“Elementary Particles” Lecture 4 Niels Tuning Harry van der Graaf Niels Tuning (1)
Thanks • Ik ben schatplichtig aan: – Dr. Ivo van Vulpen (UvA) – Prof. dr. ir. Bob van Eijk (UT) – Prof. dr. Marcel Merk (VU) Niels Tuning (2)
Plan Theory Detection and sensor techn. Quantum Quantum Forces Mechanics Field Theory Light Interactions Scintillators with Matter PM Accelerators Tipsy Bethe Bloch Medical Imag. Cyclotron Photo effect X-ray Compton, pair p. Proton therapy Bremstrahlung Experiments Cherenkov Fundamental Astrophysics Charged Particles Physics Cosmics ATLAS Particles Km3Net Grav Waves Si Neutrinos Virgo Gaseous Lisa Pixel … Special General Optics Gravity Relativity Relativity Laser Niels Tuning (3)
Plan Today Theory Detection and sensor techn. Niels 2) Niels 2) Niels 7) + 10) Quantum Quantum Forces Mechanics Field Theory 5) + 8) 4) Harry Particles 3) Harry Light RelativisticIn teractions 6) + 9) with Matter Ernst-Jan 1) Harry Martin 11) +12) Fundamental Accelerators 6) Ernst-Jan Martin Physics 13) + 14) Astrophysics Charged Excursions Particles Experiments 9) Ernst-Jan 1) Niels 9) Ernst-Jan 9) Ernst-Jan Special General Gravity Optics Relativity Relativity Niels Tuning (4)
Schedule 1) 11 Feb: Accelerators (Harry vd Graaf) + Special relativity (Niels Tuning) 2) 18 Feb: Quantum Mechanics (Niels Tuning) 3) 25 Feb: Interactions with Matter (Harry vd Graaf) 4) 3 Mar: Light detection (Harry vd Graaf) 5) 10 Mar: Particles and cosmics (Niels Tuning) 6) 17 Mar: Forces (Niels Tuning) 7) 24 Mar: Astrophysics and Dark Matter (Ernst-Jan Buis) break 8) 21 Apr: e + e - and ep scattering (Niels Tuning) 9) 28 Apr: Gravitational Waves (Ernst-Jan Buis) 10) 12 May: Higgs and big picture (Niels Tuning) 11) 19 May: Charged particle detection (Martin Franse) 12) 26 May: Applications: experiments and medical (Martin Franse) 13) 2 Jun: Nikhef excursie 14) 8 Jun: CERN excursie Niels Tuning (5)
Plan 1) Intro: Standard Model & Relativity 11 Feb 2) Basis 1900-1940 18 Feb 1) Atom model, strong and weak force 2) Scattering theory 3) Hadrons 1945-1965 10 Mar 1) Isospin, strangeness 2) Quark model, GIM 4) Standard Model 1965-1975 17 Mar 1) QED 2) Parity, neutrinos, weak inteaction 3) QCD 5) e + e - and DIS 1975-2000 21 Apr 6) Higgs and CKM 2000-2015 12 May Niels Tuning (6)
Homework 1) Homework for this and previous lecture 2) Hand in before 21 April
Outline for today: Interactions 1) Gauge invariance, and the Lagrangian 2) Electro-magnetic interaction QED § 3) Weak interaction Parity violation § 4) Strong interaction QCD § Niels Tuning (8)
Summary
Lecture 1: Standard Model & Relativity • Standard Model Lagrangian • Standard Model Particles Niels Tuning (10)
Lecture 1: Standard Model & Relativity • Theory of relativity – Lorentz transformations (“boost”) – Calculate energy in collissions • 4-vector calculus • High energies needed to make (new) particles Niels Tuning (11)
Lecture 2: Quantum Mechanics & Scattering • Schrödinger equation – Time-dependence of wave function • Klein-Gordon equation – Relativistic equation of motion of scalar particles Ø Dirac equation – Relativistically correct, and linear – Equation of motion for spin-1/2 particles – Prediction of anti-matter Niels Tuning (12)
Lecture 2: Quantum Mechanics & Scattering • Scattering Theory – (Relative) probability for certain process to happen – Cross section Scattering amplitude in Classic Quantum Field Theory • Fermi’s Golden Rule a → b + c – Decay: “decay width” Γ – Scattering: “cross section” σ a + b → c + d Niels Tuning (13)
Lecture 3: Quarkmodel & Isospin • “Partice Zoo” not elegant • Hadrons consist of quarks Ø Observed symmetries – Same mass of hadrons: isospin – Slow decay of K, Λ : strangeness – Fermi-Dirac statistics Δ ++ ,. Ω : color • Combining/decaying particles with (iso)spin – Clebsch-Gordan coefficients Niels Tuning (14)
Group theory 3 3 8 1 ⊗ = ⊕ • Mesons: – 2 quarks, with 3 possible flavours: u, d, s – 3 2 =9 possibilities = 8 + 1 q=1 Niels Tuning (15)
