10.1 Electroweak theory and the Glashow-Weinberg-Salam model
4 min read•august 14, 2024
unifies electromagnetic and weak interactions, treating them as aspects of a single force. It introduces the , predicting four gauge bosons: the photon, W^+, W^-, and Z^0.
The realizes this theory, explaining how particles gain mass through the . It accurately predicted the W and , discovered in 1983, and the , found in 2012.
Electroweak Theory Unification
Unification of Electromagnetic and Weak Interactions
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- Electroweak theory provides a unified description of electromagnetic and weak interactions, two fundamental forces of nature
- Treats electromagnetic and weak interactions as two aspects of a single, more fundamental electroweak interaction
- Unification achieved through the introduction of a non-Abelian , the SU(2)_L × U(1)_Y symmetry
- SU(2)_L represents the weak isospin symmetry
- U(1)_Y represents the weak hypercharge symmetry
- Predicts the existence of four gauge bosons: photon (γ) for electromagnetic interaction, and W^+, W^-, and Z^0 bosons for weak interaction
Spontaneous Symmetry Breaking and the Higgs Mechanism
- Electroweak symmetry is spontaneously broken through the Higgs mechanism
- Higgs mechanism gives rise to the masses of the W and Z bosons while keeping the photon massless
- Introduces a scalar field, the Higgs field, which has a non-zero vacuum expectation value
- Interaction of gauge bosons with the Higgs field generates their masses
- Higgs mechanism also gives rise to a new scalar particle, the Higgs boson, which was discovered at the LHC in 2012
Gauge Symmetries in Electroweak Model
SU(2)_L × U(1)_Y Gauge Symmetry
- Glashow-Weinberg-Salam (GWS) model is a specific realization of the electroweak theory
- Based on the SU(2)_L × U(1)_Y gauge symmetry, which describes the electroweak interaction
- SU(2)_L symmetry is associated with the weak isospin, a quantum number that distinguishes between left-handed and right-handed fermions
- Only left-handed fermions and right-handed antifermions participate in weak interactions
- U(1)_Y symmetry is associated with the weak hypercharge, a quantum number related to the electric charge and the third component of weak isospin
Gauge Fields and Electroweak Bosons
- Requirement of local gauge invariance under the SU(2)_L × U(1)_Y symmetry leads to the introduction of four gauge fields
- W^1, W^2, W^3 (associated with SU(2)_L)
- B (associated with U(1)_Y)
- These gauge fields give rise to the four electroweak gauge bosons after symmetry breaking
- W^+, W^- bosons: linear combinations of W^1 and W^2
- Z^0 boson: linear combination of W^3 and B
- Photon (γ): orthogonal combination of W^3 and B
- Gauge symmetries determine the interactions between particles and ensure the theory's renormalizability
Electroweak Theory Predictions and Confirmations
Discovery of W and Z Bosons
- Electroweak theory predicts the existence of W^+, W^-, and Z^0 bosons
- Discovered in 1983 at the Super Proton Synchrotron (SPS) at CERN
- Measured masses and decay properties agree with the predictions of the electroweak theory
- W boson mass: approximately 80.4 GeV/c^2
- Z boson mass: approximately 91.2 GeV/c^2
Neutral Current Interactions and Parity Violation
- Predicts the existence of neutral current interactions mediated by the Z^0 boson
- First observed in neutrino scattering experiments in 1973 at the Gargamelle bubble chamber at CERN
- Correctly describes the parity violation in weak interactions
- Observed in various experiments such as the Wu experiment (1956) and the Goldhaber experiment (1958)
- couple to left-handed fermions and right-handed antifermions, leading to parity violation
Discovery of the Higgs Boson
- Predicts the existence of the Higgs boson, a scalar particle responsible for and the generation of particle masses
- Higgs boson was discovered at the Large Hadron Collider (LHC) in 2012
- Measured properties consistent with the theory's predictions
- Mass: approximately 125 GeV/c^2
- Spin: 0
- Parity: even
- Discovery of the Higgs boson completes the particle content of the and provides strong support for the electroweak theory
Properties of W and Z Bosons
Masses and Electric Charges
- W and Z bosons are the massive gauge bosons of the weak interaction
- W bosons (W^+ and W^-) are charged, with electric charges of +1 and -1, respectively
- Mass: approximately 80.4 GeV/c^2
- Z boson (Z^0) is electrically neutral
