Particle Physics

1
Chapter 31

• Particle Physics

2
Atoms as Elementary Particles

• Atoms
• From the Greek for indivisible
• Were once thought to be the elementary particles
• Atom constituents
• Proton, neutron, and electron
• After 1932 these were viewed as elementary
• All matter was made up of these particles

3
Discovery of New Particles

• New particles
• Beginning in 1945, many new particles were
  discovered in experiments involving high-energy
  collisions
• Characteristically unstable with short lifetimes
• Over 300 have been cataloged
• A pattern was needed to understand all these new
  particles

4
Elementary Particles Quarks

• Physicists recognize that most particles are made
  up of quarks
• Exceptions include photons, electrons and a few
  others
• The quark model has reduced the array of
  particles to a manageable few
• Protons and neutrons are not truly elementary,
  but are systems of tightly bound quarks

5
Fundamental Forces

• All particles in nature are subject to four
  fundamental forces
• Strong force
• Electromagnetic force
• Weak force
• Gravitational force
• This list is in order of decreasing strength

6
Nuclear Force

• Holds nucleons together
• Strongest of all the fundamental forces
• Very short-ranged
• Less than 10-15 m
• Negligible for separations greater than this

7
Electromagnetic Force

• Is responsible for the binding of atoms and
  molecules
• About 10-2 times the strength of the nuclear
  force
• A long-range force that decreases in strength as
  the inverse square of the separation between
  interacting particles

8
Weak Force

• Is responsible for instability in certain nuclei
• Is responsible for decay processes
• Its strength is about 10-5 times that of the
  strong force
• Scientists now believe the weak and
  electromagnetic forces are two manifestions of a
  single interaction, the electroweak force

9
Gravitational Force

• A familiar force that holds the planets, stars
  and galaxies together
• Its effect on elementary particles is negligible
• A long-range force
• It is about 10-41 times the strength of the
  nuclear force
• Weakest of the four fundamental forces

10
Explanation of Forces

• Forces between particles are often described in
  terms of the actions of field particles or
  exchange particles
• The force is mediated, or carried, by the field
  particles

11
Forces and Mediating Particles
12
Paul Adrian Maurice Dirac

• 1902 1984
• Understanding of antimatter
• Unification of quantum mechanics and relativity
• Contributions of quantum physics and cosmology
• Nobel Prize in 1933

13
Antiparticles

• Every particle has a corresponding antiparticle
• From Diracs version of quantum mechanics that
  incorporated special relativity
• An antiparticle has the same mass as the
  particle, but the opposite charge
• The positron (electrons antiparticle) was
  discovered by Anderson in 1932
• Since then, it has been observed in numerous
  experiments
• Practically every known elementary particle has a
  distinct antiparticle
• Among the exceptions are the photon and the
  neutral pi particles

14
Diracs Explanation

• The solutions to the relativistic quantum
  mechanic equations required negative energy
  states
• Dirac postulated that all negative energy states
  were filled
• These electrons are collectively called the Dirac
  sea
• Electrons in the Dirac sea are not directly
  observable because the exclusion principle does
  not let them react to external forces

15
Diracs Explanation, cont

• An interaction may cause the electron to be
  excited to a positive energy state
• This would leave behind a hole in the Dirac sea
• The hole can react to external forces and is
  observable

16
Diracs Explanation, final

• The hole reacts in a way similar to the electron,
  except that it has a positive charge
• The hole is the antiparticle of the electron
• The electrons antiparticle is now called a
  positron

17
Pair Production

• A common source of positrons is pair production
• A gamma-ray photon with sufficient energy
  interacts with a nucleus and an electron-positron
  pair is created from the photon
• The photon must have a minimum energy equal to
  2mec2 to create the pair

18
Pair Production, cont

• A photograph of pair production produced by 300
  MeV gamma rays striking a lead sheet
• The minimum energy to create the pair is 1.022
  MeV
• The excess energy appears as kinetic energy of
  the two particles

19
Annihilation

• The reverse of pair production can also occur
• Under the proper conditions, an electron and a
  positron can annihilate each other to produce two
  gamma ray photons
• e- e 2g

20
Antimatter, final

• In 1955 a team produced antiprotons and
  antineutrons
• This established the certainty of the existence
  of antiparticles
• Every particle has a corresponding antiparticle
  with
• equal mass and spin
• equal magnitude and opposite sign of charge,
  magnetic moment and strangeness
• The neutral photon, pion and eta are their own
  antiparticles

