Particle Physics 2. Prof. Glenn Patrick . Quantum, Atomic and Nuclear Physics, Year 2 University of Portsmouth, 2012  2013. Last Week  Recap. Particle Physics & Cosmology Matter Particles, Generations Spin – Fermions & Bosons Charged Leptons Antimatter Neutral Leptons  Neutrinos
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Prof. Glenn Patrick
Quantum, Atomic and Nuclear Physics, Year 2
University of Portsmouth, 2012  2013
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
20 November Particle Physics 2
Force Carriers
Four Fundamental Interactions
Quantum Field Theory
Feynman Diagrams
Higher Orders/Radiative Corrections
Anomalous magnetic moment of muon
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
BOOKS
B.R. Martin & G. Shaw, Particle Physics, 3rd Edition, Wiley
Donald H. Perkins, Introduction to High Energy Physics, 4th edition, CUP
Coughlan et al, The Ideas of Particle Physics, Cambridge
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)
Classically, forces are described by charges and fields
Field is a physical quantity which has a value for each point in spacetime.
Can be a scalar or vector field.
Forces are transmitted by exchange of force particles between matter particles.
4 forces with different force particles.
Quantum Mechanics + Relativity
Heisenberg
Uncertainty Principle
Energy ΔE is “borrowed for a time Δt
Maximum distance 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 when we talked about the “nuclear force” in Nuclear Physics 1.
STRONG FORCE
Strength: 1, Range: 1015 m
Exchange: Gluon
ELECTROMAGNETIC FORCE
Strength: 1/137, Range: Infinite
Exchange: Photon
A FIFTH FORCE?
GRAVITY
Strength: 6x1039 m,
Range: Infinite, Exchange: ?
WEAK FORCE
Strength: 106 m, Range: 1018 m
Exchange: W±, Z0
Modified gravity?
Dark matter,
Dark energy, etc.
electron
At each ‘vertex’ charge is conserved. Heisenberg Uncertainty Principle allows energy borrowing.
Virtual Particle
Does not have mass of a physical particle.
Known as “off –mass shell”
(e.g. not zero for photon)
Richard Feynman
Quantum Electrodynamics (QED)
positron
(antielectron)
Exchange
Annihilation
Associate each vertex with the square root of the appropriate
coupling constant, i.e. .
When the amplitude is squared to yield a crosssection
there will be a factor ,
where n is the number of vertices (known as the “order” of the diagram).
For QED:
Lowest order
Second order
Add the amplitudes from all possible diagrams to get the total amplitude, M, for a process transition probability.
Fermi’s Golden Rule
+
e
QED

