Elementary Particles Lecture 4 Niels Tuning Harry van der Graaf - - PowerPoint PPT Presentation

Niels Tuning (1)

“Elementary Particles” Lecture 4

Niels Tuning Harry van der Graaf

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

Niels Tuning (3)

Fundamental Physics Astrophysics

Cosmics Grav Waves Neutrinos

Quantum Mechanics Special Relativity General Relativity

Forces Particles Gravity

Interactions with Matter

Bethe Bloch Photo effect Compton, pair p. Bremstrahlung Cherenkov

Light

Scintillators PM Tipsy Medical Imag.

Charged Particles

Si Gaseous Pixel

Optics

Laser

Experiments

ATLAS Km3Net Virgo Lisa …

Detection and sensor techn. Theory

Quantum Field Theory Accelerators

Cyclotron X-ray Proton therapy

Plan

Niels Tuning (4)

Fundamental Physics 6) Ernst-Jan Astrophysics 2) Niels Quantum Mechanics 1) Niels Special Relativity 9) Ernst-Jan General Relativity

Niels 7) + 10) Forces 5) + 8) Particles 9) Ernst-Jan Gravity

3) Harry RelativisticIn teractions with Matter 4) Harry Light 11) +12) Martin Charged Particles

9) Ernst-Jan

Optics 6) + 9) Ernst-Jan Martin 13) + 14) Excursions Experiments

Detection and sensor techn. Theory

2) Niels Quantum Field Theory 1) Harry Accelerators

Today

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

Schedule

Niels Tuning (5)

Plan

1) Intro: Standard Model & Relativity 2) Basis

1) Atom model, strong and weak force 2) Scattering theory

3) Hadrons

1) Isospin, strangeness 2) Quark model, GIM

4) Standard Model

1) QED 2) Parity, neutrinos, weak inteaction 3) QCD

5) e+e- and DIS 6) Higgs and CKM

Niels Tuning (6)

1900-1940 1945-1965 1965-1975 1975-2000 2000-2015 18 Feb 10 Mar 17 Mar 21 Apr 12 May 11 Feb

Homework

1) Homework for this and previous lecture 2) Hand in before 21 April

1) Gauge invariance, and the Lagrangian 2) Electro-magnetic interaction

§ QED

3) Weak interaction

§ Parity violation

4) Strong interaction

§ QCD

Outline for today: Interactions

Niels Tuning (8)

Summary

• Standard Model Lagrangian
• Standard Model Particles

Lecture 1: Standard Model & Relativity

Niels Tuning (10)

• Theory of relativity

– Lorentz transformations (“boost”) – Calculate energy in collissions

• 4-vector calculus
• High energies needed to make (new) particles

Lecture 1: Standard Model & Relativity

Niels Tuning (11)

• 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

Lecture 2: Quantum Mechanics & Scattering

Niels Tuning (12)

• Scattering Theory

– (Relative) probability for certain process to happen – Cross section

• Fermi’s Golden Rule

– Decay: “decay width” Γ – Scattering: “cross section” σ

Lecture 2: Quantum Mechanics & Scattering

Niels Tuning (13)

Classic Scattering amplitude in Quantum Field Theory

a → b + c a + b → c + d

• “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

Lecture 3: Quarkmodel & Isospin

Niels Tuning (14)

• Mesons:

– 2 quarks, with 3 possible flavours: u, d, s – 32 =9 possibilities = 8 + 1

Group theory

Niels Tuning (15)

q=1

1 8 3 3 ⊕ = ⊗

• Mesons:

– 2 quarks, with 3 possible flavours: u, d, s – 32 =9 possibilities = 8 + 1

Group theory

Niels Tuning (16)

1 8 3 3 ⊕ = ⊗

η'

• Baryons:

– 3 quarks, with 3 possible flavours: u, d, s – 33 =27 possibilities = 10 + 8 + 8 + 1

Group theory

Niels Tuning (17)

A M M S

1 8 8 10 3 3 3 ⊕ ⊕ ⊕ = ⊗ ⊗

sym

ψ

( )

