MKEP 1.2: Particle Physics WS 2012/13

(16.10.2012)

Stephanie Hansmann-Menzemer Physikalisches Institut, INF 226, 3.101

8. Elastic and inelastic electron Proton scattering and the quark model 9. Strong Interaction (QCD) 9.1. Symmetries and conservation laws 9.2. Local gauge invariance 9.3. Bound states 9.4. Quark Gluon Plasma 10. Weak Interaction 10.1. Parity, Wu Experiment, Goldhaber Experiment 10.2. Left right handed couplings 10.3. CKM Matrix 11. The Standard Model 11.1 Electroweak unification 11.2 Precision tests 11.3 Higgs mechanism 12. Neutral Meson Mixing 13. CP Violation 14. Neutrinos

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Content of the Lecture 1. Introduction 1.1 Natural units 1.2 Standard model basics 1.3 Relativistic kinematics 2. Interaction of Particles with Matter 3. Detectors for Particle Physics 3.1 General Detector Concepts 3.2 PID Detectors 3.3 Tracking Detectors 4. Scattering process and transition amplitudes 4.1. Fermi’s golden rule 4.2. Lorentz invariant phase space and matrix element 4.3 Decay Width and Lifetime 4.4 Two and Three Bod decay rate, Dalitz plot 4.5 Cross section 5. Description of free particles 5.1. Klein-Gordan equation 5.2. Dirac equation 5.3. Plane Wave solutions 6. QED 6.1 Interaction by particle exchange 6.2 Feynman rules 6.3. Electron-Positron annihilation 6.4. Electron Scattering 7. Radiativ correction and renormalization

Tutorials, Exam, Lecture notes

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web-page: http://www.physi.uni/heidelberg.de/~menzemer/ParticlesPhzsicsWS1213.html

tutorials: Thu 2:15-3:45 pm (Blake Levrington, english) Fri 9:15-10:45 am (Christoph Anders, german) Fri 11:15-12:45 am (Xian-Guo Lu, english) homeworks on the web-page by Tuesday evening (first one tonight, mainly a recap of Physics V lecture) hand in of homeworks at the end of Tue. lecture or at secretariat (INF 226, 3.103) by 4pm Tuesday afternoon (email to tutors are not accepted)

60% of homeworks required to participate in the exam work on homeworks in group of up to 3 students allowed/encouraged exam: 5.2.2013 2-4pm

registration for tutorial open till 23th of October http://uebungen.physik.uni/heidelberg.de/uebungen

Lecture notes are available BEFORE the lecture

Related Lectures

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Prerequisite: PEP IV, PEP V Courses which could be followed in parallel:

Statistical Methods in Particle Physics (2 SWS) Accelerator Physics (2 SWS) Colloquium for Particle Physics, Astrophysics and Cosmology [Quantum Field Theory I (4 SWS) ]

Advanced courses, build up on top of this one

Standard Model of Particle Physics Advanced Topics in Particle Physics Recent Results from LHC, Higgs Physics, …

MKEP1: Particle Physics

Experiments are interpreted in the context of the underlying theory, thus a significant fraction of the first half of the lecture will deal with mathematical description of particle interactions -> Feynman diagrams.

Literature

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General literature, bit more theoretical details in this lecture

D. H. Perkins: Introduction to High Energy Physics C. Berger, Elementarteilchenphysik D. Griffith, Introduction to Elementary Particles B. Martin, G. Shaw: Particle Physics R. Cahn, G. Goldhaber: The Experimental Foundation of Particle Physics (original papers)

Theoretical background:

F. Halzen, A. Martin, Quarks and Leptons O. Nachtmann, Elementarteilchenphysik P. Schueser, Feynman/Graphen und Eichtheorien für Experimentalphysiker

Particle Data Group: http://pdg.lbl.gov/

Where/How to Download Papers ?

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From university network you have free access to all major physics journals. For key experiments in experimental particle physics these are: Physics review letters (PRL or Phys. Rev.) e.g. C.S. Wu et al. , Phys. Rev., 105, 1413-1415 (1957) author volume page year (Discovery Parity violation)

http://prl.aps.org

NATURE http://www.nature.com/nature/archive/index.html

(all natural sciences) e.g. G.D. Rochester & C. C. Butler, Nature 160, 855-856 (1947) (Discovery of the K0)

Physics Letters B (PLB), http://www.journals.elsevier.com/physics/letters/b/

-> http://ww.sciencedirect.com/science/journal/03702693

e.g. ARGUS Collaboration, H. Albrecht et al., 192 (1987) 453 (Discovery of B0-B0 Mixing)

