Lecture 9 | New Revolutions in Particle Physics: Standard Model

Stanford

8 Jun 201095:34

EducationalLearning

32 Likes 10 Comments

TLDRThe video script delves into the intricacies of particle physics, focusing on the Higgs phenomenon and its pivotal role in assigning mass to various fundamental particles. It explains how gauge bosons, specifically the W and Z bosons, acquire mass through the Higgs field's shift from symmetry, contrasting with the massless photon. The lecture also explores the concept of the Higgs field, which interacts with particles that possess 'weak charge,' unlike ordinary electric charge. The script further elucidates the Lagrangian formulation, electrodynamics, and the significance of the Mexican hat potential in the context of the Higgs field. It also touches upon the Goldstone bosons and their transformation into the mass of gauge bosons, leading to the emergence of the Higgs bosons. The discussion extends to fermions, including electrons and quarks, and their association with the Higgs mechanism, emphasizing the importance of charge conservation and the role of the Dirac equation in understanding particle handedness. The script concludes with a reflection on the implications of the Higgs field for the properties of known particles and the potential for undiscovered particles with masses unrelated to the Higgs mechanism, hinting at the broader mysteries of the universe that remain to be explored.

Takeaways

🌟 The Higgs mechanism is responsible for giving masses to quarks and leptons, which are fundamental particles in the standard model of particle physics.
🔍 Gauge bosons, specifically the W and Z bosons, acquire mass through the Higgs field's shift from its most symmetric position, which is key to the Higgs phenomenon.
📐 Electrodynamics, while not directly discussed, shares mathematical similarities with the Higgs field's behavior, particularly in terms of Lagrangians and field tensors.
⚙️ The Higgs field's potential energy landscape, often described as a 'Mexican hat' potential, dictates that the field's minimum value is not at zero but at a non-zero value, leading to spontaneous symmetry breaking.
🎭 The Goldstone bosons, which are massless particles resulting from spontaneous symmetry breaking, are 'eaten' by the gauge bosons, giving them mass and removing the Goldstone bosons from the spectrum.
🧲 The Higgs field's radial oscillations, quantized as Higgs bosons, are massive and represent the energy cost of shifting the field away from its minimum.
🚀 The concept of mass in field theory is tied to the energy stored in a field when it is shifted homogeneously, which is indicative of the particle's inertia or resistance to acceleration.
🤔 The handedness of particles, such as electrons and neutrinos, plays a crucial role in weak interactions, with only left-handed particles interacting with W bosons.
🧬 Fermions, including electrons, muons, and quarks, receive their mass through the Higgs mechanism, which involves the spontaneous symmetry breaking and the interaction with the Higgs field.
🔬 The discovery of neutrino oscillations confirms that neutrinos have mass, which is accommodated in the standard model through the see-saw mechanism, involving left-handed neutrinos and right-handed antineutrinos.
🔬 The Higgs boson's mass is expected to be around the same order of magnitude as the W and Z bosons, and its detection would provide further evidence for the Higgs mechanism.

