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Particle Physics 2
Prof. Glenn Patrick
Quantum, Atomic and Nuclear Physics, Year 2
University of Portsmouth, 2012 - 2013
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Last Week - Recap
Particle Physics & Cosmology
Matter Particles, Generations
Spin – Fermions & Bosons
Charged Leptons
Antimatter
Neutral Leptons - Neutrinos
Hadrons
Strange Particles and Strangeness
Symmetries, Conservation Laws
Quantum Numbers, Isospin
Eightfold Way and Quark Model
Charm, Bottom, Top, Quark Counting
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Today’s Plan
BOOKS
20 November Particle Physics 2
B.R. Martin & G. Shaw,
Force Carriers
Particle Physics, 3rd Edition,
Four Fundamental Interactions
Wiley
Quantum Field Theory
Donald H. Perkins,
Introduction to High Energy
Feynman Diagrams
Physics, 4th edition, CUP
Higher Orders/Radiative Corrections
Coughlan et al, The Ideas of
Anomalous magnetic moment of muon Particle Physics, Cambridge
Charged and Neutral Currents
Z and W Vector Bosons
Gluons
Colour Charge and Quantum Chromodynamics (QCD)
Unification of Fundamental Forces,
Running Coupling Constants
Higgs Boson and Field
Copies of Lectures:
http://hepwww.rl.ac.uk/gpatrick/portsmouth/courses.htm
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I
II
III
Observed in
2000
4
Force Carriers
Last week we looked at the Matter
Particles (quarks and leptons).
This week we look at the four gauge
bosons that make up the Force Particles.
Now the smallest Particles of Matter may
cohere by strongest Attractions, and
compose bigger Particles of weaker Virtue.
There are therefore Agents in Nature able
to make Particles of Bodies stick together
by very strong Attractions. And it is the
business of experimental Philosophy to find
them out.
ISAAC NEWTON (1680)
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The Four Forces of Nature
STRONG
WEAK
ELECTRO MAGNETIC
GRAVITY
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Forces in Classical Physics
Classically, forces are described by charges and fields
Field is a physical quantity which has a value for each point in space-time.
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Can be a scalar or vector field.
Quantum Field Theory
Quantum Mechanics + Relativity
Forces are transmitted by
exchange of force particles
between matter particles.
4 forces with different force
particles.
Heisenberg
Uncertainty Principle
Energy ΔE is “borrowed for a time Δt
Maximum distance of exchange particle
Et  
t   E
x  ct   Mc
1
Range of Force 
mass of exchange particle
Photon has zero mass,
so infinite range
If we associate M with the pion mass, we get the Yukawa potential that we saw
8
when we talked about the “nuclear force” in Nuclear Physics 1.
Four Forces of Nature
STRONG FORCE
ELECTROMAGNETIC FORCE
Strength: 1, Range: 10-15 m
Exchange: Gluon
Strength: 1/137, Range: Infinite
Exchange: Photon
A FIFTH FORCE?
GRAVITY
WEAK FORCE
Strength: 6x10-39 m,
Range: Infinite, Exchange: ?
Strength: 10-6 m, Range: 10-18 m
Exchange: W±, Z0
Modified gravity?
Dark matter,
Dark energy, etc.
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g S2
S 
~1
4c
 EM
e2
1

~
4c 137
GF m 2p ~ 10 5
10
GN m 2p ~ 10 36
Fundamental Interactions
e-
EM
e-
Strong
u
u

e-
e
Weak
gluon
e-
d
d
Z0
e-
ee-
WWeak
n
d
d
u
e
u
d
u
e
p
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Feynman Diagrams
electron
At each ‘vertex’ charge is
conserved. Heisenberg
Uncertainty Principle allows
energy borrowing.

