Department of Physics and
Astronomy
SCHEDULE
26-Jan-15 13.00pm LRB
28-Jan-15 12.00pm
LRB
Intro lecture
Problem solving
(2-Feb-15 10.00am
E Problem Workshop)
4-Feb-15 12.00pm LRB 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 + + n e
• (b) n -> p + p -
• (c) e + + e -> g
• (d) p + p -> g + g
•
(e) n e
+ p -> n + e +
(a) m p
< m n
: energy conservation is violated. Also L e
=0 on lhs, but L e
=-2 on rhs
(b) m n
< m p
+ m p
: 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) L e
=-1 on both sides, but m p
< m n so energy conservation violated

• Consider the following decay chain:
 W -> X 0 + p -
 X 0 -> S + + e + n e
 p -> m + n m
 S + -> n + p +
 p + -> m + + n m
 m + -> e + + n m
 m -> e + n e
+ n e
+ n m
•
(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 10 31 years for proton.
– n -> p + + e + n e
• (b) simply add the particles up, including the products of neutron decay
 W -> p + + e + + 3e + n e
+ 3 n e
+ 2 n m
+ 2n m
 ( c) check answer to (b) for conservation of charge, baryon number, lepton numbers, and strangeness.
Find all conserved except strangeness -3 -> 0
– In fact, D
S = +/-1 is allowed in a decay that occurs via weak interaction (Tipler p.1321)

•
•
•
•
(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

• 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

• 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 ” ( q r
, q y
, q b
)
• In a meson, a red quark and its “ anti-red ” quark attract to form the particle

•
In addition to the six fundamental leptons (e , m , t , n e
, n m
, n t
) 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

•
The weak force, which is experienced by quarks and leptons, is carried by the W + , W , and Z 0 Bosons
– These have been observed and are massive (~100 GeV/c 2 )
– 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)

•
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 , W 0 , and
B 0
•
The W 0 and B 0 cannot be observed directly
•
But at ordinary energies they combine to form either the Z 0 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/c 2
– 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/c 2

•
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 & Z 0 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

Acts on
Gravity Weak Electromagnetic
Strong
Mass Flavor Electric charge
Color
Particles participating
Mediating particle
All Quarks, leptons
Graviton W + , W ,
Z 0
Electrical ly charged
Quarks,
Hadrons
Photon Gluon

•
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 10 31 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 , n e
, n m
, n t
)
– 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