⚛️Particle Physics Unit 1 – Particle Physics: The Standard Model Intro

Key Concepts and Particles

• Fundamental particles are the building blocks of matter and cannot be broken down into smaller components
• Quarks are elementary particles that combine to form composite particles called hadrons (protons, neutrons)
  • There are six types of quarks: up, down, charm, strange, top, and bottom
  • Quarks have fractional electric charges and are subject to the strong nuclear force
• Leptons are elementary particles that are not composed of quarks and do not participate in the strong interaction (electrons, muons, tau particles)
  • Leptons have integer electric charges and are subject to the weak nuclear force
• Gauge bosons are force-carrying particles that mediate the fundamental interactions (photons, gluons, W and Z bosons)
• Higgs boson is a scalar particle that gives mass to other elementary particles through the Higgs mechanism
• Antimatter particles have the same mass but opposite charge and other quantum numbers compared to their matter counterparts (positrons, antiprotons)
• Neutrinos are electrically neutral, weakly interacting leptons that come in three flavors (electron, muon, tau) and have tiny masses

Fundamental Forces

• There are four fundamental forces in nature: strong nuclear force, weak nuclear force, electromagnetic force, and gravitational force
• Strong nuclear force is the strongest of the four forces and is responsible for binding quarks together to form hadrons and holding atomic nuclei together
  • Mediated by the exchange of gluons between quarks
  • Has a very short range, approximately the size of an atomic nucleus
• Weak nuclear force is responsible for radioactive decay and certain types of particle interactions
  • Mediated by the exchange of W and Z bosons
  • Has a very short range and is much weaker than the strong force
• Electromagnetic force is the combination of electric and magnetic forces, responsible for the interactions between charged particles
  • Mediated by the exchange of photons
  • Has an infinite range but decreases in strength with distance
• Gravitational force is the weakest of the four forces but has an infinite range
  • Described by the theory of general relativity
  • Not yet fully incorporated into the Standard Model

Quantum Field Theory Basics

• Quantum field theory (QFT) is the mathematical framework that combines quantum mechanics and special relativity to describe the behavior of subatomic particles and their interactions
• In QFT, particles are represented as excitations of underlying quantum fields that permeate all of spacetime
• Particle interactions are described by the exchange of virtual particles, which are temporary fluctuations in the quantum fields
• Feynman diagrams are pictorial representations of the mathematical expressions describing particle interactions in QFT
  • Particles are represented by lines, and vertices represent the points where particles interact
  • Internal lines represent virtual particles exchanged during the interaction
• Renormalization is a mathematical technique used to handle infinities that arise in QFT calculations
  • Infinities are absorbed into the definitions of physical quantities, such as mass and charge
• Gauge symmetries play a crucial role in QFT and dictate the form of particle interactions
  • Gauge theories describe the fundamental forces and their associated gauge bosons (photons, gluons, W and Z bosons)

Standard Model Structure

• The Standard Model is a gauge theory that describes three of the four fundamental forces (strong, weak, and electromagnetic) and their interactions with matter particles (quarks and leptons)
• Based on the symmetry group $SU(3) \times SU(2) \times U(1)$, which corresponds to the strong, weak, and electromagnetic interactions, respectively
• Quarks and leptons are arranged into three generations, each containing two quarks and two leptons
  • First generation: up quark, down quark, electron, electron neutrino
  • Second generation: charm quark, strange quark, muon, muon neutrino
  • Third generation: top quark, bottom quark, tau, tau neutrino
• Particles acquire mass through the Higgs mechanism, which involves the interaction of particles with the Higgs field
  • The Higgs boson is the excitation of the Higgs field
• The Standard Model has 19 free parameters that must be determined experimentally, such as particle masses and coupling constants
• The Standard Model is a highly successful theory, accurately predicting a wide range of phenomena and discovering new particles (W and Z bosons, top quark, Higgs boson)