Q & A

What is the Higgs phenomenon and how does it relate to the masses of quarks and leptons?
-The Higgs phenomenon refers to the Higgs mechanism, which is responsible for giving masses to elementary particles such as quarks and leptons. It involves the interaction with the Higgs field, a scalar field throughout the universe, which causes these particles to acquire mass through spontaneous symmetry breaking.
Why are gauge bosons like the Z and W bosons massive, unlike the photon?
-Gauge bosons such as the Z and W bosons obtain mass through the Higgs mechanism, which involves the spontaneous symmetry breaking of the Higgs field. Unlike the photon, which remains massless because it does not interact with the Higgs field, the Z and W bosons do interact with the Higgs field, gaining mass as a result.
How does the Higgs field give mass to particles like the Z and W bosons?
-The Higgs field gives mass to particles by shifting away from the most symmetric position. This shift corresponds to a non-zero expectation value of the field, which leads to the spontaneous symmetry breaking. The interaction energy of the gauge bosons with this non-symmetric Higgs field is what gives them mass.
What is the role of the Higgs field in electrodynamics?
-In the context of electrodynamics, the Higgs field is not directly involved as the photon remains massless. However, the mathematics used to describe the Higgs mechanism is analogous to that of electrodynamics, with the Higgs field interacting with other gauge particles to give them mass.
How does the Higgs mechanism explain the mass of fermions like electrons and quarks?
-The Higgs mechanism explains the mass of fermions through the spontaneous symmetry breaking of the Higgs field. Fermions acquire mass by interacting with the Higgs field after symmetry breaking occurs. The strength of this interaction, characterized by the Yukawa coupling, determines the mass of the fermion.
What is the significance of the Higgs field's potential energy minimum value not being at zero?
-The significance is that the actual minimum value of the Higgs field's potential energy is not at zero but at a non-zero value, which represents a vacuum expectation value. This non-zero value indicates a spontaneous symmetry breaking, which is the key to the Higgs mechanism giving masses to particles.
What is the role of the Goldstone bosons in the Higgs mechanism?
-Goldstone bosons are massless particles that arise as a consequence of spontaneous symmetry breaking. However, in the Higgs mechanism, these Goldstone bosons are 'eaten' by the gauge bosons, giving them mass. The Goldstone bosons effectively disappear from the physical spectrum, and their would-be excitations contribute to the mass of the gauge bosons.
What is the connection between the Dirac equation and the handedness of particles?
-The Dirac equation describes fermions, which can have positive or negative energy and can have their spin aligned in various directions. The concept of 'handedness' refers to whether a particle's spin is aligned with or against its direction of motion. The Dirac equation allows for both left-handed and right-handed components, which can mix due to mass, and this handedness is crucial for understanding weak interactions.
Why are neutrinos in the standard model considered to be massless or have very small masses?
-In the standard model, neutrinos are considered massless or have very small masses because they only interact via the weak force, and their left-handed components do not couple to the Higgs field in the same way other fermions do. Recent evidence of neutrino oscillations, however, suggests that neutrinos do have mass, albeit very small, possibly through a mechanism beyond the standard model.
What is the importance of the Higgs boson in the context of the Higgs mechanism?
-The Higgs boson is a physical manifestation of the Higgs field. It is the fluctuation or excitation of the Higgs field around its non-zero vacuum expectation value. The discovery of the Higgs boson would confirm the Higgs mechanism as the source of mass for other particles and would be a significant milestone in particle physics.
How does the Higgs field give rise to the masses of W and Z bosons?
-The Higgs field interacts with the W and Z bosons through spontaneous symmetry breaking. The energy associated with the non-zero vacuum expectation value of the Higgs field provides mass to the W and Z bosons. The magnitude of this mass is proportional to the strength of the interaction between the bosons and the Higgs field.

Outlines

00:00

😀 Introduction to the Higgs Phenomenon

The paragraph begins with an overview of the Higgs phenomenon and its relation to the masses of quarks and leptons. It explains how gauge bosons, specifically the Z and W bosons, acquire mass through the Higgs field's shift from a symmetric position. The discussion uses electrodynamics as an analogy, highlighting the mathematics behind gauge bosons and the role of the Lagrangian in formulating the interaction between the electromagnetic field and the charge field. The Higgs field is introduced as a complex valued field, and its potential energy is described, particularly how it favors a non-zero value, leading to the mass of gauge bosons.

05:03

🧲 Higgs Field and Gauge Bosons Interaction

This section delves into the specifics of the Higgs field's interaction with gauge bosons. It discusses the dynamics of the Higgs field, represented by Phi, and how its covariant derivative leads to the Lagrangian for the field. The paragraph explores the concept of gauge transformation and how it relates to the Higgs field. It also touches on the idea that the Higgs field's energy minimum is not at zero, which is crucial for giving mass to gauge bosons.

10:03

🌀 The Higgs Mechanism and Mass of Particles

The paragraph explains the Higgs mechanism, which is responsible for giving mass to particles. It discusses how the shift in the Higgs field from zero gives mass to gauge bosons, which were initially considered massless. The text also explains the disappearance of the Goldstone boson and its role in giving mass to the gauge boson. The Higgs bosons are introduced as quanta of the Higgs field's oscillations, which are massive and have energy even at rest.

15:04

📐 Homogeneous Shifts and the Concept of Mass

This section explores the concept of mass in the context of field theory, emphasizing that mass is associated with energy stored in a field. It discusses how a uniform shift of a field does not create energy, implying that a photon is massless. The paragraph also provides examples from particle physics and field theory to illustrate the concept of mass, including the behavior of phonons in a crystal lattice and the shift of molecular positions.