2 1↔

−sym anti

ψ

( )

3 2 ↔

−sym anti

ψ

• Baryons:

– 3 quarks, with 3 possible flavours: u, d, s – 33 =27 possibilities = 10 + 8 + 8 + 1

Group theory

Niels Tuning (18)

sym

ψ

( )

2 1↔

−sym anti

ψ

( )

3 2 ↔

−sym anti

ψ

A M M S

1 8 8 10 3 3 3 ⊕ ⊕ ⊕ = ⊗ ⊗

Quarks:

• Associate production, but long lifetime: strangeness
• Many (degenerate) particles:

isospin

• Pauli exclusion principle:

color

What did we learn about quarks

Niels Tuning (19)

• How they combine into hadrons:

multiplets

• How to add (iso)spin:

Clebsch-Gordan

Niels Tuning (20)

What is a Pentaquark?

[LHCb, Phys. Rev. Lett. 115 (2015) 072001, arXiv:1507.03414]

>300 papers citing the result, with many possible interpretations.

Patrick Koppenburg Pentaquarks at hadron colliders 18/01/2017 — Physics at Veldhoven [26 / 33]

Plan

1) Intro: Standard Model & Relativity 2) Basis

1) Atom model, strong and weak force 2) Scattering theory

3) Hadrons

1) Isospin, strangeness 2) Quark model, GIM

4) Standard Model

1) QED 2) Parity, neutrinos, weak inteaction 3) QCD

5) e+e- and DIS 6) Higgs and CKM

Niels Tuning (21)

1900-1940 1945-1965 1965-1975 1975-2000 2000-2015 18 Feb 10 Mar 17 Mar 21 Apr 12 May 11 Feb

Particle Physics

Cross section Kinematics Theory of Relativity Group Theory Quantum mechanics Accele - rators Detectors

Tools Model elementary particles

Atom

Strong force Mesons Baryons Quark model Leptons Quantum numbers Conserva tion Laws Standard Model

Particles Forces

quarks/leptons Electromagnetic Weak Strong Quantum- field theory & Local gauge invariance

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

Maxwell equations

Start: Classical electro-magnetism

ρ = ⋅ ∇ E

• =

⋅ ∇ B

• t

B E ∂ ∂ − = × ∇

• j

t E B

• +

∂ ∂ = × ∇

• We wish to work relativistically
• Can we formulate this in Lorentz covariant form?

Ø Introduce a mathematical tool:

) , ( A V A

• =

µ

) , ( A

• φ

Scalar potential also called φ:

Start: Classical electro-magnetism

ρ = ⋅ ∇ E

• =

⋅ ∇ B

• t

B E ∂ ∂ − = × ∇

• j

t E B

• +

∂ ∂ = × ∇

• We wish to work relativistically
• Can we formulate this in Lorentz covariant form?
• Introduce a mathematical tool:
• Note:

Ø Choose:

) , ( A V A

• =

µ

) , ( A

• φ

Scalar potential also called φ:

not! is physical, are ,

µ

A B E

• ϕ

∇ − ∂ ∂ − = × ∇ =

• t

A E A B

Maxwell equations

Start: Classical electro-magnetism

ρ = ⋅ ∇ E

• =

⋅ ∇ B

• t

B E ∂ ∂ − = × ∇

• j

t E B

• +

∂ ∂ = × ∇

• We wish to work relativistically
• Can we formulate this in Lorentz covariant form?
• Introduce a mathematical tool:
• Note:

Ø Choose: Then automatically:

) , ( A V A

• =

µ

) , ( A

• φ

Scalar potential also called φ:

not! is physical, are ,

µ

A B E

• ϕ

∇ − ∂ ∂ − = × ∇ =

• t

A E A B

t B E B ∂ ∂ − = × ∇ = ⋅ ∇

• Maxwell equations

Rewrite Maxwell

ρ = ⋅ ∇ E

• =

⋅ ∇ B

• t

B E ∂ ∂ − = × ∇

• j

t E B

• +

∂ ∂ = × ∇

• Maxwell eqs. can then be written quite economically…:

