30'9 Conservation Laws

1
30.9 Conservation Laws

• A number of conservation laws are important in
  the study of elementary particles
• Two new ones are
• Conservation of Baryon Number
• Conservation of Lepton Number

2
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
• The sum of the baryon numbers before a reaction
  or a decay must equal the sum of baryon numbers
  after the process

3
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 a reaction or a decay must equal the sum
  of the electron-lepton number after the process

4
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

5
Which of the following reactions cannot occur?
QUICK QUIZ 30.2
6
(a). This reaction fails to conserve charge and
cannot occur.
QUICK QUIZ 30.2 ANSWER
7
30.10 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 (10-10-10-8 s) than
  particles decaying via strong interactions (10-23
  s)

8
Strangeness

• To explain these unusual properties, a new law,
  the conservation of strangeness was introduced
• Also needed a new quantum number, S
• The Law of Conservation of Strangeness states
  that the sum of strangeness numbers before a
  reaction or a decay 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

9
Bubble ChamberExample

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

10
30.11 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

11
An Eightfold Way for Baryons

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

12
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

13
30.12 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

14
Original Quark Model

• Three types
• u up
• d down
• s originally sideways, now 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
• All ordinary matter consists of just u and d
  quarks

15
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

16
Additions to the Original Quark Model Charm

• Another quark was needed to account for some
  discrepancies between predictions of the model
  and experimental results
• 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

17
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 ? meson in 1977
• t quark was found in 1995 at Fermilab

18
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

19
30.13 Colored Quarks

• Isolated quarks
• Physicist now believe that quarks are permanently
  confined inside ordinary particles
• No isolated quarks have been observed
  experimentally
• The force between quarks is called the color
  force
• Color force increases with increasing distance
• This prevents the quarks from becoming isolated
  particles

20
Colored Quarks

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

21
Quark Structure of a Meson

• A red quark is attracted to an antired quark
• The quark antiquark pair forms a meson
• The resulting meson is colorless

22
Quark Structure of a Baryon

• Quarks of different colors attract each other
• The quark triplet forms a baryon
• The baryon is colorless

23
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 carried by
  gluons
• Gluons are massless particles
• There are 8 gluons, all with color charge
• When a quark emits or absorbs a gluon, its color
  changes

24
More About Color Charge

• Like colors repel and unlike colors attract
• Different colors attract, but not as strongly as
  a color and its opposite colors of quark and
  antiquark
• The color force between color-neutral hadrons
  (like a proton and a neutron) 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

25
QCD Explanation of a Neutron-Proton Interaction

• Each quark within the proton and neutron is
  continually emitting and absorbing virtual gluons
• Also creating and annihilating virtual
  quark-antiquark pairs
• When close enough, these virtual gluons and
  quarks can be exchanged, producing the strong
  force

26
30.14 Weak Interaction

• The weak interaction is an extremely short-ranged
  force (10-18 m)
• This short range implies the mediating particles
  are very massive
• The weak interaction is responsible for the decay
  of c, s, b, and t quarks into lighter, more
  stable u and d quarks
• Also responsible for the decay of ? and ? leptons
  into electrons

27
Weak Interaction, cont.

• The weak interaction is very important because it
  governs the stability of the basic matter
  particles
• The weak interaction is not symmetrical
• Not symmetrical under mirror reflection
• Not symmetrical under charge exchange

28
Electroweak Theory

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

29
The Standard Model

• Combination of the electroweak theory and QCD
  forms 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

30
The Standard Model Chart
31
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

32
Grand Unification Theory (GUT)

• Builds on the success of the electroweak theory
• Attempted to combine electroweak and strong
  interactions (QCD)
• One version considers leptons and quarks as
  members of the same family
• They are able to change into each other by
  exchanging an appropriate particle

33
30.15 The Big Bang

• This theory of cosmology states that during the
  first few minutes after the creation of the
  universe all four interactions were unified
• All matter was contained in a quark soup
• As time increased and temperature decreased, the
  forces broke apart
• Starting as a radiation dominated universe, as
  the universe cooled it changed to a matter
  dominated universe

34
A Brief History of the Universe
35
Cosmic Background Radiation (CBR)

• CBR is represents the cosmic glow left over
  from the Big Bang
• The radiation had equal strengths in all
  directions
• The curve fits a blackbody at 3K
• There are small irregularities that allowed for
  the formation of galaxies and other objects

36
30.16 Connection Between Particle Physics and
Cosmology

• Observations of events that occur when two
  particles collide in an accelerator are essential
  to understanding the early moments of cosmic
  history
• There are many common goals between the two fields

37
Some Questions

• Why so little antimatter in the Universe?
• Do neutrinos have mass?
• Is it possible to unify electroweak and strong
  forces?
• Why do quark and leptons form similar but
  distinct families?
• Why do quarks carry fractional charge?
• What determines the masses of fundamental
  particles?
• Do leptons and quarks have a substructure?