Particle Physics
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Particle Physics. Marco G. Giammarchi Istituto Nazionale di Fisica Nucleare Via Celoria 16 – 20133 Milano (Italy) [email protected] 1. Costituents of Matter 2. Fundamental Forces 3. Particle Detectors (N. Neri)

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Particle Physics

Marco G. Giammarchi

Istituto Nazionale di Fisica Nucleare

Via Celoria 16 – 20133 Milano (Italy)

[email protected]

1. CostituentsofMatter

2. FundamentalForces

3. ParticleDetectors (N. Neri)

4. Experimentalhighlights (N. Neri)

5. Symmetries and ConservationLaws

6. RelativisticKinematics

7. The Static Quark Model

8. The WeakInteraction

9. Introductionto the Standard Model

10. CP Violation in the Standard Model (N. Neri)

A. Y. 2013/14

I Semester

6 Credits

Particle physics is a branch of physics which studies the nature of particles that are the constituents of what is usually referred to as matter and radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics. Although the word "particle" can be used in reference to many objects (e.g. a proton, a gas particle, or even household dust), the term "particle physics" usually refers to the study of the fundamental objects of the universe – fields that must be defined in order to explain the observed particles, and that cannot be defined by a combination of other fundamental fields.

The current set of fundamental fields and their dynamics are summarized in a theory called the Standard Model, therefore particle physics is largely the study of the Standard Model's particle content and its possible extensions. (Wikipedia)


  • Basicconceptsof:

  • Quantum Mechanics

  • NuclearPhysics

  • SpecialRelativity

  • Quantum FieldTheory

  • Radiation-MatterInteraction

  • General information:

  • The professor is always available in principle

  • However, he is quite often away from here

  • Professor always reads e-mails

  • These slides can be downloaded from the professor’s website

  • The Exam Committee: Nicola Neri, Lino Miramonti


Noli iurare in verba magistri

  • Bibliography:

  • D. H. Perkins – Introduction to High Energy Physics – Addison Wesley - 2000

  • K. Gottfried, V. Weisskopf – Concepts of Particle Physics – Oxford Univ. Press - 1984

  • D. C. Cheng, G.K. O’Neill – Elementary Particle Physics – 1979 - Addison Wesley

  • R. N. Cahn, G. Goldhaber – The experimental foundations of Particle Physics – 1991 – Cambridge University Press

  • E. M. Henley, A. Garcia – Subatomic Physics – 2007 – World Scientific

  • I. S. Hughes – Elementary Particles – 1991 – Cambridge University Press

  • B. Roe – Particle Physics at the new Millennium – Springer - 1996

  • F. Halzen, A. D. Martin – Quarks and Leptons – 1984 – J. Wiley

  • (Advanced) Griffith – Introduction to Elementary Particles – 2008 – J. Wiley


The bibliography is only indicative

Genesis (and other considerations)

Adam’s Creation – Michelangelo Buonarroti (1511).

(Musei Vaticani - La Cappella Sistina)

Parmenides (circa 500 AC), Zenon (circa 490 –430 AC): the experienceofmultiplicity can benegated.

Matter can bedividedwith no end. The infinite divisionofspatialextensiongivesas a result zero, nihil. Therefore the multiplicityofbodilyextensiondoesnotexist. Itisanillusory opinion.

Demokritos (circa 460 – 370 AC): the experienceofmultiplicitycannotbenegated

Matter can bedividedonly down to some fundamentalunit.

A-tomos, indivisible. The atomwasintroducedto stop the “reductiontonothing” processofspatialextension put forwardbyParmenides and Zeno.

The atomis the pointwhere the divisionprocessstops.

Thisistotallydifferentfrom the modernconceptof science.

ParticlePhysicsas a modern Science beginsaroundyear 1930.

ParticlePhysicsplays the roleof the theory “par excellence” in a reductionistapproach (understandeverythingstartingfromelementary building blocks).

For a criticalapproachtothis, see :

P.W. Anderson – More isDifferent – Science Vol 177 (1972) pag. 393.

ParticlePhysicsclaimtobe a fundamentaltheory: itdealsofmatter and energy in extremespacetimeconditions.