Virtual Particle
Does not have mass of a
physical particle.
m X2  E X2  p X2
Richard Feynman
Quantum Electrodynamics
(QED)
Known as “off –mass shell”
(e.g. not zero for photon)
positron
(anti-electron)
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Feynman Diagrams
Annihilation
Exchange
 External legs represent amplitudes of initial and final state
particles.
 Positron is drawn as electron travelling backwards in time.
 Internal lines (propagators) represent amplitude of
exchanged particle.
 Charge, baryon number and lepton number conserved at
each vertex. Quark flavour conserved for strong and EM
interactions.
 Vertices represent coupling strength of interacting
particles.
 Perturbation theory. Expand and keep the most important
terms for calculations.
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Feynman Diagrams
Associate each vertex with the square root of the appropriate
coupling constant, i.e. √𝛼.
When the amplitude is squared to yield a cross-section
there will be a factor 𝛼 𝑛 ,
where n is the number of vertices (known as the “order” of the diagram).
For QED:
Lowest order
Second order
e2
1


4c 137
Add the amplitudes from all possible diagrams to get the total amplitude,
M, for a process  transition probability.
2
2
Transition Rate 
M  (phase space)

Fermi’s Golden Rule
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Bhabha Scattering
 
 
e e e e
4 Born Diagrams (Electroweak)
e-

Amplitude =
e-
e-
eZ0
+
e+
e+
e-
+
e+
e+
e+

e-
e-
eZ0
+
e+
e+
e+
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Radiative Corrections
Higher Order Quantum Loop Diagrams (QED only)
Vacuum polarisation
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Anomalous Magnetic Moment of the Muon
Dirac theory predicts g=2, but this is modified
by quantum fluctuations.
e+
e-
QED
e+
e+
e-
B
Z0
WEAK
µ
µ
µ
µ
W
µ
W
e-
3rd order corrections
e+
e-
+ STRONG
Radiation and re-absorption of virtual photons
contributes an anomalous magnetic moment.
1

a   ( g  2) 
 0.00116 Lowest order
correction
2
2
a (exp)  116592089 10 11 (0.54 ppm)
a (the)  116591802 10 11 (0.42 ppm)
a  287  80 10 11
~3.6σ effect
New Physics?
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Hundreds of diagrams!
Muon g-2: Testing the Standard Model
athe  aQED  ahad  aweak  anew
Experimental
measurements of aμ
Beyond the
Standard Model
(BSM) Physics?
Uncertainty on aμ and physics
reach as the uncertainty has
decreased.
J.P. Miller et al,
Ann. Rev. Nucl. Part. Sci., 62 (Nov. 2012), 237
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Photon – EM Boson
1900 Planck Black Body Radiation
explained in terms of light quanta
 Nobel Prize.
Quantum energy of photon
E  h
h = Planck’s constant
 = frequency
1905 Einstein explained the
Photoelectric Effect in terms of
quanta of energy
 Nobel Prize.
1925 G.N. Lewis proposed the
name Photon for quanta of light.
1925 Compton showed quantum
(particle) nature of X-rays
 Nobel Prize.
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Charged and Neutral Currents
   N    X

  N    X


W+
Z0
N
-
X
Neutral Current
N
X
Charged Current
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Discovery of Weak Neutral Currents (1973)
Bremsstrahlung effects
electron

   e     e
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Gargamelle Bubble Chamber
Z and W Story
Carlo Rubbia (UA1)
Two Experiments:
UA1 and UA2.
Rubbia came up with
idea and led UA1.
1984
Simon van der Meer
Super Proton
Synchrotron turned
into proton-antiproton
collider. Stochastic
cooling technique.
UA1
UA2
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W Boson Discovery – UA1 (1982)
𝒑 + 𝒑 → 𝑾± + 𝑿
𝑾± → 𝒆± + 𝝂(𝝂)
“Missing Energy” = neutrino
Type equation here.
electron
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Z Boson Discovery – UA1 (1983)
𝒑 + 𝒑 → 𝒁𝟎 + 𝑿
𝒁𝟎 → 𝒆+ + 𝒆−
electron
positron
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Weak Charged Current and Quarks
Flavour Changing Charged Currents.
Quark flavour never changes except by
weak interactions that involve W±
bosons.
u
d
c
s
t
b
+ ..
W
W
W
tbcsud
 decay finally understood!
W-
n
d
d
u
In decay processes,
quark always decays to
lighter quark to conserve
energy.
u
d
u
e
p
Weak charged current
changes lepton and quark
flavours.
Possible that flavour
changing neutral currents
exist beyond (tree level)
Standard Model. 25
Gluon Discovery (1979)
PETRA e+e- Collider, DESY, Hamburg
JADE, TASSO, MARK-J, PLUTO
 