ϕ ∇ − ∂ ∂ − = × ∇ =

• t

A E A B

ν µ µ ν ν µ µ

j A A = ∂ ∂ − ∂ ∂

) , ( j j

• ρ

ν =

Maxwell equations

Rewrite Maxwell

ρ = ⋅ ∇ E

• =

⋅ ∇ B

• t

B E ∂ ∂ − = × ∇

• j

t E B

• +

∂ ∂ = × ∇

• Maxwell eqs. can then be written quite economically…:

ϕ ∇ − ∂ ∂ − = × ∇ =

• t

A E A B

µ ν ν µ µν ν µν µ ν µ µ ν ν µ µ

Λ ∂ − Λ ∂ ≡ = ∂ = ∂ ∂ − ∂ ∂ F j F j A A : with : even

• r

) , ( j j

• ρ

ν =

Maxwell equations

Ø Electromagnetic tensor Unification of electromagnetism

Gauge Invariance

Gauge invariance: Classical

ρ = ⋅ ∇ E

• =

⋅ ∇ B

• t

B E ∂ ∂ − = × ∇

• j

t E B

• +

∂ ∂ = × ∇

A = Vector potential

ϕ = Scalar potential

Physical Fields: Potentials:

φ ∇ − ∂ ∂ − =

• t

A E

A B

• ×

∇ =

Invariant under: Gauge transformations

Maxwell invariant à gauge symmetry

t ∂ Λ ∂ − = → φ φ φ '

Λ ∇ + = →

• A

A A '

) , ( t r

• Λ

= Λ Maxwell equations

Gauge invariance: Classical

ρ = ⋅ ∇ E

• =

⋅ ∇ B

• t

B E ∂ ∂ − = × ∇

• j

t E B

• +

∂ ∂ = × ∇

A = Vector potential

ϕ = Scalar potential

Physical Fields: Potentials:

φ ∇ − ∂ ∂ − =

• t

A E

A B

• ×

∇ =

Invariant under: Gauge transformations

Maxwell invariant à gauge symmetry

Λ ∂ + = →

µ µ µ µ

A A A

) , ( t r

• Λ

= Λ Maxwell equations

Not unique! Can choose extra constraints:

Coulomb-gauge: Lorenz-gauge:

Advantage: Lorentz-invariant

= ⋅ ∇ A

• =

∂ ∂ − ⋅ ∇ t A ϕ

Not unique! Can choose extra constraints:

Coulomb-gauge: Lorenz-gauge:

Advantage: Lorentz-invariant Lorenz Lorentz

Total confusion: Lorentz-Lorenz formula

= ⋅ ∇ A

• =

∂ ∂ − ⋅ ∇ t A ϕ

• (Ludvig)

(Hendrik)

Gauge invariance : QM

Charged particle moving in electro-magnetic field: Original Theory gauge invariant: (same physics with A, φ as with A’, φ’) ? A,φ

( )

x x x x

qA mv v L q L p B v E q F A v q qV mv L + = ∂ ∂ = ∂ ∂ = ⇒ × + = ⋅ + − =

• :

indeed Then 2 1 : Try

2

Schrödinger eq. Pauli eq. (spin-1/2 in EM-field) Classically: p p - qA

Rewrite and

Wave equation (A,φ)

Theory gauge invariant: (same physics with A, φ as with A’, φ’) ??

Rewrite and

Wave equation (A,φ) Wave equation (A’,φ’)

Yes! If

Theory gauge invariant: (same physics with A, φ as with A’, φ’) ??

Schrödinger equation (time-independent): Global phase: Ψ’ stays solution of Schrödinger eq!

Local gauge symmetry

Schrödinger equation (time-independent): Global phase: Ψ’ stays solution of Schrödinger eq! Local phase: Ψ’ solution of Schrödinger eq?

Local gauge symmetry

Schrödinger equation (time-independent): Global phase: Ψ’ stays solution of Schrodinger eq! Local phase: Ψ’ solution of Schrodinger eq?