Costituents of Matter

1. CostituentsofMatter

2. FundamentalForces

3. ParticleDetectors (N. Neri)

4. Experimentalhighlights (N. Neri)

5. Symmetries and ConservationLaws

6. RelativisticKinematics

7. The StaticQuark Model

8. The WeakInteraction

9. Introductionto the Standard Model

10. CP Violation in the Standard Model (N. Neri)

Fundamental Constituents of Matter: Quarks and Leptons

Structureless building blocks down to a spatialextensionof 10-18 m

Welldefinedspin and charge

Leptonshavewelldefined mass aswell

Low Mass

Matter Constituents under ordinary conditions (low energy/T)

Constituents of unstable particle (produced at high energy, in astrophysical systems). They decay to lower mass particles

High Mass

A reductionist example: the Deuterium Atom

10-15 m


Fractional charges

Semi-integer spin

10-10 m

Quarks, electrons, and photons as fundamental Constituents of the Atom

Leptons: observableparticleswith definite mass (masseigenstates)

Quarks: notdirectlyobservable. Not a welldefined mass.

A long history of discoveries down to smaller and smaller structures: quarks are now considered the innermost layer of nuclear matter.

Particles as probes to study of atomic and nuclear structures :

- The associated wave length is

(de Broglie)

High energies makes us sensitive to smaller spatial scales

De Broglie and Compton wavelengths

Suppose we want to confine a particle to within its λ Compton:

The energy corresponding to the confinement:

The energy required will be greater than the particle mass!

Creation of particles is energetically favoured with respect to confining a particle within its Compton wavelength

Non relativistic composite systems : general features

Atomic systems

Dimensions are large compared to electron’s Compton wavelength

  • A system that is large compared to the Compton wavelength of its constituents:

  • Has binding energies that are small compared to their rest masses

  • Has non-relativistic internal velocities

For a confined particle

Now, if

System larger than electron’s Compton λ

Nonrelativistic velocity

The kinetic energy is then roughly classical and

But this (Virial Theorem) is of the order of the binding energy

Internal transitions in nonrelativistic composite systems : the Bohr atom

Atomic transitions between energy levels . A variation of energy :

same order of magnitude :

If minimized with respect to Δx will give the Borh radius

Atom size and electron mass

Internal transitions in nonrelativistic composite systems : some features

  • Atomic systems

  • Emitted gammas have λ’s longer with respect to the atomic dimension

In fact, since this system is large compared to the electron’s Compton wavelength :

Radiation emitted in atomic transition :

System larger than e- Compton wavelength :

Part of the Electric Dipole Approximation

On the Electric Dipole Approximation some features

A typical interaction:

The radiation field (calculated in a specific space point)

Electric dipole moment of the system of charges

Optical transitions in Atoms:

Atomic transitions

Atom size

Gamma transitions in Nuclei:

Gamma transitions

Nucleus size

Constituents properties: some features

  • Quarks:

  • Electric charge

  • Color

  • Effective mass

  • Spin (1/2)

  • Leptons:

  • Electric charge

  • Mass

  • Spin (1/2)


3 families

All Contituents (Quarks, Leptons) are Fermions.

Force Carriers

Costituents of Matter

Costituents and Force Carriers: the Spin/Statistics Theorem some features

Half-integer Spin Particles


Fermi-Dirac Statistics

Bose-Einstein Statistics

(W. Pauli, 1940)


Integer Spin Particles

  • Consequences of the Spin/Statistics Theorem:

  • formal: wave functions, field operators commutation rules

  • experimental: nuclear and atomic structure, Bose-Einstein condensates

The Wave Function must have the correct symmetry under interchange of identical particles. If 1, 2 are identical particles :

(probability must be conserved upon excange of identical particle)

Identical Bosons identici (symmetric)

Identical Fermions (antisymm.)

A consequence of the Spin/Statistics Theorem: for two identical Fermions 1,2 in the same quantum state x:

Pauli Exclusion Principle!

Because identical

Spin/Statistics Theorem

Particles and Antiparticles: the “birth” of Particle Physics

1928: Dirac Equation, merging Special Relativity and Quantum Mechanics.

A relativistic invariant Equation for spin ½ particles. E.g. the electron

Rest frame solutions: 4 independent states:

  • E>0, s=+1/2

  • E>0, s=-1/2

  • E<0, s= +1/2

  • E<0, s= -1/2

Upon reinterpretation of negative-energy states as antiparticles of the electron:

Electron, s=+1/2

Electron, s=-1/2

The positron, a particle identical to the electron e- but with a positive charge: e+. The first prediction of the relativistic quantum theory.