21
Hideki Yukawa

• 1907 1981
• Nobel Prize in 1949 for predicting the existence
  of mesons
• Developed the first theory to explain the nature
  of the nuclear force

22
Mesons

• Developed from a theory to explain the nuclear
  force
• Yukawa used the idea of forces being mediated by
  particles to explain the nuclear force
• A new particle was introduced whose exchange
  between nucleons causes the nuclear force
• It was called a meson

23
Mesons, cont

• The proposed particle would have a mass about 200
  times that of the electron
• Efforts to establish the existence of the
  particle were made by studying cosmic rays in the
  late 1930s
• Actually discovered multiple particles
• Pi meson (pion)
• Muon
• Not a meson

24
Pion

• There are three varieties of pions
• ? and ?-
• Mass of 139.6 MeV/c2
• ?0
• Mass of 135.0 MeV/c2
• Pions are very unstable
• For example, the ?- decays into a muon and an
  antineutrino with a lifetime of about 2.6 x10-8 s

25
Muons

• Two muons exist
• µ- and its antiparticle µ
• The muon is unstable
• It has a mean lifetime of 2.2 µs
• It decays into an electron, a neutrino, and an
  antineutrino

26
Richard Feynman

• 1918 1988
• Developed quantum electrodynamics
• Shared the Noble Prize in 1965
• Worked on Challenger investigation and
  demonstrated the effects of cold temperatures on
  the rubber O-rings used

27
Feynman Diagrams

• A graphical representation of the interaction
  between two particles
• Feynman diagrams are named for Richard Feynman
  who developed them
• A Feynman diagram is a qualitative graph of time
  on the vertical axis and space on the horizontal
  axis
• Actual values of time and space are not important
• The actual paths of the particles are not shown

28
Feynman Diagram Two Electrons

• The photon is the field particle that mediates
  the interaction
• The photon transfers energy and momentum from one
  electron to the other
• The photon is called a virtual photon
• It can never be detected directly because it is
  absorbed by the second electron very shortly
  after being emitted by the first electron

29
The Virtual Photon

• The existence of the virtual photon seems to
  violate the law of conservation of energy
• But, due to the uncertainty principle and its
  very short lifetime, the photons excess energy
  is less than the uncertainty in its energy
• The virtual photon can exist for short time
  intervals, such that ?E ? / 2?t

30
Feynman Diagram Proton and Neutron (Yukawas
Model)

• The exchange is via the nuclear force
• The existence of the pion is allowed in spite of
  conservation of energy if this energy is
  surrendered in a short enough time
• Analysis predicts the rest energy of the pion to
  be 100 MeV / c2
• This is in close agreement with experimental
  results

31
Nucleon Interaction More About Yukawas Model

• The time interval required for the pion to
  transfer from one nucleon to the other is
• The distance the pion could travel is cDt
• Using these pieces of information, the rest
  energy of the pion is about 100 MeV

32
Nucleon Interaction, final

• This concept says that a system of two nucleons
  can change into two nucleons plus a pion as long
  as it returns to its original state in a very
  short time interval
• It is often said that the nucleon undergoes
  fluctuations as it emits and absorbs field
  particles
• These fluctuations are a consequence of quantum
  mechanics and special relativity

33
Nuclear Force

• The interactions previously described used the
  pion as the particles that mediate the nuclear
  force
• Current understanding indicate that the nuclear
  force is more fundamentally described as an
  average or residual effect of the force between
  quarks

34
Feynman Diagram Weak Interaction

• An electron and a neutrino are interacting via
  the weak force
• The Z0 is the mediating particle
• The weak force can also be mediated by the W
• The W and Z0 were discovered in 1983 at CERN

35
Classification of Particles

• Two broad categories
• Classified by interactions
• Hadrons interact through strong force
• Leptons interact through weak force
• Note on terminology
• The strong force is reserved for the force
  between quarks
• The nuclear force is reserved for the force
  between nucleons
• The nuclear force is a secondary result of the
  strong force

36
Hadrons

• Interact through the strong force
• Two subclasses distinguished by masses and spins
• Mesons
• Decay finally into electrons, positrons,
  neutrinos and photons
• Integer spins (0 or 1)
• Baryons
• Masses equal to or greater than a proton
• Half integer spin values (1/2 or 3/2)
• Decay into end products that include a proton
  (except for the proton)
• Not elementary, but composed of quarks