- Mass: approximately 91.2 GeV/c^2
- Masses of W and Z bosons arise from their interaction with the Higgs field through the Higgs mechanism
Weak Interactions and Parity Violation
- W bosons mediate the charged current weak interactions
- Responsible for processes such as beta decay and nuclear fusion in the Sun
- Couple to left-handed fermions and right-handed antifermions, leading to parity violation
- Z boson mediates the neutral current weak interactions
- Involves the exchange of a Z boson between fermions
- Couples to both left-handed and right-handed fermions
- Interactions of W and Z bosons with fermions are described by the weak coupling constant, related to the Fermi coupling constant G_F
Spin, Antiparticles, and Decay Properties
- W and Z bosons have spin 1 and are their own antiparticles
- Finite lifetime and decay into fermion-antifermion pairs
- W bosons decay into a charged lepton and a neutrino, or a quark-antiquark pair
- Z boson decays into a fermion-antifermion pair (leptons or quarks)
- Decay widths and branching ratios of W and Z bosons have been precisely measured and agree with the predictions of the electroweak theory
- W boson decay width: approximately 2.1 GeV
- Z boson decay width: approximately 2.5 GeV
Key Terms to Review (21)
Abdus Salam: Abdus Salam was a Pakistani theoretical physicist who made significant contributions to the field of particle physics and cosmology. He is best known for his role in the development of the electroweak theory, which unifies the electromagnetic force and weak nuclear force, forming a cornerstone of the Glashow-Weinberg-Salam model, pivotal for our understanding of fundamental interactions in nature.
Electromagnetism: Electromagnetism is a fundamental interaction in nature that describes the forces between electrically charged particles and the behavior of electromagnetic fields. This interaction is crucial for understanding a wide range of physical phenomena, including how light behaves and how electric charges interact. The principles of electromagnetism also play a significant role in particle physics, particularly in the context of discrete symmetries and unification of forces.
Electroweak Theory: Electroweak theory is a unified framework that describes the electromagnetic force and the weak nuclear force as two different aspects of a single fundamental interaction. This groundbreaking theory, developed by Sheldon Glashow, Abdus Salam, and Steven Weinberg, shows how these forces are interconnected and provides a foundation for understanding particle interactions at high energies, leading to the development of the Glashow-Weinberg-Salam model.
Feynman diagrams: Feynman diagrams are pictorial representations of the interactions between particles in quantum field theory. They simplify complex calculations in particle physics by visually depicting the paths and interactions of particles, facilitating the understanding of processes like scattering and decay.
Gauge symmetry: Gauge symmetry is a fundamental concept in physics that refers to the invariance of a system under local transformations of certain fields. It plays a crucial role in the formulation of physical theories, particularly in defining interactions between particles and fields without changing the observable outcomes. This principle helps unify forces and leads to the conservation laws that govern particle interactions and their dynamics.
Glashow-Weinberg-Salam Model: The Glashow-Weinberg-Salam Model is a unified theory of the weak and electromagnetic interactions, which are two of the four fundamental forces in nature. This model forms the backbone of electroweak theory, showing that these forces are manifestations of a single underlying force at high energy levels. It successfully describes how particles interact through the exchange of gauge bosons, specifically the W and Z bosons, and establishes the mechanism of electroweak symmetry breaking through the Higgs field.
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 boson discovery: The Higgs boson discovery refers to the detection of a fundamental particle that confirms the existence of the Higgs field, a key component of the Standard Model of particle physics. This particle, associated with the mechanism that gives mass to other particles, was discovered at CERN's Large Hadron Collider in 2012, providing crucial evidence for electroweak theory and enhancing our understanding of the Glashow-Weinberg-Salam model.