Ø (How) can you keep the Schrödinger equation invariant ?

Local gauge symmetry

No:

Before going to Quantum Field Theory, lets remind ourselves of the Lagrange formalism

Lagrangian

• Euler-Lagrange equations:
• Least-action, or Hamilton’s principle:

Euler-Lagrange

Niels Tuning (44)

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ = ∂ ∂ q L dt d q L

• V

T L V T H − = + =

) , (

2 1

= ∂ = ∂

∫

t t

q q dtL S

pendulum 2) Euler-Lagrange vergelijking

Equation of motion

1) Lagrangiaan

Lagrangian and Equation of motion: Example

q: generalized coordinates

• Replace Lagrangian by a Lagrangian density

in terms of field φ(x):

• Least-action principle:
• Euler-Lagrange equations:

Lagrangian in Field Theory

Niels Tuning (46)

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ = ∂ ∂ q L dt d q L

• (classic)

• spin-0 particles (Klein-Gordon)
• spin-1/2 fermions (Dirac)
• Photons

Lagrangian è Equation of motion

Niels Tuning (47)

Klein-Gordon equation Dirac equation Maxwell equations

QED

Schrödinger equation (time-independent): Global phase: Ψ’ stays solution of Schrödinger eq! Local phase: Ψ’ solution of Schrödinger eq?

Ø (How) can you keep the Schrödinger equation invariant ?

Local gauge symmetry

No:

• Quantum Mechanics:

– Expectation value: – Observation is invariant under transformation:

• But what happens to the Lagrangian density, ?

– Depends also on derivative..., so:

Phase Invariance

Niels Tuning (50)

• Quantum Mechanics:

– Expectation value: – Observation is invariant under transformation:

• But what happens to the Lagrangian density, ?

– Depends also on derivative..., so:

Ø Replace by “gauge-covariant derivative”:

Phase Invariance

Niels Tuning (51)

• Quantum Mechanics:

– Expectation value: – Observation is invariant under transformation:

• But what happens to the Lagrangian density, ?

– Depends also on derivative..., so:

Ø Replace by “gauge-covariant derivative”:

• And with :

Phase Invariance

Niels Tuning (52)

1) Assume symmetry ψ→ψ’= ψeiα(x) 2) Keep Eqs valid Ø Covariant derivative

Gauge Invariance

Niels Tuning (53)

1) Arbitrary gauge 2) Keep Eqs valid Ø Need ψ→ψ’= ψeiα

We started globally: Then we went local:

Λ ∂ + = ʹ →

µ µ µ µ

A A A

µ µ µ µ

iqA D + ∂ ≡ → ∂

1) Assume symmetry ψ→ψ’= ψeiα(x) 2) Keep Eqs valid Ø Covariant derivative

Gauge Invariance

Niels Tuning (54)

1) Arbitrary gauge 2) Keep Eqs valid Ø Need ψ→ψ’= ψeiα

We started globally: Then we went local:

Λ ∂ + = ʹ →

µ µ µ µ

A A A

µ µ µ µ

iqA D + ∂ ≡ → ∂

• Let’s replace the derivative in the Dirac equation by the

gauge-covariant derivative: Ø Gauge invariance leads to: gauge fields, and their interactions!

Quantum Electro Dynamics - QED

Niels Tuning (55)

• For completeness, let’s also add the piece that describes

the free photons:

Quantum Electro Dynamics - QED

Niels Tuning (56)

Quantum Electro Dynamics - QED

Niels Tuning (57)

Quantum Electro Dynamics - QED

Niels Tuning (58)

Fermion ψ with mass m Interaction with coupling q Photon field Aµ

m qγµ

Local gauge symmetry Gauge field(+ interactions)

Basis of forces in Standard Model

Fundamental symmetry and Forces arise beautifully!

Local gauge symmetry Gauge field(+ interactions)

Basis of forces in Standard Model

Pragmatic: We have forces and Can be described mathematically

Half-way there?!