37
Leptons

• Do not interact through strong force
• Do participate in electromagnetic (if charged)
  and weak interactions
• All have spin of ½
• Leptons appear truly elementary
• No substructure
• Point-like particles

38
Leptons, cont

• Scientists currently believe only six leptons
  exist, along with their antiparticles
• Electron and electron neutrino
• Muon and its neutrino
• Tau and its neutrino
• Neutrinos may have a small, but nonzero, mass

39
Conservation Laws

• A number of conservation laws are important in
  the study of elementary particles
• Already have seen conservation of
• Energy
• Linear momentum
• Angular momentum
• Electric charge
• Two additional laws are
• Conservation of Baryon Number
• Conservation of Lepton Number

40
Conservation of Baryon Number

• Whenever a baryon is created in a reaction or a
  decay, an antibaryon is also created
• B is the Baryon Number
• B 1 for baryons
• B -1 for antibaryons
• B 0 for all other particles
• Conservation of Baryon Number states the sum of
  the baryon numbers before a reaction or a decay
  must equal the sum of baryon numbers after the
  process

41
Conservation of Baryon Number and Proton Stability

• There is a debate over whether the proton decays
  or not
• If baryon number is absolutely conserved, the
  proton cannot decay
• Some recent theories predict the proton is
  unstable and so baryon number would not be
  absolutely conserved
• For now, we can say that the proton has a
  half-life of at least 1033 years

42
Conservation of Baryon Number, Example

• Is baryon number conserved in the following
  reaction?
• Baryon numbers
• Before 1 1 2
• After 1 1 1 (-1) 2
• Baryon number is conserved
• The reaction can occur as long as energy is
  conserved

43
Conservation of Lepton Number

• There are three conservation laws, one for each
  variety of lepton
• Law of Conservation of Electron-Lepton Number
  states that the sum of electron-lepton numbers
  before the process must equal the sum of the
  electron-lepton number after the process
• The process can be a reaction or a decay

44
Conservation of Lepton Number, cont

• Assigning electron-lepton numbers
• Le 1 for the electron and the electron neutrino
• Le -1 for the positron and the electron
  antineutrino
• Le 0 for all other particles
• Similarly, when a process involves muons,
  muon-lepton number must be conserved and when a
  process involves tau particles, tau-lepton
  numbers must be conserved
• Muon- and tau-lepton numbers are assigned
  similarly to electron-lepton numbers

45
Conservation of Lepton Number, Example

• Is lepton number conserved in the following
  reaction?
• Check electron lepton numbers
• Before Le 0 After Le 1 (-1) 0 0
• Electron lepton number is conserved
• Check muon lepton numbers
• Before Lµ 1 After Lµ 0 0 1 1
• Muon lepton number is conserved

46
Strange Particles

• Some particles discovered in the 1950s were
  found to exhibit unusual properties in their
  production and decay and were given the name
  strange particles
• Peculiar features include
• Always produced in pairs
• Although produced by the strong interaction, they
  do not decay into particles that interact via the
  strong interaction, but instead into particles
  that interact via weak interactions
• They decay much more slowly than particles
  decaying via strong interactions

47
Strangeness

• To explain these unusual properties, a new
  quantum number, S, called strangeness, was
  introduced
• A new law, the conservation of strangeness, was
  also needed
• It states that whenever a reaction or decay
  occurs via the strong force, the sum of
  strangeness numbers before the process must equal
  the sum of the strangeness numbers after the
  process
• Strong and electromagnetic interactions obey the
  law of conservation of strangeness, but the weak
  interaction does not

48
Bubble ChamberExample of Strange Particles

• The dashed lines represent neutral particles
• At the bottom,
• ?- p ? ?0 K0
• Then ?0 ? ?- p and

49
Creating Particles

• Most elementary particles are unstable and are
  created in nature only rarely, in cosmic ray
  showers
• In the laboratory, great numbers of particles can
  be created in controlled collisions between
  high-energy particles and a suitable target

50
Measuring Properties of Particles

• A magnetic field causes the charged particles to
  curve
• This allows measurement of their charge and
  linear momentum
• If the mass and momentum of the incident particle
  are known, the product particles mass, kinetic
  energy, and speed can usually be calculated
• The particles lifetime can be calculated from
  the length of its track and its speed

51
Resonance Particles

• Short-lived particles are known as resonance
  particles
• They exist for times around 10-20 s
• In the lab, times for around 10-16 s can be
  detected
• They cannot be detected directly
• Their properties can be inferred from data on
  their decay products

