Elementary Particles Lecture 1 Niels Tuning Harry van der Graaf - - PowerPoint PPT Presentation

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Elementary Particles Lecture 1 Niels Tuning Harry van der Graaf Martin Fransen Ernst-Jan Buis Niels Tuning (1) Plan Theory Detection and sensor techn. Quantum Quantum Forces Mechanics Field Theory Light Interactions

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SLIDE 1

Niels Tuning (1)

“Elementary Particles” Lecture 1

Niels Tuning Harry van der Graaf Martin Fransen Ernst-Jan Buis

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SLIDE 2

Plan

Niels Tuning (2)

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

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SLIDE 3

Plan

Niels Tuning (3)

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

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SLIDE 4

1) 11 Feb: Accelerators (Harry) + Special relativity (Niels)

§ Layout, structure § Thomson Tube, vdGraaff, Cockroft Walton, cyclotron, synchrotron, § (Synchrotron radiation (ESRF), neutron sites (ESS), WakeField accelerators, proton beam therapy ?) § 4-vectors, Lorentz transformation, Special relativity

2) 18 Feb: Quantum Mechanics (Niels)

§ QM basics, wave function, Schrodinger, Klein-Gordon, Dirac equation, Rutherford scattering

3) 25 Feb: Interactions with Matter (Harry)

§ EM interactions, Bethe Bloch, Landau distributions, Ionisation in gas and Si § Three photon interactions (Photo effect, Compton, Pair Production) § Bremstrahlung, Cherenkov radiation. Equivalence of Pair Production and Brehmstrahlung

4) 3 Mar: Light detection? (Harry)

§ Scintillators (including photon detectors, from ZiSulfide to Tipsy)) § Calorimeters?

5) 10 Mar: Particles and cosmics (Niels)

§ Cosmics, quark model, strangeness

6) 17 Mar: Astrophysics and Dark matter (Ernst-Jan)

§ Cosmic rays (Showers (protons/gammas/neutrinos/dark matter); Signals (Cherenkov radiation, fluorescence,radio); Experiments (PA/IceCube/Anatares/KM3NeT/TA); Cherenkov gamma-ray telescope(Magic/Hess/ CTA) ) § Low background experiments (PMTs; Shielding; Experiments (Kamiokande/Xenon/DAMA) § Space based experiments (cosmic rays from space and spaceweather (AMS/ACE); Gamma/X-ray space based astrophysics, Optics/coded masks, Swift, Integral, XMM/Chandra, planetaire mission)

7) 24 Mar: Forces (Niels)

§ Symmetries, Gauge invariance, QED, weak and strong interaction

Schedule

Niels Tuning (4)

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SLIDE 5

8) 21 Apr: e+e- and ep scattering (Niels)

§ R (colors), running coupling, charm, gluon, tt, WZ, DIS

9) 28 Apr: Gravitational waves (Ernst-Jan)

§ Interferometry (Michelson, Sagnac; lasers, optics) § Ground based experiments (Virgo/LIGO/Karga/ET) § Spaced based experiments (LISA) § Multimessenger (Space+ground; triggers; Future, big questions)

10) 12 May: Higgs and big picture (Niels)

§ Higgs mechanism and Standard Model completion

11) 19 May: Charged particle detection (Martin)

§ Gaseous detectors (from Geiger to GridPix) § Semiconductor (Si) detectors; pixel detectors

12) 26 May: Applications: experiments and medical (Martin)

§ Pixels, ATLAS, 4D tracking § medical imaging, CT, spectral X-ray, PET scan

13) 2 Jun: Nikhef excursie

§ ATLAS? ALICE? Km3Net? Virgo? LHCb?

14) 8 Jun: CERN excursie

§ CERN lecture (H. Ten Kate); ATLAS underground; Synchro-cyclotron; LHCb; AD antimatter ?

