vital role in confirming the validity of the theory
  • The discovery of the Higgs boson at the Large Hadron Collider (LHC) in 2012 provided experimental confirmation of the Higgs mechanism and its role in the Standard Model

Higgs Mechanism in the Standard Model

Crucial Component of the Standard Model

  • The Higgs mechanism is a crucial component of the Standard Model, as it provides a consistent explanation for the origin of particle masses without violating gauge invariance
  • The introduction of the Higgs field and the spontaneous symmetry breaking mechanism allows the Standard Model to describe the observed masses of the W and Z bosons
  • It also generates masses for the fermions in the Standard Model through their Yukawa couplings to the Higgs field
    • The strength of the Yukawa couplings determines the masses of the fermions, with larger couplings resulting in heavier particles (top quark, bottom quark)

Consistency with Experimental Observations

  • The properties of the Higgs boson, such as its mass and couplings to other particles, have been measured and found to be consistent with the predictions of the Standard Model
  • The discovery of the Higgs boson and the measurements of its properties provide strong support for the Higgs mechanism and its role in the Standard Model
  • The consistency between the theoretical predictions and experimental observations strengthens the validity of the Standard Model as a description of particle physics at the fundamental level

Experimental Evidence for the Higgs Boson

Discovery at the Large Hadron Collider

  • The Higgs boson was discovered in 2012 by the ATLAS and CMS collaborations at the Large Hadron Collider (LHC) at CERN
  • The discovery was based on the observation of excess events in the decay channels predicted by the Standard Model, such as H → γγ (two photons) and H → ZZ* → 4l (four leptons)
  • The mass of the Higgs boson was measured to be approximately 125 GeV/c², which is consistent with the range predicted by the Standard Model

Measurements of Higgs Boson Properties

  • Subsequent measurements of the Higgs boson's properties, such as its spin, parity, and couplings to other particles, have been performed to test the predictions of the Standard Model
    • The Higgs boson has been found to have zero spin and positive parity, consistent with the Standard Model expectations
    • The couplings of the Higgs boson to other particles, such as the gauge bosons and fermions, have been measured and found to be in agreement with the Standard Model predictions within experimental uncertainties
  • These measurements provide further confirmation of the Higgs mechanism and its role in the Standard Model, as well as the consistency between theory and experiment

Ongoing and Future Experiments

  • Ongoing and future experiments at the LHC and other facilities aim to further study the properties of the Higgs boson and search for any deviations from the Standard Model predictions, which could hint at new physics beyond the Standard Model
  • Precision measurements of the Higgs boson's couplings to other particles can provide insights into the nature of the Higgs mechanism and potentially reveal any discrepancies with the Standard Model
  • The search for additional Higgs bosons, as predicted by some theories beyond the Standard Model (supersymmetry, two-Higgs-doublet models), is also an active area of research in particle physics experiments

Key Terms to Review (17)