e e  qq g
Third jet produced by
gluon bremsstrahlung
3-Jet Event
quark
anti-quark
gluon
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Inside the Proton
There are 3 “valence” quarks
inside the proton bound together
by gluons.
Quantum theory allows quarks to
change into quark-antiquark pairs
for a short time.
There is a bubbling “sea” of
gluons,
quarks and antiquarks.
There is however a problem with the basic quark model…..
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Colour Charge
Some particles apparently contain quarks in the same state
 violates Pauli Exclusion Principle (e.g. ++ = uuu).
Proposed that quarks carry an extra quantum number
called “colour”.
Red
Green
Blue
Quarks
Cyan
Magenta
Yellow
Anti-quarks
All physical particles are colour neutral or “white”.
baryon
meson
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Quark Species
quarks
antiquarks
u u
d d
c c
u
d
c
s s
t t
b b
s
t
b
u
up
down d
charm c
strange s
top
t
bottom b
u
u
d
c
d
c
s
s
t t
b b
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8 Interacting Gluons
Expect 9 gluons from all combinations (3 colours x 3 anti-colours):
rb, rg, gr, gb, bg, br, rr, gg, bb
However, real gluons are a linear combinations of states.
This combination is
colourless and
symmetric.
Does not take part in
the strong interaction.
rr  bb  gg
3
rr  bb  2 gg
6
rr  bb
2
Hence, we have 8 gluons. These two plus
those from 𝑟𝑏, 𝑟𝑔, 𝑔𝑟, 𝑔𝑏, 𝑏𝑔, 𝑏𝑟
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Counting Colours
In Particle Physics 1, we counted quarks. Can also count colours using R.
below top
energy
threshold
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Quantum Chromodynamics (QCD)
Quantum Chromodynamics (QCD) is the theory of the
Strong Interaction in the Standard Model.
Gluons carry colour+anti-colour
charge, e.g. red-anti blue.
Colour charge always conserved
so quarks can change colour when
emitting a gluon.
Since gluons (8) carry colour charge,
they can interact with one another!
Fragmentation
If a quark is pulled from a neighbour,
the colour field “stretches”.
At some point, it is easier for the field
to snap into two new quarks.
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Confinement
Confinement
Confinement is a property of the strong force.
The strong force works by gluon exchange,
but at “large” distance the self-interaction of the gluons
breaks the inverse square-law forming “flux tubes”:
Quarks and gluons carry “colour “ quantum numbers
analogous to electric charge –
but only “colourless” objects like baryons (3-quark states)
and mesons (quark-antiquark states) escape confinement.
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Quark Interactions
Only one pair of quarks interact, the rest are spectators.
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Residual Forces
How do molecules form if
atoms are electrically neutral?
Residual EM Force
Electrons in one atom are
attracted to protons in another
atom.
How do protons bind to form
the nucleus? Protons & neutrons
are colour neutral.
Residual Strong Interaction
between quarks in different
protons overcomes EM
repulsion.
35
Force Particles
Bosons = Spin 1
Force
Particle Charge
Mass
(GeV)
0
Strong
gluon (g)
0
EM
photon ()
0
0
Weak
Z0 boson
W boson
0
1
91.2
80.4
Relative
Strength
1
Range
(m)
10-15
1/137
infinite
10-5
10-18
Bosons = Spin 2
Gravity
graviton
0
(not observed yet!)
0
10-39
infinite
36
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Particles and Forces
Summary of how different particles feel the different forces:
u quark
d quark
electron
e
c quark
s quark
muon