Content for Today

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1. Introduction 1.1. Natural units 1.2. Standard model basis particles & interactions 1.3 Relativistic mechanics 2. Interaction of particles with material

recap of PEP5

Natural Units

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SI units (systeme international d’units):

mass: kg length: m time: s

Natural units (ħ=1, c=1):

action: ħ [ = 1.055 10-34 kg m2/s ] velocity: c [ = 2.998 108 m/s ] energy: GeV [ = 1.6 10-10 kg m2] m0(proton)c2 ~ 1 GeV

not that important for HEP: el. Current: A temperature: K amount of substance: mol luminous intensity: cd [candela]

Quantity natural units SI

energy GeV 1.6 10-10 J momentum GeV x 1/c 5.34 10-19 kg m/s mass GeV x 1/c2 1.78 10-27 kg

time GeV-1 x ħ 1.5 1024 s length GeV-1 x ħc 0.197 fm

area GeV-1 x (ħc)2 0.389 mb = 0.389 10-31 m2

HEP convention: skip c and ħ, can always be derived by dimension analysis

Charge in Natural Units

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Charge determines the strength of the electromagnetic interaction. To get a dimensionless estimate of this strength compare energy of repulsion between two electrons one natural unit apart with the rest mass energy of the proton VC = e2/4πε0r E0 ~ 1 GeV r = ħc/GeV-1

α ≡ Vc/E0 = e2/4πε0 ħc ~ 1/137 fine structure constant

use heavy side units: (ħ = 1, c = 1, ε0 = 1, μ0=1) e = (4πα) -1/2

Change of system of units changes the value of e (quantity with dimension) but not of α (dimensionless quantity).

Fundamental building Blocks of Matter

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pointlike = without observable structure Δx Δp ≥ ħ LEP: √s = 90 GeV Δx ~ 10-18 m

ħc = 197 MeV fm

Quark flavours are conserved in elm and strong IA, but not in CC (charged current) weak IA, e.g. W Lepton flavour violation (forbidden in first order)? Originally neutrinos assumed to be massless in SM. Observation of neutrino oscillation indicated small but finite mass. Direct observation of LFV challenging: SM prediction BR(μ-> 3e) < 10-50

experimental limits BR(μ-> 3e) < 10-11

charge leptons quarks

u c t +2/3

d s b -1/3

νe νμ ντ 0 e μ τ -1

W

W Z

Lepton & Quark Masses

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Masses of quarks cannot be measured directly but must be determined through their Influence on hadron properties Constituent mass: Observed hadron spectra + assumed binding energies

m(u) ~ m(d) ~ 0.3 GeV m(p) = 0.938 GeV m(s) ~ 0.5 GeV m(φ) = 1.1 GeV m(c) ~ 1.6 GeV m(J/ψ) = 3.1 GeV m(b) ~ 4.6 GeV m(Y) = 10.2 GeV m(t) ~ 171 GeV Current mass: Quark masses are theory parameters which Depend on the renormalization scheme (see later lectures)

m(e) = 511 keV m(μ) = 106 MeV m(τ) = 1.78 GeV m(νe) < 3 eV m(νμ) < 190 keV m(ντ) < 18.2 MeV

Mass of Leptons:

u

u

Definition of “nacked”quark and thus its mass depends on the scale/precision we look at it!

Bound States

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Bound quark states are colour neutral, either mesons |qq> or baryons |qqq>

Ground state mesons (L=0): mesons are named after the heaviest quark they contain: K -> s; D -> c; B -> b;

Examples for baryons: p = |uud>, n = |udd>, Λ =|uds>, Λc = |udc>, Λb = |udb> Top quark decays (τ ~ 10-24s) before it hadronizes (10-22 s)

Meson Summary Table

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Tabel from Particle Data Group Particle listings

Interactions are described by exchange of virtual particles (off-shell) vertex Feynman diagrams: f1 f2 left side: initial state, real particles right side: final state, real particles time arrow to the right side (choice of convention)

f3 f4 antiparticles have arrows against time direction time energy, momentum, QN, angular momentum, charge … conserved at all vertices f: fermions, real (free) particles X = γ, g, W±, Z “exchange bosons” Virtual particles (allowed for inner parts of the diagrams): E2 ≠ p2 + m2

Standard Model (SM) Interactions

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po

siti

on

X

Feynman Diagrams

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fermion flow conserved

lepton number conservation

Change of quark flavour

W-

Feynman diagrams are visualisation of rules to compute matrix elements! (lowest order diagram of a decay … the one with the lowest number of vertices)

Standard Model Vertices

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Electromagnetic IA charged fermions never changes flavour acts on charged fermions α ~ 1/137 Weak CC IA all fermions always changes flavour acts on all fermions αW ~ 1/40 (larger than elm coupling but

further suppressed by mW)

Weak NC IA all fermions never changes flavour acts on all fermions αZ ~ 1/40 Strong IA acts on all quarks and gluo never changes flavour all quarks and gluons αS ~1 further allowed vertices in SM: (consequence of symmetry group and gauge theory)

Relativistic Kinematic

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contravariant 4-vector:

covariant 4-vector: matrix tensor:

scalar product: contravariant derivative: covariant derivative:

μ = 0,1,2,3 τ = 0,1,2,3 ν = 0,1,2,3

Lorentz invariance

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scalars and balanced products of co-and contravariant variables are invariant under Lorentz transformation “indices are balanced”

aμ aμ ҅ β = v bμ bμ ҅ γ = (1-β2)-1/2

v

x x ҅

of particle A of particle B

Lorentz transformation (analog for bμ)

exercise to show Lorentz invariance of scalar Product: Application: Many observables are Lorentz scalars or can

easily be transformed into them.