20:05

🤔 Fermions and the Higgs Phenomenon

The paragraph discusses fermions, including electrons and muons, and how they acquire mass from the Higgs phenomenon through spontaneous symmetry breaking. It touches on experimental data about weak interactions and beta decay, highlighting the discovery that reflection symmetry is not a fundamental symmetry of nature. The discussion also includes the concept of particle 'handedness' and how it relates to the weak interactions.

25:08

🔄 Dirac Equation and Particle Handedness

The paragraph focuses on the Dirac equation and its connection to particle handedness. It explains the Dirac field's four components and how they correspond to different spin and energy states. The text also discusses how the mass term in the Dirac equation couples left-handed and right-handed components, and the implications of charge conservation on the possibility of a particle having mass.

30:08

🤲 Charge Conservation and the Higgs Field

This section explores the concept of charge conservation in relation to the Higgs field. It discusses how the Dirac equation can be altered to include a Higgs field without violating charge conservation. The paragraph introduces the idea of a coupling constant, which represents the strength of the interaction between particles and the Higgs field. It also touches on the possibility of the Higgs field being a source of mass for fermions.

35:09

🧬 Fermion Mass and the Higgs Field

The paragraph discusses how the Higgs field can give fermions mass through spontaneous symmetry breaking. It explains that the mass of a fermion is proportional to the product of a coupling constant and the Higgs field's shift parameter F. The text also explores the concept of Yukawa couplings and how they relate to the masses of different fermions, from electrons to top quarks.

40:12

🎭 Higgs Boson and Its Interaction with Fermions

This section delves into the properties of the Higgs boson and its interaction with fermions. It explains that the same coupling constant that determines the mass of fermions also governs the process of a fermion becoming a Higgs boson and another fermion. The paragraph discusses the importance of detecting the Higgs boson and studying its properties to confirm the theoretical models of particle interactions.

45:14

⚖️ Mass and the Standard Model

The paragraph discusses the role of the Higgs field in giving mass to all known particles in the standard model. It explains that without the Higgs field, these particles would be massless. The text also touches on the possibility of undiscovered particles with masses much larger than the Higgs field parameter F, and the implications for dark matter theories.

50:15

🤓 Neutrinos, Antiparticles, and the Higgs Mechanism

This section explores the properties of neutrinos and their interaction with the Higgs mechanism. It discusses the possibility of neutrinos being Majorana particles, which are their own antiparticles, and the implications for lepton number conservation. The paragraph also touches on the weak interactions of neutrinos and antineutrinos and how they differ in their interactions with the Z boson.

Mindmap

Keywords

💡Higgs Phenomenon

The Higgs phenomenon refers to the mechanism by which particles acquire mass. It involves the Higgs field, a field of energy that permeates all of space. When certain particles interact with this field, they gain mass. This concept is central to understanding how gauge bosons, fermions, and the recently discovered Higgs boson itself obtain mass, as discussed in the video.

💡Gauge Bosons

Gauge bosons are particles that mediate the fundamental forces in the standard model of particle physics. The video specifically mentions the W and Z bosons, which are responsible for the weak nuclear force. These particles obtain mass through their interaction with the Higgs field, a process explained in the context of the Higgs phenomenon.

💡Spontaneous Symmetry Breaking

Spontaneous symmetry breaking is a concept in physics where a system appears to violate a symmetry that is present in its underlying laws. In the context of the video, this is a key mechanism behind the Higgs phenomenon, where the Higgs field acquires a non-zero value, leading to the acquisition of mass by gauge bosons and fermions.

💡Lagrangian

In physics, the Lagrangian is a mathematical function that describes the dynamics of a system. It is used to derive the equations of motion. In the video, the Lagrangian is mentioned in the context of electrodynamics and is used to describe the energy of the electromagnetic field and later, how the Higgs field interacts with other particles.

💡Dirac Equation

The Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac. It describes the behavior of fermions, such as electrons, and predicts the existence of antimatter. In the video, the Dirac equation is discussed in relation to the properties of particles, including their mass and charge, and how these properties allow for the possibility of particles having different 'handedness'.

💡Yukawa Coupling

Yukawa coupling is a term in quantum field theory that describes the strength of the interaction between a fermion and a scalar boson, such as the Higgs boson. The video explains that the mass of a fermion is proportional to the Yukawa coupling constant times the vacuum expectation value (VEV) of the Higgs field, which is denoted by F in the transcript.