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.
Lep experiments: LEP (Large Electron-Positron Collider) experiments refer to a series of high-energy physics experiments conducted at CERN from 1980 to 2000, focusing on electron-positron collisions. These experiments played a crucial role in studying the properties of the weak force and the electromagnetic force, providing insights that supported the electroweak theory and the Glashow-Weinberg-Salam model. By producing large amounts of data on particle interactions, LEP experiments helped refine our understanding of fundamental particles and their interactions.
Quantum Chromodynamics: Quantum Chromodynamics (QCD) is the theory that describes the strong interaction, one of the four fundamental forces in nature, which binds quarks together to form protons, neutrons, and other hadrons. QCD is a non-Abelian gauge theory based on the symmetry group SU(3), which accounts for the interactions of color charge carried by quarks and gluons.
Sheldon Glashow: Sheldon Glashow is a theoretical physicist known for his pivotal contributions to the development of the electroweak theory, which unifies the electromagnetic force and weak nuclear force. His work, along with that of Abdus Salam and Steven Weinberg, led to the formulation of the Glashow-Weinberg-Salam model, a cornerstone of the Standard Model of particle physics that describes how these forces interact through gauge bosons.
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.
Standard Model: The Standard Model is a theoretical framework in particle physics that describes the fundamental particles and their interactions, unifying electromagnetic, weak, and strong forces. It includes various particles such as quarks, leptons, and gauge bosons, showcasing how they interact via fundamental forces mediated by exchange particles. This model is essential for understanding the electroweak force, mass generation through the Higgs mechanism, and the strong interaction in Quantum Chromodynamics.
Steven Weinberg: Steven Weinberg was a prominent theoretical physicist whose work significantly advanced the understanding of fundamental forces in nature, particularly through his contributions to the development of quantum field theory and electroweak unification. His groundbreaking research laid the groundwork for the Glashow-Weinberg-Salam model, which describes the unification of electromagnetic and weak interactions, and he was instrumental in the formulation of effective field theories, which provide a framework for understanding physical phenomena at different energy scales.
Su(2)_l × u(1)_y symmetry: The su(2)_l × u(1)_y symmetry is a gauge symmetry that underpins the electroweak interaction, combining weak isospin (su(2)_l) and weak hypercharge (u(1)_y) to describe how particles interact via the weak force and electromagnetism. This symmetry is a cornerstone of the Glashow-Weinberg-Salam model, which unifies these two fundamental forces into a single framework. It allows for the unification of the electromagnetic force and the weak nuclear force, giving rise to phenomena such as the production of W and Z bosons, which mediate weak interactions and are responsible for processes like beta decay in nuclear physics.
Unification of forces: The unification of forces refers to the theoretical framework in physics where different fundamental forces, specifically the electromagnetic force and the weak nuclear force, are described as manifestations of a single underlying force. This concept aims to simplify our understanding of the universe by showing that what appear as distinct forces at low energies become unified at high energies, leading to groundbreaking models that explain particle interactions.
W bosons: W bosons are elementary particles that mediate the weak nuclear force, one of the four fundamental forces of nature. They are responsible for processes such as beta decay in radioactive materials and play a crucial role in the electroweak interaction, which unifies the electromagnetic force and weak nuclear force within the framework of modern particle physics.
Weak Nuclear Force: The weak nuclear force is one of the four fundamental forces of nature responsible for mediating processes like beta decay in atomic nuclei. This force plays a crucial role in the behavior of subatomic particles, particularly in changing one type of particle into another, which is essential for processes such as nuclear fusion in stars and the overall stability of matter.
Z bosons: Z bosons are elementary particles that mediate the weak nuclear force, one of the four fundamental forces in nature. They are neutral gauge bosons associated with the electroweak interaction, which unifies electromagnetic and weak forces, playing a crucial role in processes like beta decay and particle interactions involving neutrinos.