Schedule

Niels Tuning (5)

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SLIDE 6

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: Astrophysics and Dark Matter (Ernst-Jan Buis) 7) 24 Mar: Forces (Niels Tuning) 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 (6)

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SLIDE 7

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 (7)

1900-1940 1945-1965 1965-1975 1975-2000 2000-2015 18 Feb 10 Mar 24 Mar 21 Apr 12 May 11 Feb

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SLIDE 8
  • M. Thomson

“Modern Particle Physics” (2013, 49 EUR)

  • D. Griffiths

“Introduction to Elementary Particles” (2008, 68 EUR)

  • C. Tully

“Elementary Particle Physics in a Nutshell” (2011, 65 EUR)

  • F. Halzen & A.D.Martin

“Quarks and Leptons” (1984, 68 EUR)

Books

Niels Tuning (8)

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SLIDE 9
  • Lecture 1:

– ch.3 Relativistic kinematics

  • Lecture 2:

– ch.5.1 Schrodinger equation – ch.7.1 Dirac equation – ch.6.5 Scattering

  • Lecture 3:

– ch.1.7 Quarkmodel – ch.4 Symmetry/spin

  • Lecture 4:

– ch.7.4 QED – h.11.3 Gauge theories

  • Lecture 5:

– ch.8.2 e+e- – ch.8.5 e+p

  • Lecture 6:

– ch.11.8 Higgs mechanism

  • D. Griffiths

“Introduction to Elementary Particles”

Niels Tuning (9)

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SLIDE 10
  • Introduction

– Start with the end... : Higgs! – The Standard Model

  • How to calculate with high energies? A reminder.

– Lorentz Transformation – Invariants – Colliding particles

Outline of today

Niels Tuning (10)

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SLIDE 11
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SLIDE 12
  • Why is the Higgs particle so special?
  • The Standard Model
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SLIDE 13
  • Prof. P. Higgs

What are the rules for subatomic particles?

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SLIDE 14

Ø Describes the behaviour of particles

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SLIDE 15

Photons Fµν

(Maxwell equations! E-field, B-field, electro-magnetic waves, …)

Particles ψ

(“normal” matter, electrons, quarks, …)

Interactions D

(how the partiles “feel” eachother)

φ Higgs

ψψφ ψψφ Mass

(for “normal” particles)

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SLIDE 16

Ø Half of the mug is about Higgs!

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SLIDE 17

For sale in the CERN shop…

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SLIDE 18

Higgs and Mass?

  • Mass is “exchange rate” between force and acceleration

But… what is it ?

  • Mass is energy

But… where does it come from ?

  • Mass is friction with Higgs field!

F = m x a E = m x c2 m: ψψφ

ψψφ

Newton Einstein Higgs

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SLIDE 19

“Wij zwemmen in een oceaan van Higgs deeltjes, … alsof we vissen zijn en nu hebben vastgesteld dat er water om ons heen is.”

  • Prof. Robbert Dijkgraaf
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SLIDE 20
  • Introduction

– Start with the end... : Higgs! – The Standard Model

  • How to calculate with high energies? A reminder.

– Lorentz Transformation – Invariants – Colliding particles

Outline of today

Niels Tuning (20)

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SLIDE 21

These lectures deal with the

  • Formalism
  • Concepts
  • n
  • Particles
  • Interactions

jointly known as the Standard Model

The Standard Model

Niels Tuning (21)

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SLIDE 22

All “matter” particles are described here as Ψ (fermions)

The Standard Model

Niels Tuning (22)

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SLIDE 23

The Standard Model

Niels Tuning (23)

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SLIDE 24

Particles

Niels Tuning (24)

  • Quarks and leptons…:
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SLIDE 25

Particles…

Niels Tuning (25)

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SLIDE 26

Particles

Niels Tuning (26)