Effective potential: Effective potential is a concept used in quantum field theory and classical mechanics to describe the potential energy landscape that incorporates both the actual potential and the effects of additional fields or degrees of freedom. It becomes particularly important when analyzing systems with spontaneous symmetry breaking, as it helps identify stable vacua and allows for the understanding of particle mass generation through mechanisms like the Higgs mechanism.
Electroweak unification: Electroweak unification is the theoretical framework that describes the unification of the electromagnetic force and the weak nuclear force into a single fundamental interaction. This concept is central to the Standard Model of particle physics, where it explains how these forces manifest at high energies and how they are related through the exchange of gauge bosons, specifically the photon and the W and Z bosons. The electroweak theory is essential for understanding particle interactions and is intimately connected to spontaneous symmetry breaking and the Higgs mechanism.
Gauge symmetry breaking: Gauge symmetry breaking refers to a phenomenon in quantum field theory where a system that is originally symmetric under certain transformations loses this symmetry due to the presence of a non-zero vacuum expectation value of some field. This process is crucial for explaining how particles acquire mass and plays a vital role in the Higgs mechanism, which underlies the Standard Model of particle physics.
Global Symmetry: Global symmetry refers to a type of symmetry in which the transformations act uniformly across all points in a space or field. This means that the physical laws governing a system remain unchanged under these transformations, leading to conserved quantities according to Noether's theorem. Global symmetries play a crucial role in understanding the fundamental forces and particles in nature, particularly in contexts involving conserved currents and spontaneous symmetry breaking.
Goldstone Bosons: Goldstone bosons are massless scalar particles that arise in quantum field theories when spontaneous symmetry breaking occurs. When a system exhibits spontaneous symmetry breaking, certain symmetries of the underlying theory are not reflected in the ground state, leading to the emergence of these massless excitations which signal the presence of broken symmetries.
Higgs boson: The Higgs boson is a fundamental particle associated with the Higgs field, which is crucial for explaining how particles acquire mass. Its discovery in 2012 confirmed the existence of this field, solidifying the standard model of particle physics and providing insights into the mechanisms behind mass generation in elementary particles.
Higgs mechanism: The Higgs mechanism is a process in particle physics that explains how particles acquire mass through spontaneous symmetry breaking in a quantum field. It introduces a scalar field, known as the Higgs field, which permeates all of space, and through interactions with this field, certain particles gain mass while others remain massless, providing an essential framework for understanding the mass of fundamental particles.
Lagrangian: The Lagrangian is a mathematical function that summarizes the dynamics of a physical system by representing the difference between kinetic and potential energy. It plays a central role in formulating physical laws, particularly in the context of classical mechanics, quantum mechanics, and field theories, acting as a bridge between the action principle and equations of motion.
Leonard Susskind: Leonard Susskind is a prominent theoretical physicist known for his work in quantum mechanics, string theory, and quantum field theory. He is one of the founding figures of the holographic principle, which connects concepts of gravity and quantum information, and has significantly contributed to understanding spontaneous symmetry breaking and the Higgs mechanism in particle physics.
LHC Discovery: The LHC Discovery refers to the groundbreaking detection of the Higgs boson at the Large Hadron Collider (LHC) in 2012, a particle that is essential to understanding the mechanism of mass generation in particle physics. This discovery confirmed the existence of the Higgs field, which is responsible for spontaneous symmetry breaking, allowing particles to acquire mass through their interactions with this field. The significance of this discovery extends beyond just identifying a particle; it also validates the Standard Model of particle physics and deepens our understanding of fundamental forces and particles.
Local Symmetry: Local symmetry refers to the property of a physical system where its laws remain invariant under transformations that can vary from point to point in space and time. This concept plays a crucial role in modern physics, particularly in formulating gauge theories, which describe fundamental interactions and lead to conserved quantities through symmetries. It is closely linked to the concepts of Noether's theorem and spontaneous symmetry breaking, highlighting how symmetries dictate the behavior of fields and particles in quantum field theory.
Mass generation: Mass generation refers to the process by which particles acquire mass through interactions with a scalar field, particularly in the context of spontaneous symmetry breaking. This phenomenon is a fundamental aspect of modern physics, leading to the explanation of how elementary particles like W and Z bosons gain mass while maintaining gauge invariance in the underlying theory. It also plays a crucial role in understanding the Higgs mechanism, which provides a mechanism for mass generation in the Standard Model of particle physics.
Particle collisions: Particle collisions refer to the interactions that occur when two or more particles collide at high energies, resulting in various outcomes, such as the production of new particles, scattering processes, or other transformations. These events are crucial for understanding fundamental forces and the behaviors of subatomic particles, particularly in the context of mechanisms like spontaneous symmetry breaking and the Higgs mechanism, where energy fluctuations can lead to significant changes in particle properties.
Peter Higgs: Peter Higgs is a British theoretical physicist best known for his contribution to the development of the Higgs mechanism, which explains how particles acquire mass through spontaneous symmetry breaking. His work laid the foundation for understanding the role of the Higgs boson in the Standard Model of particle physics, particularly in relation to mass generation and symmetry principles in quantum field theory.
Spontaneous Symmetry Breaking: Spontaneous symmetry breaking occurs when a system that is symmetric under a certain transformation chooses a specific configuration that does not exhibit that symmetry. This phenomenon is crucial in various fields, leading to the emergence of distinct states and particles, and it helps explain many physical processes, including mass generation and phase transitions.
Vacuum expectation value: The vacuum expectation value (VEV) is the average value of a field in its lowest energy state, or vacuum state. It plays a crucial role in many areas of quantum field theory, particularly in understanding how fields can have non-zero values even in the absence of particles, which leads to phenomena like spontaneous symmetry breaking and mass generation for particles.
W and Z bosons: W and Z bosons are fundamental particles that mediate the weak nuclear force, one of the four fundamental forces in nature. They are crucial in processes such as beta decay, where they facilitate the transformation of one type of subatomic particle into another. These bosons play a significant role in electroweak theory, which unifies electromagnetic and weak interactions, and are essential for understanding how particles interact in the context of non-Abelian gauge theories and spontaneous symmetry breaking.
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