Positron, s=1/2

Positron, s=-1/2

Beginning of the story of Particle Physics: the discovery of the Positron

Positrons discovered in cosmic rays interaction observed in a Cloud Chamber (Anderson,1932)

Existence of Antiparticles: a general (albeit non unversal) property of fermions and bosons

Antiparticle: same mass of the particle but oppiste charge and magnetic moment

All fundamental constituents have their antiparticle

Discovery of the first «Elementary» Particles the Positron

Faraday, Goldstein, Crookes, J. J Thomson (1896)

  • Known particles at the end of the 30’s

  • Electron

  • Proton

  • Photon

  • Neutron

  • Positron

  • Muon

  • Pion

Avogadro, Prout (1815)

Einstein (1905), Compton (1915)

Chadwick (1932)

Conventionalbirth date of NuclearPhysics

Anderson (1932)

Cosmic rays interaction studies. Pion/Muon separation

Neutrino: a particle whose existence was hypotesized without a discovery!

The discovery of Muon and Pion the Positron

A little preview about the fundamental interactions:

  • Gravitational Interactions: known since forever. Classical theory (A. Einstein) in 1915. Responsible of macroscopic-scale matter stability.

  • Electromagnetic Interactions: Classical theory (Faraday, Maxwell) completed in 1861. Responsible of the interaction between charged (and therefore of the stability of atomic structures). Important also at the nuclear scale.

  • Strong Nuclear Interactions: responsible of forces at the nuclear level (and of nuclear stability). It is a very short range interaction: 10-15 m (1 fermi, fm).

  • Weak Nuclear Interactions: responsible of some relevant nuclear processes (weak fusion, weak radioactivity). Also, a short (subnuclear) range interaction.

Search for the Pion was motivated (Yukawa) by the research on the Carrier of the Strong Nuclear Force. And by the observation of a new particle.

Yukawa Hypotesis: the existence of the Pion as Mediator of the Strong Nuclear Force



The first cosmic rays researchers found (in the 30’s) a particle with a mass that was intermediate between the Electron and the Proton



It was thought that this was the carrier of the force between two nucleons (Yukawa, 1935):

Relativistic relation between energy, momentum, mass

A quantization recipe

The Klein-Gordon Equation

The static solution:

Interaction range

Using the Strong Nuclear Force the UncertaintlyPrinciple

Interactionlength of a force  Compton wavelength of the Carrier



The creation of the carrier requires ∆E = mc2


The event is restricted to take place on a time scale:

During this time the carrier can travel:


In the case of the Strong Interaction, since the range is known to be 10-15 m

…the expected «meson» mass

A few remarks: the Strong Nuclear Force

The expected «meson» mass was of about 200 MeV

The «meson» interactionwaspostulated to be the Strong Nuclear Force carrier

Todayweknowthatthisis just a residual force of the «true» Strong Interaction

(Van derWaals)

Strong residual force

Electromagneticresidual force

This is not the fundamental Strong Nuclear Interaction !

Conversi, Pancini, Piccioni (1947) the Strong Nuclear Force experiment: the general idea

How to distinguish between two cases: absorption or decay ?

Decaying particle

Useful numbers:

Absorbed particle

Bohr orbit




Fraction of time spent in the nuclei



At the Bohr orbit speed (Zc/137) the distance travelled in nuclear matter during the «meson» observed lifetime (2x10-6 s) would be of 1 cm (in carbon)! Therefore this particle does not interact strongly in nuclear matter. It turned out to be the MUON, not the PION.

Lifetime the Strong Nuclear Force of a particle

Decay of an unstable particle: a quantum mechanical process, analog to radioactive decay. For many particles, the number will change as :

Lifetime in the rest frame

Lifetime in the laboratory frame

Path travelled by the particle in the laboratory frame

The the Strong Nuclear Force Pionwasdiscovered in 1947 by Lattes, Powell and Occhialini

Pion and Muondecaysequence: a cascade of decays

Muon decay




In allthesedecays, neutrinos are emitted !

Pion the Strong Nuclear Force – Muon – Electron sequencesobserved in emulsions

Experimental strategy:

Exposure of Emusions to Cosmic Rays

The pion in term of quarks

The early era of cosmic rays particle physics experiments : the Strong Nuclear Force

AGS Sunchrotron at Brookhaven

The first big particle accelerator

33 GeV reached in 1960

1950 : AGS di Brookhaven

Particle the Strong Nuclear Force PhysicsLaboratories in the World

CERN (LHC. Large Hadron Collider)

Hadron (proton) accelerators

Electron-Positron machines

Electron-proton accelerators

Secondary Beams

Small scale synchrotron (Orsay)

Cosmic the Strong Nuclear Force RaysLaboratories in the World (yes, today!)