Charge

+2/3 e

  • 1/3 e
  • 1 e

0 e

quarks

Three generations:

leptons

(1956)

u d

I

e νe

(1895)

t b

III

τ ντ

(1973) (2000) (1978) (1995)

c s

II

µ νµ

(1936) (1963) (1947) (1976)

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SLIDE 27

Particles and Anti-particles

Niels Tuning (27)

Charge

+2/3 e

  • 1/3 e
  • 1 e

0 e

quarks

Three generations

leptons

(1956)

u d

I

e νe

(1895)

t b

III

τ ντ

(1973) (2000) (1978) (1995)

c s

II

µ νµ

(1936) (1963) (1947) (1976)

  • 2/3 e

+1/3 e +1 e

0 e

u d c s t b e τ µ νe νµ ντ

Charge

III I II

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SLIDE 28

Where did the anti-matter go?

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SLIDE 29

b b c u proton proton

Vcb Vub

Yij è Vcb, Vub

Difference between matter and anti-matter Personal Intermezzo

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SLIDE 30
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SLIDE 31

LHCb detector

proton proton

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SLIDE 32

atom nucleus 10-15 m

What energy is needed?

How to make energies around 100.000.000 eV or more ? Energy of 1 e- that passes a potential difference of 1 V: 1 eV Energy of mass of 1 proton: m = E/c2: 1 GeV

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SLIDE 33

Search for elementary building blocks

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SLIDE 34

LHC accelerator

Geneve

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SLIDE 35

LHC

Energy limited by field of 1232 dipole magnets: B= 8.4 T

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SLIDE 36

Klassiek botsen Quantummechanisch botsen

proton proton

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SLIDE 37

E = mc2

Create new particles if energy is large enough (and if they exist…)

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SLIDE 38
  • Introduction

– Start with the end... : Higgs! – The Standard Model

  • How to calculate with high energies? A reminder.

– Lorentz Transformation – Invariants – Colliding particles

Outline of today

Niels Tuning (38)

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SLIDE 39
  • Lorentz transformation
  • Length contraction & Time dilatation
  • Adding velocities
  • Relativistic energies
  • Relativistic kinematics
  • Collision
  • Decay

Summary special relativity

Niels Tuning (39)

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SLIDE 40

1) Speed of light constant 2) Every (inertial) coordinate system equivalent

Lorentz transformation

Niels Tuning (40)

x=ct becomes x’=ct’

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SLIDE 41

1) Speed of light constant 2) Every (inertial) coordinate system equivalent Ø Find transformation rules:

Lorentz transformation

Niels Tuning (41)

Galilei: Lorentz: x=ct becomes x’=ct’ : Ø Find γ :

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SLIDE 42

1) Speed of light constant 2) Every (inertial) coordinate system equivalent Ø Find transformation rules:

Lorentz transformation

Niels Tuning (42)

Galilei: Lorentz: x=ct becomes x’=ct’ : Ø Find γ :

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SLIDE 43
  • Stick with length L0 in system S’ :

– moving relative to system S with speed v – Observer in S sees length L – At same time t in fixed frame: t1 = t2

Ø Length L is factor 1/γ smaller in rest frame S:

Consequences: Lorentz contraction

Niels Tuning (43)

v S’ S L L0

(Length L as seen in frame S, is difference between coordinates x2 and x1 in frame S.)

x2 x1

(Length L0 as seen in moving frame S’, is at rest)

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SLIDE 44
  • Clock is moving in frame S’ with relative speed v
  • Suppose clock is emitting light pulses

– Time interval between pulses in frame S’: Δt’ = t2’-t1’ – Light pulses are emitted from same point x’ in moving frame: x1’ = x2’

  • What sees the observer at rest in frame S?