💡Higgs Field

The Higgs field is a scalar field that permeates the universe and is responsible for giving particles their mass. The video discusses the Higgs field in the context of the Higgs mechanism, explaining how its non-zero vacuum expectation value allows for the spontaneous symmetry breaking that leads to the acquisition of mass by particles.

💡Fermions

Fermions are particles that follow the principles of quantum mechanics and include all quarks and leptons, such as electrons, neutrinos, and protons. The video explains that fermions, like the electron, muon, and quarks, acquire mass through their interaction with the Higgs field, a process mediated by the Higgs mechanism.

💡Chirality

Chirality in particle physics refers to the handedness of particles, which is a property related to their spin and momentum. The video discusses how particles like electrons can be classified as left-handed or right-handed based on their spin direction relative to their motion. This concept is important for understanding the weak interactions of particles with the W and Z bosons.

💡Neutrinos

Neutrinos are nearly massless leptons that interact via the weak force. The video touches on the fact that while the standard model predicts neutrinos to be massless, experimental evidence from neutrino oscillations indicates that they have a very small mass. This discovery has implications for the understanding of the Higgs mechanism and the nature of mass in the universe.

💡Weak Interactions

Weak interactions, also known as weak nuclear force, are one of the four fundamental forces and are responsible for processes like beta decay. The video explains that weak interactions are mediated by W and Z bosons and are asymmetric, only involving left-handed particles, which is a key aspect of the Higgs mechanism and the generation of mass.

Highlights

The Higgs phenomenon is explained in relation to the masses of quarks and leptons, detailing how gauge bosons obtain mass from the Higgs field.

Electrodynamics is used as an analogy to describe the mathematics of gauge bosons, emphasizing the shift from a symmetric position for mass acquisition.

The Higgs field is introduced as a complex valued field that interacts with charged particles, specifically those with weak charges.

The Mexican hat potential is used to illustrate the energetics of the Higgs field, showing how the minimum value of potential energy is not at zero but at a non-zero field value.

The concept of massless Goldstone bosons and their role in the Higgs mechanism is discussed, leading to the absorption into massive gauge bosons.

The Higgs field's radial oscillations are quantified, revealing that these oscillations are massive and correspond to the Higgs bosons.

The relationship between mass and energy is explored, with mass being described as energy at rest from a field theory perspective.

The importance of the Higgs field in giving mass to gauge bosons and fermions through spontaneous symmetry breaking is emphasized.

The handedness of particles, specifically electrons and neutrinos, is discussed in the context of weak interactions and beta decay.

The Dirac equation is presented to explain the connection between fermions and their handedness, highlighting the role of mass in coupling left-handed and right-handed components.

The concept of Yukawa coupling is introduced to estimate the mass of fermions, showing a spectrum of different coupling constants for various fermions.

The potential existence of right-handed neutrinos in extended models beyond the standard model is mentioned, with their typically large mass.

Neutrino oscillations are discussed as evidence for neutrinos having mass, despite the standard model treating them as massless.

The role of the Higgs mechanism in providing fermions with mass is further explained through the interaction of right-handed fermions with Higgs particles.

The possibility of multiple Higgs bosons in more complicated theories beyond the standard model is briefly touched upon.

The expectation that the Higgs particle will have a mass of the same order of magnitude as the W and Z bosons is discussed.

The idea that all known particles in the standard model have masses proportional to the symmetry breaking parameter F is highlighted.

The potential for dark matter particles to have masses not originating from spontaneous symmetry breaking is explored.

Transcripts

Browse More Related Video

Lecture 8 | New Revolutions in Particle Physics: Standard Model

Lecture 7 | New Revolutions in Particle Physics: Standard Model

Electroweak Theory and the Origin of the Fundamental Forces

The Standard Model - Particle Physics Reactions Part 1/3 (High School Physics)

Lecture 10 | New Revolutions in Particle Physics: Standard Model

Lecture 6 | New Revolutions in Particle Physics: Standard Model

Related Tags

Higgs Phenomenon Particle Physics Stanford Lecture Mass of Quarks Leptons Gauge Bosons Spontaneous Symmetry Electrodynamics Quantum Mechanics Dirac Equation Cosmic Rays