The Pierre Auger Observatory

The HESS array (Namibia)

The Neutrino case: a particle first hypotesized and then discovered

Understanding beta decays (energy, angularmomentum)


The spectrum of the recoiling electron (non monoenergetic) wasindicating the presence of invisibleenergy

Neutrino mass effects on the spectrum endpoint

  • Pauli hypotesis (1932): the presence of a new particle could save the energy conservation of:

  • Energy

  • Momentum

  • Angular momentum

Neutrino hypotesis!

Experimentalconfirmation in 1956 (Reines & Cowanexperiment)

Why is the Neutrino a typical case ? discovered

  • Beta particles (electrons) are emitted with a continumm spectrum in beta decay. This is incompatibie with a two-body decay (since energy levels in the nucleus are known to be discrete).

  • The electron trajectory is not collinear with the trajectory of the recoiling nucleus.

  • Nuclear spin variation is not compatible with the emission of a single electron (∆=0,±1).

Experimental problems

Two possibilities:

  • E conservation

  • P conservation

  • M conservation

Abbandonment of well consolidated physical laws

Introduction of new particles/fields

Neutrino hypotesis!

Why is the Neutrino a typical case ? discovered

  • Star rotation curves in Galaxies show excessive peripheral velocities

  • The motion of Galaxies Galaxy Clusters features excessive velocities

Experimental problems

Two possibilities:

  • Theory of Gravitation

Abandonment of well consolidated physical laws

Introduction of new particles/fields

Dark Matter hypotesis !

Why is the Neutrino a typical case ? discovered

  • The Universe has identical properties in causally disconnected domains (Horizon problem)

  • The Universe at large scale is flat to an extremely good accuracy (Flatness problem)

  • CMB perturbations (structure formation)

Experimental problems

Two possibilities:

  • Incompleteness of the Big Bang Model ?

Abandonment of well consolidated physical laws

Introduction of new particles/fields

Inflation hypotesis !

Neutrino discovery: discovered

Principle of the experiment

Water and cadmium (400l)

In a nuclear power reactor, antineutrinos come from  decay of radioactive nuclei produced by 235U and 238U fission.

Liquid scintillator

Inverse beta decay

The antineutrino reacts with a proton in water and produces a neutron and a positron

The positron annihilates almost immediately in gamma rays

The neutron gets slowed down and captured by a Cd nucleus, with the emission of gamma rays, several microseconds after the event

Gammas are detected by the scintillator: the signature of the event are the two gamma pulses detected by the photomultipliers

A first classification of know Elementary Particles discovered

The photon

Leptons (heaviercopies of the electron)

The neutrino, postulated to explain beta decay and observed in inverse beta decay, isalwaysassociated to a chargedlepton.

The hadrons, particles made up of quarks and obeyingmainly to strong nuclearinteraction

Particles with Strangeness discovered

Presence of unknownparticles in experiments with cloudchambers or emulsions on atmospheric balloons (1947, Rochester and Butler).

Theyturned out to be secondaryparticles with a characteristic “V” shapedecay

  • Theseparticleswereproduced and weredecaying in twodifferentmodes:

  • Strong Interaction production (cross section)

  • WeakInteractiondecays (lifetimes)

Interazione forte

Associated production of particles with a new property: Strangeness

Interazione debole

Particles with Strangeness s : a new quark (different from u,d) !

BR = 64.1%

BR = 35.7%

BR = 69.2%

BR = 30.7%

K particles (Kaons), similar to Pions but with the s Quark

The long lifetime was explained by the disappearance of a «strange» quark

The Neutral Pion u,d) !

Decay mode

Electromagnetic decay !

BR =98.8%

BR =1.2%

Decay lifetime

Experimental evidence. Cosmic ray studies of «star-like» events in high resolution nuclear emulsions (1950, Carlson, Hooper, King).

High energy experiments at the Berkeley Cyclotron.

The detachment from the “primary vertex” of the interaction is caused by the neutral pion lifetime

“Primary” vertex

A first classification (updated) u,d) !


Proton-like particles (baryons)


Leptons (heaviercopies of the electron)

The neutrino, postulated to explain beta decay and observed in inverse beta decay, isalwaysassociated to a chargedlepton.

The hadrons, particles made up of quarks and obeyingmainly to strong nuclearinteraction