– First pulse: t1 = γ(t1 ’+ vx1’/c2) – Second pulse: t2 = γ(t2 ’+ vx2’/c2) – Hence: Δt = t2 - t1 = γ(t1 ’ - t2 ’+ v/c2 (x1’-x2’)) = γ Δt’

Ø Clock period is seen factor γ longer for observer at rest

Consequences: Time dilatation

Niels Tuning (44)

Δt = γ Δt’

v

= 0

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SLIDE 45
  • Time and space transformation:
  • Hence observer in frame S sees velocity ux:
  • Ex: If train goes fast (v=c), then velocity ux seen by observer:

ux = (u’+c)/(1+u’/c) = c Adding velocities

Niels Tuning (45)

/dt’

v u'

(Galilei: u = u’ + v)

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SLIDE 46

Niels Tuning (46)

1) Photon is emitted from box 2) Momentum conservation: box moves 3) Photon is absorbed by box: box stops NB: Centre-of-mass of entire system remains at rest

  • Photon must carry a “mass equivalent to the energy of the photon, m”

– Box: mass M over length Δx: MΔx – Photon: mass m over length L: mL – System at rest: (MΔx + mL)=0

E=mc2

Einstein’s(box:(

Doos A

Δx = vΔt v = pbox M = − pphoton M = − Ephoton Mc ,Δt = L c Δx = − EphotonL Mc2

MΔx + mL

( ) = 0 ⇒

L(− E c2 + m) = 0 ⇒ E = mc2

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SLIDE 47

Relativistic energies

Niels Tuning (47)

  • Momentum:

– In rest: p = m0v (or at low speeds, to satisfy Newtonian dynamics) – Moving mass: p = γm0v (Relativistic momentum must be conserved in all frames)

  • Einstein: equivalence between energy and mass

– In rest: E = m0c2 – Moving mass: E = γm0c2 E = pc2/v v/c=pc/E

Ø E:

  • Btw, a Taylor expansion gives classical kinetic energy:

γ = 1 1− v2 / c2 = 1 1− p2c2 / E 2 E =γm0c2

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SLIDE 48

Relativistic energies

Niels Tuning (48)

E = γmoc2

E E

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SLIDE 49
  • Write (t, x) as 4-vector xµ:
  • Nicely symmetric form of Lorentz

transformation:

4-vectors

Niels Tuning (49)

Λ “Boost” in x-direction:

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SLIDE 50
  • Write (t, x) as 4-vector xµ:
  • Covariant and contravariant 4-vector related through

metric g:

  • Any pair of 4-vectors is invariant as:

– (similar to the length of a vector in Euclidean space)

Invariants (“fixed length”)

Niels Tuning (50)

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SLIDE 51
  • Special relativity

– Flat (“Minkowski”) spacetime

  • General relativity

– Curved spacetime

Spacetime

Niels Tuning (51)

gµν = g00 g01 g02 g03 g10 g11 g12 g13 g20 g21 g22 g23 g30 g31 g32 g33 ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

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SLIDE 52
  • General relativity

– Curved spacetime – Line element (invariant) – Christoffel symbols: – Riemann curvature tensor: – Einstein equations:

Spacetime

Niels Tuning (52)

ds2 = gµνdxµdxν

gµν = g00 g01 g02 g03 g10 g11 g12 g13 g20 g21 g22 g23 g30 g31 g32 g33 ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

Tμν: Energy-momentum tensor

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SLIDE 53

The famous Dirac equation: Remember! § µ : Lorentz index § 4x4 γ matrix: Dirac index Less compact notation:

Intermezzo: Use of 4-vectors

Niels Tuning (53)

  • 4-vectors

– Use for relativistic kinematics in particle collisions – Use for quantum-field description of matter fields: – – –

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SLIDE 54
  • Example of invariant: rest mass (“invariant mass”)
  • Lorentz transformation on energy-momentum 4-vector:

Energy-momentum 4-vector

Niels Tuning (54)

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SLIDE 55
  • Elastic collission of two particles a and b: a + b c + d
  • Take c=1 (“natural units”)
  • Invariant mass of initial state:
  • Invariant mass of initial state = invariant mass of final state:

