Quarks

1
Quarks Leptons 4Quarks and antiquarks
Conservation rules

• Unit 1.1b4
• Breithaupt chapters 2.4 2.5
• pages 24 to 27

2
AS specification

• Up (u), down (d) and strange (s) quarks only.
• Properties of quarks charge, baryon number and
  strangeness.
• Combinations of quarks and antiquarks required
  for baryons (proton and neutron only),
  antibaryons (antiproton and antineutron only) and
  mesons (pion and kaon) only.
• Change of quark character in ß - and ß decay.
• Application of the conservation laws for charge,
  baryon number, lepton number and strangeness to
  particle interactions. The necessary data will be
  provided in questions for particles outside those
  specified.
• Breithaupt chapters 2.4 2.5 pages 24 to 27

3
Baryon number (B)(equivalent to lepton number)

• Conservation of baryon number
• In all interactions the total baryon number is
  conserved.
• You are expected to recall baryon numbers in the
  AS examination!

4
Sigma particles

• These are all baryons (B 1) and they all have
  rest energies of 1.97 GeV (about 2x the protons
  0.938 GeV)
• sigma-plus S
• charge 1 (equals proton charge)
• sigma-zero S0
• charge 0
• sigma-minus S (Note This is NOT the
  antiparticle of S )
• charge - 1
• Like all baryons they eventually decay into
  protons for example S ? n p - , after
  which the neutron decays into a proton

5
Use baryon numbers to check whether or not the
following strong force interactions can occur.
6
Answers
7
Strangeness number (S)

• The final reaction, strangely, does not in fact
  occur even though properties such as baryon
  number and charge are conserved.
• Some other predicted reactions also fail to occur
  with K mesons, sigma and other particles.
• To be able to predict what will and what will not
  happen a further property needs to be assigned to
  some particles called strangeness.
• The K meson, the first strange particle to be
  discovered, is defined to have a strangeness
  number of 1

• For the antiparticle K-, S - 1
• Following the K meson strangeness definition
  sigma particles all have strangeness of, - 1 and
  anti-sigma particles, 1
• Further subsequently discovered strange particles
  have been shown to have strange numbers between
  3 and 3
• Non-strange particles such as protons, neutrons,
  pions and all leptons have strangeness 0

8
Conservation of strangeness

• Strangeness is always conserved in all strong
  interactions (no leptons involved).
• Strangeness is not always conserved in weak
  interactions.

• Strangeness conserved
• S 0 0 ? -1 1
• Non-conservation of strangeness in a weak
  interaction
• S - 1 ? 0 0 0

K - ? p p - p -
9
Even more complication !

• Since the 1970s further particles discovered have
  be found to have other properties like
  strangeness that need to be conserved in
  interactions their names being charm, topness and
  bottomness.
• It became clear that baryons and mesons were not
  fundamental particles of matter (unlike leptons)
  but were composed of smaller particles now called
  quarks.
• This model for the composition of hadrons is
  called the Standard Model.

10
The Standard Model

• All hadrons consist of quarks
• Baryons (e,g. protons and neutrons) consist of
  three quarks
• Antibaryons (e.g. anti-protons) consist of three
  antiquarks
• Mesons (e.g. pions and kaons) consist of a quark
  and an antiquark

11
Quarks and antiquarks

• Quarks are currently thought to be fundamental
  particles.
• Quarks feel the strong interaction (unlike
  leptons)
• Quarks are never found in isolation but always in
  pairs or triplets.
• There are six types (flavours) of quarks and six
  corresponding antiquarks.
• Only two types are stable. They are called up (u)
  and down (d).

• Charm (c) and strange (s) quarks are more massive
  versions of the up and down quarks.
• Top (t) and bottom (b) quarks are more massive
  versions of the charm and strange quarks.
• Quarks can change type through the weak
  interaction.
• Only knowledge of the up, down and strange quarks
  is required for AS physics.

12
Properties of quarks(antiquarks have the same
mass but opposite charge, baryon number and
strangeness)
13
Protons and neutrons

• Protons consist of two up and one down quark
  (uud)
• Charge ? ? - ? 1
• Baryon number ? ? ? 1
• Neutrons consist of one up and two down quarks
  (udd)
• Charge ? - ? - ? 0
• Baryon number ? ? ? 1

14
Beta-minus decay

• With beta-minus decay a neutron (udd) changes
  into a proton (uud)
• This can be represented on a Fenyman diagram as a
  down quark changing into an up quark

Corrected from text book
15
Beta-plus decay

• With beta-plus decay a proton (uud) changes into
  a neutron (udd)
• This can be represented on a Fenyman diagram as
  an up quark changing into a down quark