Prof.dr. J. Ellis

“Famous” QED processes (I)

time

“Famous” QED processes (II)

time

Weak Interaction

• We had:
• How about?

More gauge transformations

Niels Tuning (65)

• We had:
• How about?
• Why? Historical origin:

proton and neutron exhibit isospin symmetry

More gauge transformations

Niels Tuning (66)

• We had:
• How about?
• Introduce new covariant derivative:
• Bµ is now 2x2 matrix:

Ø with three gauge fields:

More gauge transformations

Niels Tuning (67)

group SU(2) the from matrices Pauli the are Btw,τ

• The three b, are associated to the W+,W- and Z0

Electro-weak theory

Niels Tuning (68)

Ø We measured that left and right are different!

• Instead of “strong” isospin, switch to “weak” isospin:
• Formalism the same

Electroweak theory

Niels Tuning (69)

( )

L L L L L kinetic

iqA b ig i D i L ψ τ γ ψ ψ γ ψ ψ

µ µ µ µ µ µ

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⋅ + ∂ = =

• 2

1

(What is difference between chirality and helicity…?)

Ø We measured that left and right are different!

• Instead of “strong” isospin, switch to “weak” isospin:
• Formalism the same

Electroweak theory

Niels Tuning (70)

( )

L L L L L kinetic

iqA b ig i D i L ψ τ γ ψ ψ γ ψ ψ

µ µ µ µ µ µ

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⋅ + ∂ = =

• 2

1

( ) ( )

( )

... 2 2 2 1 , ,

3 3 2 2 1 1

− − − ∂ + ∂ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + + ∂ =

+ − L L L L L L L L L L L weak

u W d g d W u g d d i u u i d u b b b ig d u i d u L

kinetic

µ µ µ µ µ µ µ µ µ µ µ µ µ

γ γ γ γ τ τ τ γ

dL

g

W+µ uL

• 1956:

– C.-S. Wu discovered that neutrino’s are always left-handed – The process involved: 60

27Co à 60 28Ni + e- + νe

–

60 27Co is spin-5 and 60 28Ni is spin-4, both e- and νe are spin-½

Parity violation

Niels Tuning (71)

• 60Co

νe

• e-

Ø All neutrino’s are left-handed Ø All antineutrinos are right-handed

• W. Pauli: "That's total nonsense!" “Then it must be repeated!” “I

refuse to believe that God is a weak left-hander.”

• 1956:

– C.-S. Wu discovered that neutrino’s are always left-handed – The process involved: 60

27Co à 60 28Ni + e- + νe

–

60 27Co is spin-5 and 60 28Ni is spin-4, both e- and νe are spin-½

Parity violation

Niels Tuning (72)

• 60Co

νe

• e-

Ø All neutrino’s are left-handed Ø All antineutrinos are right-handed

Fermions and interactions

Niels Tuning (73)

• Neutrino’s only feel the weak force

Ø Parity violation is most obvious for neutrino’s

Ø We measured that left and right are different! Ø Weak interaction only couples to left-handed particles (or right-handed anti-particles)

Electroweak theory

Niels Tuning (74)

( )

L L L L L kinetic

iqA b ig i D i L ψ τ γ ψ ψ γ ψ ψ

µ µ µ µ µ µ

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⋅ + ∂ = =

• 2

1

( ) ( )

( )

... 2 2 2 1 , ,

3 3 2 2 1 1

− − − ∂ + ∂ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + + ∂ =

+ − L L L L L L L L L L L weak

u W d g d W u g d d i u u i d u b b b ig d u i d u L

kinetic

µ µ µ µ µ µ µ µ µ µ µ µ µ

γ γ γ γ τ τ τ γ

dL

g

W+µ uL

QCD

Symmetries

Niels Tuning (76)

• Charge
• Isospin
• Color

ψ

L

d u ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ψ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = b g r ψ

• We had:

U(1) (QED)

• Then:

SU(2) (Weak)

• How about:

SU(3) (QCD)

More gauge transformations

Niels Tuning (77)

( )