Experimental Evidence

• Particle accelerators, such as the Large Hadron Collider (LHC), collide particles at high energies to study their interactions and search for new particles predicted by the Standard Model
• Bubble chambers and wire chambers are used to track the trajectories of charged particles produced in collisions
• Calorimeters measure the energy of particles by absorbing them and converting their energy into measurable signals
• The discovery of the W and Z bosons at CERN in 1983 provided strong evidence for the electroweak theory, which unifies the electromagnetic and weak interactions
• The top quark, the last quark predicted by the Standard Model, was discovered at Fermilab in 1995
• The tau neutrino, the last lepton predicted by the Standard Model, was discovered at Fermilab in 2000
• The Higgs boson, a crucial component of the Standard Model, was discovered at the LHC in 2012, confirming the existence of the Higgs mechanism

Limitations and Open Questions

• The Standard Model does not include a description of gravity, which is described by the theory of general relativity
  • Attempts to develop a quantum theory of gravity, such as string theory and loop quantum gravity, are ongoing areas of research
• The Standard Model does not explain the observed matter-antimatter asymmetry in the universe
  • The amount of CP violation in the Standard Model is insufficient to account for the dominance of matter over antimatter
• Dark matter, which makes up a significant portion of the universe's mass, is not explained by the Standard Model
  • Possible candidates for dark matter include weakly interacting massive particles (WIMPs) and axions
• The hierarchy problem refers to the vast difference between the weak scale and the Planck scale, which is the energy scale at which quantum gravitational effects become important
  • The Standard Model does not provide a natural explanation for this difference in scales
• The strong CP problem arises from the fact that the strong interaction does not seem to violate CP symmetry, despite the presence of a term in the QCD Lagrangian that would allow for such violation
  • The proposed solution involves the existence of a new particle called the axion
• Neutrino masses and oscillations are not explained by the original formulation of the Standard Model
  • Extensions to the Standard Model, such as the seesaw mechanism, have been proposed to account for non-zero neutrino masses

Real-World Applications

• Particle physics has led to the development of new technologies and applications in various fields
• Medical imaging techniques, such as positron emission tomography (PET) and proton therapy, rely on the understanding of particle interactions and detectors developed in particle physics research
• The World Wide Web was invented at CERN to facilitate the sharing of information among particle physicists worldwide
• Particle accelerators are used in materials science to study the structure and properties of materials at the atomic and subatomic levels
• The development of superconducting magnets for particle accelerators has led to advancements in magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) spectroscopy
• Particle physics has contributed to the development of advanced computing techniques, such as grid computing and machine learning, to handle the vast amounts of data generated by experiments
• The study of cosmic rays, high-energy particles originating from space, has led to a better understanding of astrophysical phenomena and the composition of the universe

Math and Calculations

• The Lagrangian formalism is used to describe the dynamics of particles and fields in the Standard Model
  • The Lagrangian is a function of the fields and their derivatives, and the principle of least action determines the equations of motion
• Feynman rules are a set of rules for translating Feynman diagrams into mathematical expressions that can be used to calculate the probability amplitudes for particle interactions
  • The rules specify how to assign factors to each element of the diagram (propagators, vertices, and external lines) and how to combine them
• Cross sections are a measure of the likelihood of a particular interaction occurring and are calculated using the probability amplitudes obtained from Feynman diagrams
  • Differential cross sections describe the angular distribution of the interaction products
• Decay rates and lifetimes of unstable particles are calculated using the Fermi golden rule, which relates the decay rate to the matrix element of the interaction and the density of final states
• Renormalization group equations describe how the coupling constants and masses of the theory change with the energy scale at which they are measured
  • The running of coupling constants is a key feature of the Standard Model and has been experimentally verified
• Symmetries and conservation laws play a crucial role in the Standard Model and constrain the possible interactions and decays of particles
  • Examples include the conservation of electric charge, baryon number, and lepton number
• The Cabibbo-Kobayashi-Maskawa (CKM) matrix describes the mixing of quark flavors in weak interactions and is parameterized by three mixing angles and one complex phase
  • The complex phase is responsible for the CP violation observed in the quark sector