= “center-of-mass energy” , √s:

Calculate with 4-vectors: colliding particles

Niels Tuning (55)

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SLIDE 56
  • Calculate center-of-mass energy for

beam of 450 GeV protons: 1) Fixed target: 2) Colliding beams:

“Fixed target” vs “colliding beams”

Niels Tuning (56)

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SLIDE 57
  • Standard Model Lagrangian
  • Standard Model Particles

Summary: Standard Model

Niels Tuning (57)

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SLIDE 58
  • Theory of relativity

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

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

Summary: Relativity

Niels Tuning (58)

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SLIDE 59
  • Introduce “matter particles”

– spinor ψ from Dirac equation

  • Introduce “force particles”
  • Introduce basic concepts of scattering processes

Next: QM

Niels Tuning (59)

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SLIDE 60

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 (60)

1900-1940 1945-1965 1965-1975 1975-2000 2000-2015 19 Feb 12 Mar 19 Mar 7 May 21 May 12 Feb

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SLIDE 61

Backup slides: on accelerators

Niels Tuning (61)

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SLIDE 62

Accelerators

How do you create enough energy?

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SLIDE 63

From bubble chamber to LHC

  • 2012: Higgs discovered

Niels Tuning (63)

Discoveries made with the help of Accelerators:

The Nobel Prize in Physics 2013

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SLIDE 64

Cockcroft-Walton

Cockcroft Walton

Operation principle

1932: 800 kV 0.8 MeV: energy threshold to split atoms Li + p à He + something 1951: Nobelprize

100 V 200 V 400 V

Cavendish lab Cambridge

Bart Hommels

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SLIDE 65

Van de Graaff

Robert van de Graaff

High voltage electro static generator

1) Gas ionizes (ΔV) 2) Moving belt transports charge Harry van der Graaf

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SLIDE 66

Van de Graaff

Robert van de Graaff

1929: 80,000 volt 1931: 1,000,000 volt 1933: 7,000,000 volt

Nowadays: Oak Ridge 25 MeV Vivitron 35 MeV

Harry van der Graaf

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SLIDE 67

Van de Graaff

+ + + + +

H- p

electronen strippers

1) Single acceleration 2) Tandem mode

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SLIDE 68

Cyclotron

Ernest “atom smasher” Lawrence

Nobelprijs 1939

First cyclotron 1930

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SLIDE 69

Dee

Cyclotrons in real life

Dee

1931: r = 12 cm à 1 MeV protons 1974: B = 0.46 [T], r = 9 [m] à 520 MeV protons

First Largest

TRIUMF

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SLIDE 70

Synchrotron

In a synchrotron, particles move in fixed

  • rbit

Known synchrotrons:

  • Bevatron
  • Tevatron (Fermilab)

collider

  • LEP (CERN)

collider

  • LHC (CERN)

collider

  • M. Oliphant

Accelerate: higher E à higher p r constant: also higher B

versnellen afbuigen

r = p qB

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SLIDE 71

~

Hollow tube (no field)

Linac (principle)

+ +

  • Equal frequency, larger velocity

à (space between) tubes increasingly larger Linac typically first step in acceleration chain Typical: ~50m, ~100 MeV

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SLIDE 72

Linac’s & traveling wave guide

SLAC: Stanford Linear Accelerator Center (San Francisco) 3.2 km long à 50 GeV electrons

Big Linac’s

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SLIDE 73

Niels Tuning (73)

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SLIDE 74

Future Circular Collider (FCC) ???

  • Ph. Lebrun

From: CLIC Workshop – Feb 2014

16 T ⇒ 100 TeV in 100 km 20 T ⇒ 100 TeV in 80 km

  • 80-100 km tunnel infrastructure in Geneva area
  • design driven by pp-collider requirements
  • with possibility of e+-e- (TLEP) and p-e (VLHeC)
  • CERN-hosted study performed in international collaboration