ψ λ θ ψ ψ 2 exp

8 , 1

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ʹ →

∑

= a a a x

i

(Why 8…? Group theory: 3x3=8+1 … )

• We had:

U(1) (QED)

• Then:

SU(2) (Weak)

• How about:

SU(3) (QCD)

SU(2) à SU(3)

Niels Tuning (78)

( )

ψ λ θ ψ ψ 2 exp

8 , 1

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ʹ →

∑

= a a a x

i

Ø Gell-Mann matrices:

SU(3)-equivalent of Pauli-matrices

Symmetries

Niels Tuning (79)

• Charge

U(1) (QED)

• Isospin

SU(2) (Weak)

• Color

SU(3) (QCD)

ψ

L

d u ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ψ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = b g r ψ

( )

ψ λ θ ψ ψ 2 exp

8 , 1

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ʹ →

∑

= a a a x

i

(Why 8…? Group theory: 3x3=8+1 … )

• We had:

U(1) (QED)

• Then:

SU(2) (Weak)

• How about:

SU(3) (QCD)

More gauge transformations

Niels Tuning (80)

( )

ψ λ θ ψ ψ 2 exp

8 , 1

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ʹ →

∑

= a a a x

i

a=1,8: 8 gluons Another covariant derivative: with 8 Aµ fields: which transform as: Gluonic field tensor:

QCD Lagrangian

Niels Tuning (81)

Fermion ψ with mass m Interaction with coupling q 8 Gluon fields Aµ

m

Self-interaction

qγµ

• Local SU(3) gauge transformation
• Introduce 8 Aµ

a gauge fields

• Non-“Abelian” theory,
• Self-interacting gluons

– Gluons have (color) charge

• Different “running”
• Local U(1) gauge transformation
• Introduce 1 Aµ gauge field
• “Abelian” theory,
• No self-interacting photon

– Photons do not have (electric) charge

• Different “running”

QED QCD

Niels Tuning (82)

( )

ψ λ θ ψ ψ 2 exp

8 , 1

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ʹ →

∑

= a a a x

i

QED and QCD

Which symmetries do we impose ?

QED: U(1)Y à 1 degree of freedom: γ Weak Force: SU(2)L à 3 degrees of freedom: W+, W- en Z0 Strong Force: SU(3)C à 8 degrees of freedom: 8 gluons All spin-1

Rotations in color space Rotations in weak isospin space Rotations in hypercharge space For example SU(2)L: 2x2 complex matrices (det=1) à 3 basis-rotations à 3 vector fields

Standard Model now (almost) complete!

Niels Tuning (84)

Standard Model

Niels Tuning (85)

( )

µν µν µ µ

ψ γ F F m D i ψ 4 1 − − = L

Fermion fields ψ Gauge fields Aµ Interactions through Dµ

( )

µν µν µ µ

ψ γ F F m D i ψ 4 1 − − = L

Niels Tuning (86)

Prof.dr. J. Ellis

Standard Model

Standard Model

Niels Tuning (87)

Todo-list:

• e+e- scattering

– QED at work (LEP): R, neutrinos

• e+p scattering

– QCD at work (HERA): DIS, structure functions, scaling

• No masses for W, Z

– (LHC/ATLAS) Higgs mechanism, Yukawa couplings

• Consequences of three families

– (LHC/LHCb) CKM-mechanism, CP violation

( )

µν µν µ µ

ψ γ F F m D i ψ 4 1 − − = L

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

Schedule

Niels Tuning (88)

You are here

Plan

1) Intro: Standard Model & Relativity 2) Basis

1) Atom model, strong and weak force 2) Scattering theory

3) Hadrons

1) Isospin, strangeness 2) Quark model, GIM

4) Standard Model

1) QED 2) Parity, neutrinos, weak inteaction 3) QCD

5) e+e- and DIS 6) Higgs and CKM

Niels Tuning (89)

1900-1940 1945-1965 1965-1975 1975-2000 2000-2015 18 Feb 10 Mar 17 Mar 21 Apr 12 May 11 Feb