t quark
b quark
tau

Charge
+2/3
-1/3
-1
0
+2/3
-1/3
-1
0
+2/3
-1/3
-1
0
Strong
Yes
Yes
No
No
Yes
Yes
No
No
Yes
Yes
No
No
EM
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Weak
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
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Unification of the Forces
Grand Unification – Unite strong
interaction with electroweak
interaction.
Grand Unified Theories (GUTs)
predict that protons are unstable.
~Planck scale
Final step would then be to add
quantum gravity to form a Theory
of Everything (TOE).
Because gravitons interact with
one another field theory is nonre-normalisable. Graviton has
not been discovered!
Planck Units
Length
Time
Energy
Temp
1.62 x 10-35 m
5.39 x 10-44 s
19
2
1.22 x 10
3832 GeV/c
38
1.42 x 10 K
Electroweak Force
or EW symmetry breaking
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Running Coupling Constants
e2
at low
energy
1


4 0 c 137.035999074
GF M 2 c
5
~
1
.
03

10
Weak  W 
3
g S2 ( E )
~1
Strong  S ( E ) 
c
GN M 2
 40
~ 5 10
Gravity  g 
4c
EM coupling constant
𝛼 = fine structure constant
Coupling constants have an energy dependence due to (higher
order) virtual interactions.
These change the measured value of the coupling constant and
make it depend on the energy scale at which it is measured
(logarithmic dependence).
The strong and weak couplings decrease with energy whilst the EM
coupling increases.
It is therefore possible that at some energy scale, all 3 forces
40
become equal.
Grand Unification
 Grand-Unified Theories (GUT), favoured,
(e.g. by non-zero 𝜈 masses) predict the 3
coupling constants (QED, Weak, QCD) to
unify at GUT scale of 3x1016 GeV.
 This unification does not happen in the
Standard Model (+GUT), but does in
Supersymmetry with a 1 TeV scale.
 Starting from the measured values of
αQED(mZ) and sin2W as input, one can
predict:
 S (mZ )  0.073  0.002 (Standard GUT)
 S (mZ )  0.129  0.010 (SUSY GUT)
Standard Model + GUT
LEP, Amaldi et al, 1991
To be compared to the experimental
value (mostly constrained by LEP):
 S (mZ )  0.118  0.003
 Baryon Number violated in GUTs.
Conflict with measurements?
 ( p  e  0 )  1034 yrs (SuperK)
SUSY at 1 TeV + GUT
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Missing Ingredient: Higgs Sector
Generates mass?
Graviton
not yet found
42
The Mystery of Mass
The masses of composite
particles like protons and
neutrons are mainly given by the
motion of the constituents.
u
d
However, for fundamental
particles, like electrons and
quarks it has long been a
mystery how they acquire their
masses and why they are so
different.
u
Why do some particles
have large masses
whilst others have little
or no mass?
W
Electron
Mass = 511 eV
W boson
Mass = 80 x 109 eV
Photon
Mass < 10-18 eV
e
Neutrino
Mass < 2 eV
43
Top Quark Heavier than Silver Atom!
M(top) = 172 GeV ± 0.9 ± 1.3 GeV
Silver
(A=108)
44
Higgs Mechanism
Standard Model in basic form leads to massless particles.
1961- 1968: Glashow, Weinberg & Salam developed
theory that unifies EM and weak forces into one
electroweak force. Predicted weak neutral current.
Nobel Prize: 1979
1964: Higgs, Kibble, Brout, Englert et al introduced
the Higg’s field. Gives mass to Z and W bosons.
Nobel Prize: ??
Peter Higgs
1971: Veltman, t Hooft - Solved the problems of
infinities through renormalisation.
Nobel Prize: 1999

Higgs boson is a neutral, scalar (spin=0) particle.