52
Murray Gell-Mann

• 1929
• Studies dealing with subatomic particles
• Named quarks
• Developed pattern known as eightfold way
• Nobel Prize in 1969

53
The Eightfold Way

• Many classification schemes have been proposed to
  group particles into families
• These schemes are based on spin, baryon number,
  strangeness, etc.
• The eightfold way is a symmetric pattern proposed
  by Gell-Mann and Neeman
• There are many symmetrical patterns that can be
  developed
• The patterns of the eightfold way have much in
  common with the periodic table
• Including predicting missing particles

54
An Eightfold Way for Baryons

• A hexagonal pattern for the eight spin ½ baryons
• Stangeness vs. charge is plotted on a sloping
  coordinate system
• Six of the baryons form a hexagon with the other
  two particles at its center

55
An Eightfold Way for Mesons

• The mesons with spins of 0 can be plotted
• Strangeness vs. charge on a sloping coordinate
  system is plotted
• A hexagonal pattern emerges
• The particles and their antiparticles are on
  opposite sides on the perimeter of the hexagon
• The remaining three mesons are at the center

56
Eightfold Way for Spin 3/2 Baryons

• The nine particles known at the time were
  arranged as shown
• An empty spot occurred
• Gell-Mann predicted the missing particle and its
  properties
• About three years later, the particle was found
  and all its predicted properties were confirmed

57
Quarks

• Hadrons are complex particles with size and
  structure
• Hadrons decay into other hadrons
• There are many different hadrons
• Quarks are proposed as the elementary particles
  that constitute the hadrons
• Originally proposed independently by Gell-Mann
  and Zweig

58
Original Quark Model

• Three types or flavors
• u up
• d down
• s strange
• Associated with each quark is an antiquark
• The antiquark has opposite charge, baryon number
  and strangeness
• Quarks have fractional electrical charges
• 1/3 e and 2/3 e
• Quarks are fermions
• Half-integral spins

59
Original Quark Model Rules

• All the hadrons at the time of the original
  proposal were explained by three rules
• Mesons consist of one quark and one antiquark
• This gives them a baryon number of 0
• Baryons consist of three quarks
• Antibaryons consist of three antiquarks

60
Quark Composition of Particles Examples

• Mesons are quark-antiquark pairs
• Baryons are quark triplets

61
Additions to the Original Quark Model Charm

• Another quark was needed to account for some
  discrepancies between predictions of the model
  and experimental results
• A new quantum number, C, was assigned to the
  property of charm
• Charm would be conserved in strong and
  electromagnetic interactions, but not in weak
  interactions
• In 1974, a new meson, the J/? was discovered that
  was shown to be a charm quark and charm antiquark
  pair

62
More Additions Top and Bottom

• Discovery led to the need for a more elaborate
  quark model
• This need led to the proposal of two new quarks
• t top (or truth)
• b bottom (or beauty)
• Added quantum numbers of topness and bottomness
• Verification
• b quark was found in a Y- meson in 1977
• t quark was found in 1995 at Fermilab

63
Numbers of Particles

• At the present, physicists believe the building
  blocks of matter are complete
• Six quarks with their antiparticles
• Six leptons with their antiparticles

64
Particle Properties
65
More About Quarks

• No isolated quark has ever been observed
• It is believed that at ordinary temperatures,
  quarks are permanently confined inside ordinary
  particles due to the strong force
• Current efforts are underway to form a
  quark-gluon plasma where quarks would be freed
  from neutrons and protons

66
Color

• It was noted that certain particles had quark
  compositions that violated the exclusion
  principle
• Quarks are fermions, with half-integer spins and
  so should obey the exclusion principle
• The explanation is an additional property called
  the color charge
• The color has nothing to do with the visual
  sensation from light, it is simply a name

67
Colored Quarks

• Color charge occurs in red, blue, or green
• Antiquarks have colors of antired, antiblue, or
  antigreen
• These are the quantum numbers of color charge
• Color obeys the Exclusion Principle
• A combination of quarks of each color produces
  white (or colorless)
• Baryons and mesons are always colorless

68
Quantum Chromodynamics (QCD)

• QCD gave a new theory of how quarks interact with
  each other by means of color charge
• The strong force between quarks is often called
  the color force
• The strong force between quarks is mediated by
  gluons
• Gluons are massless particles
• When a quark emits or absorbs a gluon, its color
  may change

