⚛️Nuclear Physics Unit 12 – Particle Physics and the Standard Model

Fundamental Particles and Forces

• Fundamental particles are the building blocks of matter and cannot be broken down into smaller constituents
• Quarks and leptons are the two main categories of fundamental particles
  • Quarks combine to form composite particles called hadrons (protons, neutrons)
  • Leptons include electrons, muons, taus, and their corresponding neutrinos
• Four fundamental forces govern particle interactions: strong, weak, electromagnetic, and gravitational
• Particles that mediate the fundamental forces are called gauge bosons
  • Gluons mediate the strong force, W and Z bosons mediate the weak force, and photons mediate the electromagnetic force
• Higgs boson plays a crucial role in giving particles their mass through the Higgs mechanism
• Antimatter particles have the same mass but opposite charge and other quantum numbers compared to their matter counterparts (positron, antiproton)

Quantum Field Theory Basics

• Quantum Field Theory (QFT) is the mathematical framework that combines quantum mechanics and special relativity to describe particle physics
• Fields are fundamental entities in QFT, with particles being excitations of these fields
  • Each type of particle corresponds to a specific field (electron field, quark fields)
• Interactions between particles are described by the exchange of virtual particles, which are temporary fluctuations in the corresponding fields
• Feynman diagrams visually represent particle interactions and aid in calculating interaction probabilities
• Renormalization is a technique used in QFT to handle infinities that arise in calculations by redefining physical quantities at different energy scales
• Gauge theories, such as Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), are specific QFTs that describe the electromagnetic and strong interactions, respectively

The Standard Model Framework

• The Standard Model is a highly successful theory that describes three of the four fundamental forces (strong, weak, and electromagnetic) and classifies all known elementary particles
• Particles are organized into three generations, with each generation having similar properties but increasing masses
  • 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
• The Standard Model is based on the concept of gauge symmetries, which give rise to the fundamental forces
  • $SU(3)$ symmetry for the strong force, $SU(2) \times U(1)$ symmetry for the electroweak force
• Spontaneous symmetry breaking through the Higgs mechanism explains why the weak force has a short range while the electromagnetic force has an infinite range
• The Standard Model has been extensively tested and has made accurate predictions, such as the existence of the Higgs boson and the top quark before their experimental discovery

Particle Interactions and Feynman Diagrams

• Particle interactions involve the exchange of virtual particles, which are not directly observable but have measurable effects
• Feynman diagrams are pictorial representations of particle interactions, with each diagram corresponding to a specific mathematical expression
  • Particles are represented by lines, with fermions (quarks, leptons) having solid lines and bosons (gauge bosons) having wavy or curly lines
  • Vertices represent interaction points where particles are created, destroyed, or change type
• Feynman rules are a set of guidelines for translating Feynman diagrams into mathematical expressions to calculate interaction probabilities
• Higher-order Feynman diagrams involve more complex interactions and are typically less probable than lower-order diagrams
• Feynman diagrams are essential tools for making predictions and interpreting results in particle physics experiments
  • Example: the decay of a Higgs boson into two photons can be represented by a Feynman diagram with a Higgs boson line splitting into two photon lines

Symmetries and Conservation Laws

• Symmetries play a crucial role in particle physics, as they give rise to conservation laws and constrain possible interactions
• Noether's theorem states that every continuous symmetry corresponds to a conserved quantity
  • Translation symmetry in time leads to energy conservation
  • Translation symmetry in space leads to momentum conservation
  • Rotational symmetry leads to angular momentum conservation
• Gauge symmetries, such as $U(1)$, $SU(2)$, and $SU(3)$, are local symmetries that give rise to the fundamental forces and their corresponding gauge bosons
• Discrete symmetries include parity (P), charge conjugation (C), and time reversal (T)
  • CPT theorem states that the combined symmetry of C, P, and T is conserved in all interactions
• Conservation laws limit the possible decay modes and interaction channels for particles
  • Example: the decay of a neutral pion into two photons ($\pi^0 \rightarrow \gamma + \gamma$) is allowed, while its decay into a single photon is forbidden by energy and momentum conservation

Experimental Methods in Particle Physics

• Particle accelerators, such as the Large Hadron Collider (LHC), are used to study high-energy particle interactions by colliding beams of particles at near-light speeds
• Detectors, such as ATLAS and CMS at the LHC, are designed to track and measure the properties of particles produced in collisions
  • Tracking devices (silicon trackers) measure the trajectories of charged particles
  • Calorimeters measure the energy of particles by absorbing them and converting their energy into measurable signals
  • Muon chambers detect muons, which are the only charged particles that can penetrate through the calorimeters
• Event reconstruction involves combining data from various detector components to identify particles and their properties
• Statistical analysis is essential for interpreting experimental results and determining the significance of observations
  • Example: the discovery of the Higgs boson required a statistical significance of 5 sigma ($5\sigma$), corresponding to a probability of less than 1 in 3.5 million that the observed signal was due to a random fluctuation

Beyond the Standard Model

• Despite its success, the Standard Model is incomplete and does not account for several observed phenomena, such as neutrino oscillations, dark matter, and the matter-antimatter asymmetry in the universe
• Neutrino oscillations imply that neutrinos have non-zero masses, which are not predicted by the Standard Model
  • Extensions of the Standard Model, such as the seesaw mechanism, can explain the small neutrino masses
• Dark matter, which makes up a significant portion of the universe's mass, does not interact electromagnetically and cannot be explained by the Standard Model
  • Theories beyond the Standard Model, such as Supersymmetry (SUSY), propose new particles that could be dark matter candidates (neutralinos)
• The observed matter-antimatter asymmetry in the universe requires a greater degree of CP violation than what is predicted by the Standard Model
• Grand Unified Theories (GUTs) attempt to unify the strong, weak, and electromagnetic forces into a single force at high energies
  • Example: $SU(5)$ and $SO(10)$ GUTs predict the existence of new particles, such as leptoquarks and magnetic monopoles

Real-World Applications and Future Directions

• Particle physics has numerous real-world applications, ranging from medical imaging to energy production
  • Positron Emission Tomography (PET) scans use antiparticles (positrons) to create detailed 3D images of metabolic processes in the body
  • Proton therapy uses high-energy proton beams to precisely target and destroy cancer cells while minimizing damage to healthy tissue
• Accelerator-driven systems (ADS) are being developed for nuclear waste transmutation and energy production
  • ADS can convert long-lived radioactive waste into shorter-lived or stable isotopes, reducing the need for long-term storage
• Future particle accelerators, such as the proposed Future Circular Collider (FCC) and the International Linear Collider (ILC), will explore even higher energy frontiers and search for new physics beyond the Standard Model
• Precision measurements of rare processes, such as the muon g-2 experiment and the search for neutrinoless double beta decay, can provide indirect evidence for new physics and constrain theories beyond the Standard Model
• Advancements in detector technology, such as the development of high-granularity calorimeters and advanced tracking devices, will improve the sensitivity and resolution of future experiments
• Theoretical developments, such as the exploration of extra dimensions, string theory, and loop quantum gravity, may provide a more complete understanding of the fundamental laws of nature and potentially unify all four fundamental forces, including gravity