Coupling to particles is proportional to their mass.

No prediction for Higgs mass.

Vacuum should be filled with Higgs field – boson is the quantum of this field
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in the same way that the photon is the quantum of the EM field.
Space is not Empty
The classical vacuum just consists of empty space-time and is featureless.
In reality, it’s sea of virtual particle-antiparticle pairs from quantum fluctuations.
Vacuum is the state of minimum energy for the Universe.
WARNING: Quantum field theory gives
cosmological constant (or zero point energy)
120 orders of magnitude too high!
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Higgs Field and Higgs Boson
Higg’s Boson
H
H
H
H
H
H
H
H
H
H
H
H
H
Higg’s Field
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Mexican Hat Potential
State in which the Higgs field is zero is not the lowest energy state.
EM - Electric & Magnetic Fields
(Vector)
Energy lowest when
field is zero.
EW - Higgs Field
(Scalar)
Energy lowest when
field is not zero.
Law is basically symmetric, but equilibrium state is not.
Symmetry is said to be spontaneously broken.
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Electroweak Symmetry Breaking
At high enough
temperatures, particles
were (symmetrically)
massless.
As the Universe cooled, ring
of stable points appeared.
W and Z got mass from the
field, but the  stayed
massless.
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Higgs Hunting
Indirect
Fit to LEP EW Measurements
Direct Searches
at LEP Collider
f
e-
f
Z*
Z0
H
e+
f
f
mH  114.4 GeV (95% CL)
Also, limits from Tevatron
Preferred Value 
29
94
- 24
GeV
mH  185 GeV (95% CL)50
Higgs Particle Discovery?
4 Jul 2012, CERN
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Francois Englert & Peter Higgs
𝑯 → 𝜸𝜸 𝑪𝒉𝒂𝒏𝒏𝒆𝒍
Higgs does not couple to zero mass photon.
Possible via a top quark loop.
CMS
ATLAS
Phys. Lett. B 716 (17 Sept 2012), Issue 1
52
𝑯 → 𝒁𝒁∗ → 𝟒ℓ 𝑪𝒉𝒂𝒏𝒏𝒆𝒍
ℓ 𝒎𝒆𝒂𝒏𝒔 𝒍𝒆𝒑𝒕𝒐𝒏
ATLAS
Phys. Lett. B 716 (17 Sept 2012), Issue 1
CMS
53
Higgs Particle – Properties?
MASS
M H  126.0  0.4( stat )  0.4( sys) GeV ATLAS
M H  125.3  0.4( stat )  0.5( sys) GeV CMS
Phys. Lett. B 716 (17 Sept 2012), Issue 1
Spin/Parity of Standard Model Higgs is expected to be JP = 0+
Spin 0 consistent with decay channels seen so far.
Spin 1 already ruled out.
The first scalar elementary particle.
54
Higgs Spin
Spin is quantised and measured wrt an axis. Sz = -S, -S+1, -S+2, … +S-1, +S
However, photon is massless, so in this case Sz can only be +1 or -1
c/o Aidan Randle, ATLAS
ATLAS and CMS will need to do a proper spin analysis by analysing angular
55
distributions of decay products to get the definitive answer.
Beyond the Standard Model?
● 18 input parameters from
experiment (e.g. particle masses,
coupling constants).
● Gravity not included. Hierarchy
problem.
● Why 3 generations of particles?
● Are these particles fundamental?
● What is mass? (Higg’s particle)

● Missing antimatter?
● Missing matter (dark matter &
dark energy)?
● Neutrino masses.
● Cosmological constant predicted
56
to be 10120 too large for vacuum.
End
CONTACT
Professor Glenn Patrick
email: [email protected]