69
More About Color Charge

• Particles with like colors repel and those with
  opposite colors attract
• Different colors attract, but not as strongly as
  a color and its anticolor
• The color force between color-neutral hadrons is
  negligible at large separations
• The strong color force between the constituent
  quarks does not exactly cancel at small
  separations
• This residual strong force is the nuclear force
  that binds the protons and neutrons to form nuclei

70
Quark Structure of a Meson

• A green quark is attracted to an antigreen quark
• The quark antiquark pair forms a meson
• The resulting meson is colorless

71
Quark Structure of a Baryon

• Quarks of different colors attract each other
• The quark triplet forms a baryon
• Each baryon contains three quarks with three
  different colors
• The baryon is colorless

72
QCD Explanation of a Neutron-Proton Interaction

• Each quark within the proton and neutron is
  continually emitting and absorbing gluons
• The energy of the gluon can result in the
  creation of quark-antiquark pairs
• When close enough, these gluons and quarks can be
  exchanged, producing the strong force

73
Elementary Particles A Current View

• Scientists now believe there are three
  classifications of truly elementary particles
• Leptons
• Quarks
• Field particles
• These three particles are further classified as
  fermions or bosons
• Quarks and leptons are fermions
• Field particles are bosons

74
Weak Force

• The weak force is believed to be mediated by the
  W, W-, and Z0 bosons
• These particles are said to have weak charge
• Therefore, each elementary particle can have
• Mass
• Electric charge
• Color charge
• Weak charge
• One or more of these charges may be zero

75
Electroweak Theory

• The electroweak theory unifies electromagnetic
  and weak interactions
• The theory postulates that the weak and
  electromagnetic interactions have the same
  strength when the particles involved have very
  high energies
• Viewed as two different manifestations of a
  single unifying electroweak interaction

76
The Standard Model

• A combination of the electroweak theory and QCD
  for the strong interaction form the standard
  model
• Essential ingredients of the standard model
• The strong force, mediated by gluons, holds the
  quarks together to form composite particles
• Leptons participate only in electromagnetic and
  weak interactions
• The electromagnetic force is mediated by photons
• The weak force is mediated by W and Z bosons
• The standard model does not yet include the
  gravitational force

77
The Standard Model Chart
78
Mediator Masses

• Why does the photon have no mass while the W and
  Z bosons do have mass?
• Not answered by the Standard Model
• The difference in behavior between low and high
  energies is called symmetry breaking
• The Higgs boson has been proposed to account for
  the masses
• Large colliders are necessary to achieve the
  energy needed to find the Higgs boson
• In a collider, particles with equal masses and
  equal kinetic energies, traveling in opposite
  directions, collide head-on to produce the
  required reaction

79
Particle Paths After a Collision
80
The Big Bang

• This theory states that the universe had a
  beginning, and that it was so cataclysmic that it
  is impossible to look back beyond it
• Also, during the first few minutes after the
  creation of the universe all four interactions
  were unified
• All matter was contained in a quark-gluon plasma
• As time increased and temperature decreased, the
  forces broke apart

81
A Brief History of the Universe
82
Hubbles Law

• The Big Bang theory predicts that the universe is
  expanding
• Hubble claimed the whole universe is expanding
• Furthermore, the speeds at which galaxies are
  receding from the earth is directly proportional
  to their distance from us
• This is called Hubbles Law

83
Hubbles Law, cont

• Hubbles Law can be written as v H R
• H is called Hubbles constant
• H 17 x 10-3 m / s ly

84
Remaining Questions About The Universe

• Will the universe expand forever?
• Today, astronomers are trying to determine the
  rate of expansion
• The universe seems to be expanding more slowly
  than 1 billion years ago
• It depends on the average mass density of the
  universe compared to a critical density
• The critical density is about 3 atoms / m3
• If the actual density is less than the critical
  density, the expansion will slow, but still
  continue
• If the actual density is more than the critical
  density, expansion will stop and contraction will
  begin

85
More Questions

• Missing mass in the universe
• The amount of non-luminous (dark) matter seems to
  be much greater than what we can see
• Various particles have been proposed to make up
  this dark matter
• Exotic particles such as axions, photinos and
  superstring particles have been suggested
• Neutrinos have also been suggested
• It is important to determine the mass of the
  neutrino since it will affect predictions about
  the future of the universe

86
Another Question

• Is there mysterious energy in the universe?
• Observations have led to the idea that the
  expansion of the universe is accelerating
• To explain this acceleration, dark energy has
  been proposed
• It is energy possessed by the vacuum of space
• The dark energy results in an effective repulsive
  force that causes the expansion rate to increase