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Department of Physics and
Astronomy
Option 212: UNIT 2
Elementary Particles
SCHEDULE
26-Jan-15 13.00pm LRB
28-Jan-15 12.00pm
LRB
(2-Feb-15 10.00am
4-Feb-15 12.00pm LRB
E
Intro lecture
Problem solving
Problem Workshop)
Follow-up
UNIT 2: OUTLINE SYLLABUS:
1st Lecture Introduction
Hadrons and Leptons
Spin & Anti-Particles
The conservation laws: Lepton Number
Baryon number
Strangeness
2nd Lecture Problem solving
Check a decay for violation of conservation laws
Quarks
Properties of a particle given quark combination
3rd Lecture Follow-up
Fundamental forces and field particles
The standard model
• State which of the following decays or reactions violates
one or more of the conservation laws, and give the law(s)
violated in each case:
• (a) p -> n + e+ + ne
• (b) n -> p + p• (c) e+ + e- -> g
• (d) p + p -> g + g
• (e) ne + p -> n + e+
(a) mp < mn : energy conservation is violated. Also Le=0 on lhs, but Le=-2 on rhs
(b) mn < mp + mp : energy conservation is violated
(c) Momentum conservation is violated: in pair annihilation, two photons (g rays)
must be emitted to conserve momentum
(d) Allowed
(e) Le=-1 on both sides, but mp < mn so energy conservation violated
• Consider the following decay chain:







W- -> X0 + pX0 -> S+ + e- + ne
p- -> m- + nm
S+ -> n + p+
p+ -> m+ + nm
m+ -> e+ + nm + ne
m- -> e- + ne + nm
• (a) are all the final products stable?
• (b) write the overall decay reaction for W- to the final
products
• (c) Check the overall decay reaction for the conservation of
electric charge, baryon number, lepton number, and
strangeness
• (a) neutron is not stable. Lifetime is 930s,
compared to 1031 years for proton.
– n -> p+ + e- + ne
• (b) simply add the particles up, including the
products of neutron decay
 W- -> p+ + e+ + 3e- + ne + 3ne + 2nm + 2nm
 (c) check answer to (b) for conservation of charge,
baryon number, lepton numbers, and strangeness.
Find all conserved except strangeness -3 -> 0
– In fact, DS = +/-1 is allowed in a decay that occurs via
weak interaction (Tipler p.1321)
True or false?
• (a) Leptons consist of three quarks
• (b) Mesons consist of a quark and an antiquark
• (c) The six flavors of quark are up, down,
charmed, strange, left and right
• (d) Neutrons have no charm
(a) False: leptons are fundamental particles e.g e(b) True
(c) False: there is no left and right quark, but there are top and
bottom quarks
(d) True: neutrons are made of udd quarks
Quark confinement
• No isolated quark has ever been observed
• Believed impossible to obtain an isolated quark
• If the PE between quarks increases with separation
distance, an infinite amount of energy may be required to
separate them
• When a large amount of energy is added to a quark system,
like a nucleon, a quark-antiquark pair is created
– Original quarks remain confined in the original system
• Because quarks always confined, their mass cannot be
accurately known
Quark color
•
•
•
Consider the W- particle, which consists of three strange quarks
Remember that quarks have spin ½
The W- has spin 3/2, so its three strange quarks must be arranged thus:
•
But Pauli exclusion principle forbids these identical (same flavor, same mag of
spin, same direction of spin) quarks occupying identical quantum states
The only way for this to work is if each quark possesses a further property,
color:
•
•
•
Quarks in a baryon always have these three colours, such that when combined
they are “color-less” ( qr , qy , qb )
In a meson, a red quark and its “anti-red” quark attract to form the particle
Field Particles
• In addition to the six fundamental leptons (e-, m-, t-, ne, nm, nt)
and six quarks, there are field particles associated with the
fundamental forces (weak, strong, gravity and electromagnetic)
• For example, the photon mediates the electro-magnetic
interaction, in which particles are given the property “charge”
– The theory governing electro-magnetic interactions at the quantum
level is called Quantum Electrodynamics (QED)
• Similarly, gravity is mediated by the graviton
– The “charge” in gravity is mass
– The graviton has not been observed
Field Particles
• The weak force, which is experienced by quarks and
leptons, is carried by the W+, W-, and Z0 Bosons
– These have been observed and are massive (~100 GeV/c2)
– The “charge” they mediate is flavor
• The strong force, which is experienced by quarks and
hadrons, is carried by a particle called a gluon
– The gluon has not been observed
– The “charge” is color
– The field theory for strong interactions (analagous to QED) is
called Quantum Chromodynamics (QCD)
Electroweak theory
• The electromagnetic and weak interactions are considered to be
two manifestations of a more fundamental electroweak
interaction
• At very high energies, >100GeV the electroweak interaction
would be mediated (or carried) by four Bosons: W+, W-, W0, and
B0
• The W0 and B0 cannot be observed directly
• But at ordinary energies they combine to form either the Z0 or the
massless photon
• In order to work, electroweak theory requires the existence of a
particle called the Higgs Boson
– The Higgs Boson was expected have a rest mass up to > 1TeV/c2
– Head-on collisions between protons at energies ~20TeV are required to
produce a Higgs Boson.Such energies can only be achieved by particle
accelerators like the Large Hadron Collider at CERN
– The Higgs Boson was found in July 2012 at CERN with a rest mass ~ 126
GeV/c2
The Standard Model
• The combination of the quark model, electroweak theory and QCD is
called the Standard Model
• In this model, the fundamental particles are the leptons, the quarks and
the force carriers (photon, W+, W- & Z0 Bosons and gluons)
• All matter is made up of leptons or quarks
– Leptons can only exist as isolated particles
– Hadrons (baryons and mesons) are composite particles made of quarks
• For every particle there is an anti-particle
• Leptons and Baryons obey conservation laws
• Every force in nature is due to one of four basic interactions:
– Strong, electromagnetic, weak and gravitational
• A particle experiences one of these basic interactions if it carries a
charge associated with that interaction
Properties of the basic interactions
Gravity
Weak
Electro- Strong
magnetic
Acts on
Mass
Flavor
Electric
charge
Particles
participating
All
Quarks,
leptons
Mediating
particle
Graviton W+, W-,
Z0
Electrical Quarks,
ly
Hadrons
charged
Photon
Gluon
Color
Grand Unified Theories (GUTs)
• In a GUT, leptons and quarks are considered to be two
aspects of a single class of particle
– Under certain conditions a quark could change into a lepton and
vice-versa
– Particle quantum numbers are not conserved
• These conditions are thought to have existed in the very
early Universe
– A fraction of a second after the Big Bang
– In this period a slight excess of quarks over anti-quarks existed,
which is why there is more matter than anti-matter in out Universe
today
• One of the predictions of GUTs is that the proton will
decay after 1031 years
– In order to observe one decay, a large number of protons must be
observed
– Such experiments are being attempted
Crib sheet
(or what you need to know to pass the exam)
• The zoo of particles and their properties
–
–
–
–
Leptons (e-, m-, t-, ne , nm, nt)
Hadrons (baryons and mesons)
Their anti-particles
The conservation laws and how to apply them (energy, momentum,
baryon number, lepton numbers, strangeness)
• Quarks and their properties
–
–
–
–
Flavors: up, down, strange, charm, top ,bottom
How to combine quarks to form baryons and mesons
Quark spin and color
The eight-fold way patterns
• Fundamental forces and field particles
• The standard model
• And from special relativity, its important to understand the concepts of
rest mass and energy, and the equations of conservation of relativistic
energy and momentum