Group theory 3 3 8 1 ⊗ = ⊕ • Mesons: – 2 quarks, with 3 possible flavours: u, d, s – 3 2 =9 possibilities = 8 + 1 η ' Niels Tuning (16)
Group theory 3 3 3 10 8 8 1 ⊗ ⊗ = ⊕ ⊕ ⊕ S M M A • Baryons: – 3 quarks, with 3 possible flavours: u, d, s – 3 3 =27 possibilities = 10 + 8 + 8 + 1 ( ) ( ) 1 ↔ 2 2 ↔ 3 ψ ψ ψ sym anti − sym anti − sym Niels Tuning (17)
Group theory 3 3 3 10 8 8 1 ⊗ ⊗ = ⊕ ⊕ ⊕ S M M A • Baryons: – 3 quarks, with 3 possible flavours: u, d, s – 3 3 =27 possibilities = 10 + 8 + 8 + 1 ( ) ( ) 1 ↔ 2 2 ↔ 3 ψ ψ ψ sym anti − sym anti − sym Niels Tuning (18)
What did we learn about quarks Quarks: • Associate production, but long lifetime: strangeness • Many (degenerate) particles: isospin • Pauli exclusion principle: color • How they combine into hadrons: multiplets • How to add (iso)spin: Clebsch-Gordan Niels Tuning (19)
[LHCb, Phys. Rev. Lett. 115 (2015) 072001, arXiv:1507.03414] What is a Pentaquark? > 300 papers citing the result, with many possible interpretations. Niels Tuning (20) Patrick Koppenburg Pentaquarks at hadron colliders 18/01/2017 — Physics at Veldhoven [26 / 33]
Plan 1) Intro: Standard Model & Relativity 11 Feb 2) Basis 1900-1940 18 Feb 1) Atom model, strong and weak force 2) Scattering theory 3) Hadrons 1945-1965 10 Mar 1) Isospin, strangeness 2) Quark model, GIM 4) Standard Model 1965-1975 17 Mar 1) QED 2) Parity, neutrinos, weak inteaction 3) QCD 5) e + e - and DIS 1975-2000 21 Apr 6) Higgs and CKM 2000-2015 12 May Niels Tuning (21)
Model elementary particles Tools Cross section Detectors Kinematics Strong Atom Mesons force Particle Physics Accele - Theory of Quark rators Relativity Leptons Baryons model Quantum Group Quantum Conserva Standard mechanics Theory numbers tion Laws Model Particles Forces Quantum- field theory & Local gauge quarks/leptons Electromagnetic invariance Weak Strong
Lecture 4: Forces Niels Tuning (23)
Electro-Magnetism
Electro-magnetism § Towards a particle interacting with photon Quantum Electro Dynamics, QED § Ø Start with electric and magnetic fields J.C. Maxwell
Start: Classical electro-magnetism Maxwell equations � � � � � B ∂ E ∇ E ∇ × = − ⋅ = ρ t ∂ � � � � � � E ∂ ∇ B 0 B j ⋅ = ∇ × = + t ∂ • We wish to work relativistically • Can we formulate this in Lorentz covariant form? Scalar potential also called φ : � � ( , A ) A ( V , A ) µ Ø Introduce a mathematical tool : φ =
Start: Classical electro-magnetism Maxwell equations � � � � � B ∂ E ∇ E ∇ × = − ⋅ = ρ t ∂ � � � � � � E ∂ ∇ B 0 B j ⋅ = ∇ × = + t ∂ • We wish to work relativistically • Can we formulate this in Lorentz covariant form? Scalar potential also called φ : � � ( , A ) A ( V , A ) µ • Introduce a mathematical tool : φ = � � E , B are physical, A is not! µ • Note: � � � B A Ø Choose: = ∇ × � � � A ∂ E = − − ∇ ϕ t ∂
Start: Classical electro-magnetism Maxwell equations � � � � � B ∂ E ∇ E ∇ × = − ⋅ = ρ t ∂ � � � � � � E ∂ ∇ B 0 B j ⋅ = ∇ × = + t ∂ • We wish to work relativistically • Can we formulate this in Lorentz covariant form? Scalar potential also called φ : � � ( , A ) A ( V , A ) µ • Introduce a mathematical tool : φ = � � E , B are physical, A is not! µ • Note: � � � � � B A Ø Choose: Then automatically : = ∇ × B 0 ∇ ⋅ = � � � � � � A B ∂ ∂ E E = − − ∇ ϕ ∇ × = − t t ∂ ∂
Rewrite Maxwell Maxwell equations � � � � � B ∂ E ∇ E ∇ × = − ⋅ = ρ t ∂ � � � � � � E ∂ ∇ B 0 B j ⋅ = ∇ × = + t ∂ • Maxwell eqs. can then be written quite economically …: � � � � A A j B A µ ν ν µ ν = ∇ × ∂ ∂ − ∂ ∂ = ν = j ( , j ) µ µ ρ � � � A ∂ E = − − ∇ ϕ t ∂
Rewrite Maxwell Maxwell equations � � � � � B ∂ E ∇ E ∇ × = − ⋅ = ρ t ∂ � � � � � � E ∂ ∇ B 0 B j ⋅ = ∇ × = + t ∂ • Maxwell eqs. can then be written quite economically …: � � � µ A ν ν A µ j ν � B A ∂ ∂ − ∂ ∂ = = ∇ × ν = j ( , j ) µ µ ρ � � � A or even : F µ ν j ν ∂ = ∂ E µ = − − ∇ ϕ t ∂ with : F µ ν µ ν ν µ ≡ ∂ Λ − ∂ Λ Ø Electromagnetic tensor Unification of electromagnetism
Gauge Invariance
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