e
B
µ
µ
0
Z
µ
µ
WEAK
W
W
µ
+
e
+
e
+
e

e


e
e
3rd order corrections
Dirac theory predicts g=2, but this is modified
by quantum fluctuations.
+ STRONG
Radiation and reabsorption of virtual photons contributes an anomalous magnetic moment.
Lowest order correction
~3.6σ effect
New Physics?
Hundreds of diagrams!
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
Quantum energy of photon
h = Planck’s constant
= frequency
1900Planck Black Body Radiation explained in terms of light quanta
Nobel Prize.
1905Einstein explained the
Photoelectric Effectin terms of quanta of energy
Nobel Prize.
1925G.N. Lewisproposed the name Photon for quanta of light.
1925Compton showed quantum (particle) nature of Xrays
Nobel Prize.
Carlo Rubbia (UA1)
Simon van der Meer
Two Experiments:
UA1 and UA2.
Rubbia came up with idea and led UA1.
Super Proton Synchrotron turned into protonantiproton collider. Stochastic cooling technique.
1984
UA1
UA2
t
b
u
d
c
s
W
W
W
W
d
n
d
e
u
u
d
p
u
Flavour Changing Charged Currents.
Quark flavour never changes except by weak interactions that involve W± bosons.
In decay processes,
quark always decays to
lighter quark to conserve energy.
t b c s u d
+ ..
decay finally understood!
Weak charged current changes lepton and quark flavours.
Possible that flavour changing neutral currents exist beyond (tree level) Standard Model.
PETRA e+e Collider, DESY, Hamburg
JADE, TASSO, MARKJ, PLUTO
Third jet produced by
gluon bremsstrahlung
3Jet Event
quark
antiquark
gluon
There are 3 “valence”quarks
inside the proton bound together
by gluons.
Quantum theory allows quarks to
change into quarkantiquark 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…..
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”.
Green
Blue
Red
Quarks
Cyan
Magenta
Yellow
Antiquarks
All physical particles are colour neutral or “white”.
baryon
meson
Expect 9 gluons from all combinations (3 colours x 3 anticolours):
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.
Hence, we have 8 gluons. These two plus those from , , , , ,
In Particle Physics 1, we counted quarks. Can also count colours using R.
below top energy threshold
Gluons carry colour+anticolour
charge, e.g. redanti blue.
Colour charge always conserved
so quarks can change colour when
emitting a gluon.
Quantum Chromodynamics (QCD)is the theory of the
Strong Interaction in the Standard Model.
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.
Confinement
Confinement is a property of the strong force.
The strong force works by gluon exchange,
but at “large” distance the selfinteraction of the gluons
breaks the inverse squarelaw forming “flux tubes”:
Quarks and gluons carry “colour “ quantum numbers
analogous to electric charge –
but only “colourless” objects like baryons (3quark states)
and mesons (quarkantiquark states) escape confinement.
Only one pair of quarks interact, the rest are spectators.
How do molecules form if
atoms are electrically neutral?
How do protons bind to form
the nucleus? Protons & neutrons
are colour neutral.
Residual EM Force
Electrons in one atom are attracted to protons in another atom.
Residual Strong Interaction
between quarks in different protons overcomes EM
repulsion.
Bosons = Spin 1
Force Particle Charge Mass Relative Range
(GeV) Strength (m)
Strong gluon (g) 0 0 1 1015
EM photon () 0 0 1/137infinite
Weak Z0 boson 091.2 105 1018
W boson 180.4
Bosons = Spin 2
Gravity graviton 0 0 1039 infinite
(not observed yet!)
Summary of how different particles feel the different forces:
Charge Strong EM Weak
u quark +2/3 Yes Yes Yes
d quark 1/3 Yes Yes Yes
electron 1 No Yes Yes
e 0 No No Yes
c quark +2/3 Yes Yes Yes
s quark 1/3 Yes Yes Yes
muon 1 No Yes Yes
0 No No Yes
t quark +2/3 Yes Yes Yes
b quark 1/3 Yes Yes Yes
tau 1 No Yes Yes
0 No No Yes
Grand Unification – Unite strong interaction with electroweak interaction.
Grand Unified Theories (GUTs) predict that protons are unstable.
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 nonrenormalisable. Graviton has not been discovered!
~Planck scale
Planck Units
Length 1.62 x 1035 m
Time 5.39 x 1044 s
Energy 1.22 x 1019 GeV/c2
Temp 1.42 x 1032 K
or EW symmetry breaking
at low
energy
EM coupling constant
= fine structure constant
Weak
Strong
Gravity
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 become equal.
Standard Model + GUT
LEP, Amaldi et al, 1991
SUSY at 1 TeV + GUT
The masses of composite
particles like protons and neutrons are mainly given by the motion of the constituents.
u
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.
d
u
Proton
Why do some particles
have large masses
whilst others have little
or no mass?
W
Electron
Mass = 511 eV
Photon
Mass < 1018 eV
e
W boson
Mass = 80 x 109 eV
Neutrino
Mass < 2eV
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: ??
1971: Veltman, t Hooft  Solved the problems of infinities through renormalisation.
Nobel Prize: 1999
Peter Higgs
The classical vacuum just consists of empty spacetime and is featureless.
In reality, it’s sea of virtual particleantiparticle 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!
State in which the Higgs field is zero is not the lowest energy state.
EW  Higgs Field
(Scalar)
EM  Electric & Magnetic Fields
(Vector)
Energy lowest when
field is zero.
Energy lowest when
field is not zero.
Law is basically symmetric, but equilibrium state is not.
Symmetry is said to be spontaneously broken.
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.
f
f
e
Z*
Z0
H
e+
f
f
Indirect
Fit to LEP EW Measurements
Direct Searches
at LEP Collider
Also, limits from Tevatron
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
MASS
Phys. Lett. B 716 (17 Sept 2012), Issue 1
Spin/Parity of Standard Model Higgs is expected to be J 0+
Spin 0 consistent with decay channels seen so far.
Spin 1 already ruled out.
The first scalar elementary particle.
Spin is quantised and measured wrt an axis. Sz = S, S+1, S+2, … +S1, +S
c/o Aidan Randle, ATLAS
ATLAS and CMS will need to do a proper spin analysis by analysing angular distributions of decay products to get the definitive answer.