Corrected from text book
16
Antiprotons and antineutrons

• Antiprotons consist of two up antiquarks and one
  down antiquark (uud)
• Charge - ? - ? ? -1
• Baryon number - ? - ? - ? -1
• Antineutrons consist of one up antiquark and two
  down antiquarks (udd)
• Charge - ? ? ? 0
• Baryon number - ? - ? - ? -1

17
Charged p-mesons

• These are made up of a quark and an antiquark
  pair made of of up and down quarks and antiquarks

• p ud
• charge ? ? 1
• B ? - ? 0
• p - ud
• charge - ? - ? -1
• B - ? ? 0

18
Uncharged p-mesons

• These are made up of a quark and an antiquark
  pair of up, down or strange quarks

• p 0 uu
• charge ? - ? 0
• B ? - ? 0
• S 0 0 0
• OR p 0 dd
• charge - ? ? 0
• B ? - ? 0
• S 0 0 0
• OR p 0 ss
• charge - ? ? 0
• B ? - ? 0
• S -1 1 0

19
K-mesons

• These combinations a strange quark along with an
  up or down quark
• normal particles
• K us (S 0 1 1)
• K0 ds
• antiparticles
• K- su (S 1 0 1)
• K0 ds

pions and kaons
20
Sigma particlesThese are baryons and so contain
three quarksComplete the table below

• sigma-plus S
• Quarks uus
• Charge ? ? - ? 1
• B ? ? ? 1
• S 0 0 1 1
• sigma-zero S0
• sigma-minus S
• Quarks dds
• Charge - ? - ? - ? 1
• B ? ? ? 1
• S 0 0 1 1

• anti-sigma-plus S
• anti-sigma-zero S0
• Quarks u d s
• Charge - ? ? ? 0
• B - ? - ? - ? 1
• S 0 0 1 1
• anti-sigma-minus S

21
Sigma particlesThese are baryons and so contain
three quarksCompleted table

• sigma-plus S
• Quarks uus
• Charge ? ? - ? 1
• B ? ? ? 1
• S 0 0 1 1
• sigma-zero S0
• Quarks uds
• Charge ? - ? - ? 0
• B ? ? ? 1
• S 0 0 1 1
• sigma-minus S
• Quarks dds
• Charge - ? - ? - ? 1
• B ? ? ? 1
• S 0 0 1 1

• anti-sigma-plus S
• Quarks u u s
• Charge - ? - ? ? 1
• B - ? - ? - ? 1
• S 0 0 1 1
• anti-sigma-zero S0
• Quarks u d s
• Charge - ? ? ? 0
• B - ? - ? - ? 1
• S 0 0 1 1
• anti-sigma-minus S
• Quarks d d s
• Charge ? ? ? 1
• B - ? - ? - ? 1
• S 0 0 1 1

22
Complete the table below
23
Answers
24
Interaction conservation rules

• All interactions must conserve
• ENERGY
• CHARGE
• LEPTON NUMBER TYPE
• BARYON NUMBER
• and with strong interactions only STRANGENESS

25
Quark annihilation interaction

• In quark terms the interaction is
• u u d u u d ? u d u d
• An up quark and an up antiquark annihilate each
  other in a strong force interaction producing two
  pions with the release of radiation.
• ENERGY mass-energy is converted into kinetic
  energy and photons
• CHARGE 1 1 1 1 conserved
• LEPTON NUMBER strong interaction no leptons
  involved
• BARYON NUMBER 1 1 0 0 conserved
• STRANGNESS NUMBER 0 0 0 0 conserved
• This reaction can occur.

26
Use the conservation rules to determine whether
or not the following interactions could occur.

• 1.
• 2.
• 3.

27
Answers

• 1.
• YES
• 2.
• NO Charge is not conserved
• 3.
• YES

28
Notes from Breithaupt pages 24 to 27

• Why is it necessary for some particles to be
  assigned a strangeness number. Show how the
  strangeness numbers for K-mesons and sigma
  particles are allocated.
• Copy table 1 on page 25. Define baryons,
  antibaryons and mesons in terms of quark
  composition.
• State the quark compositions of protons,
  neutrons, antiprotons and the three varieties of
  pion.
• Explain beta-minus and beta-plus decay in terms
  of quark change. Illustrate with Fenyman
  diagrams.
• Define what is meant by Baryon number. State the
  baryon numbers of quarks, antiquarks, protons,
  neutrons, antiprotons and mesons.
• List the conservation rules that must apply to
  all interactions. State how strangeness is
  exceptional.
• Give and explain an example of an interaction
  where quarks are annihilated.
• Try the summary questions on pages 25 27

29
Answers to the summary questions on page 25
30
Answers to the summary questions on page 27