Interaction of Particles/Radiation with Material

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Reminder of used terminology:

φ =𝑁

𝑖

𝐴 𝑁𝑖

=𝑑𝑁𝑖

𝑑𝑡 particle flux:

𝐴

d

φ

nb of scattering centers in target: Nt = nt A d = ρ 𝑁𝐴

𝑀𝑚𝑜𝑙

𝐴 𝑑

target density V

rate of scattered particles: 𝑁 𝑠 = φ Nt σ = 𝑁 i nt σ d

cross section

1

λ

Interaction probability: W = 𝑁

𝑠

𝑁𝑖

= nt σ d dW(x) = nt σ dx

x dx mean free path length λ = 1

𝑛𝑡 σ

Two Kinds of Matter Interaction

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a) IA results in absorption of the particle b) IA results in energy loss (e.g. γ)

Intensity :

𝐼(𝑥) = 𝐼0 𝑒−𝑥/λ = 𝐼0𝑒

−μ𝑥

𝐼 𝐼

mean range ≠ mean free path length

μ : absorption coefficient

Intensity constant till particle is stopped

all statistical process result in energy and angle (direction) uncertainties

20 20

20

E(t) E0 θ0

Θ(t)

Interaction of Particles/Radiation with Material

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Energy Loss of Heavy Charged Particles

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- 𝑑𝐸

𝑑𝑥 = K ρ

𝑍

𝐴 𝑧2

β2 1

2𝑙𝑛

2 𝑚𝑒 𝑐2β2γ2

𝐼2 − β2 −

δ

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a) Ionisation and excitation in scattering process MEAN energy loss given by Bethe Bloch formula

NA Avogadro’s number z charge of incident particle Z atomic number of absorber A atomic mass of absorber [g/mol] K/A = 4π NA re

2 me c2/A = 0.307075 MeV g-1 cm2 for A = 1 g/mol re classical electron radius e2/4πε0 me c2 I mean excitation energy [eV] (for Z > 20: I = 10 Z eV) ρ density δ density correction to ionization energy loss

γ = E/m β = p/E

Bethe Bloch is an empirical formula/approximation valid of ± 5% up to several 100 GeV. Not valid at very low momenta.

Bethe Bloch I

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- 𝑑𝐸

𝑑𝑥 = K ρ

𝑍

𝐴 𝑧2

β2 1

2𝑙𝑛

2 𝑚𝑒 𝑐2β2γ2

𝐼2 − β2 (−

δ

2) γ = E/m

β = p/E

0) very small energies: Bethe Bloch not valid 1) small energies (βγ > 0.1): -

𝑑𝐸

𝑑𝑥~

1

β2

strong ionisation of slow particles get stucked

dE/dx

x

Bragg peak

2) large energies β ~ 1: −𝑑𝐸

𝑑𝑥~ ln(βγ) relativistic rise

higher field density due to contraction of field lines

v 3) Minimum at βγ (=p/m) є [3,4] typical value ~ 1-2 MeV cm2/g

4) Density correction due to screening of charge at large energies smaller net charge for distant (nucleus/e-)

- 𝑑𝐸

𝑑𝑥~ β

Bethe Bloch II

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Bragg Peak

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Large energy deposit just before the particle is stopped

exploited in tumor therapy

Mean Energy Loss and Delta Electrons

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Ddelta electron

detector

particle track

mean energy loss

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How does a bubble chamber work?

Target filled with liquid gas (e.g. He), relax pressure shortly before particle traverse detector pressure goes down thus boiling point goes down bubbles start to form at ions, produced by traversing particle photos from different perspective allow 3D reconstruction of particle trajectory

Caveat:

- process needs to be triggered externally - active times of several ms, dead times of several s - someone must look a the photos … Nowadays bubble chambers are for demonstration purposes only.

Similar (older) concept, cloud chamber: Initial state: pressure at saturation vapor pressure Co-existance of liquid and gas phase. Adiabatic extension of volume, thus temperature goes down, liquid drops are produced at ions

Nobel prize in 1960 – Donald A. Glaser (famous bubble chamber experiment – Gargamelle 1970-1978 at CERN – discovery of neutral currents)

Particle Identification via dE/dx

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Energy deposit of particles of known momentum can be used to conclude on its particle type.