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
Particle Physics 2
Prof. Glenn Patrick
Quantum, Atomic and Nuclear Physics, Year 2
University of Portsmouth, 2012 - 2013
Particle Physics & Cosmology
Matter Particles, Generations
Spin – Fermions & Bosons
Neutral Leptons - Neutrinos
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
Four Fundamental Interactions
Quantum Field Theory
Higher Orders/Radiative Corrections
Anomalous magnetic moment of muon
Charged and Neutral Currents
Z and W Vector Bosons
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
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 space-time.
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
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.
Strength: 1, Range: 10-15 m
Strength: 1/137, Range: Infinite
A FIFTH FORCE?
Strength: 6x10-39 m,
Range: Infinite, Exchange: ?
Strength: 10-6 m, Range: 10-18 m
Exchange: W±, Z0
Dark energy, etc.
At each ‘vertex’ charge is conserved. Heisenberg Uncertainty Principle allows energy borrowing.
Does not have mass of a physical particle.
Known as “off –mass shell”
(e.g. not zero for photon)
Quantum Electrodynamics (QED)
Associate each vertex with the square root of the appropriate
coupling constant, i.e. .
When the amplitude is squared to yield a cross-section
there will be a factor ,
where n is the number of vertices (known as the “order” of the diagram).
Add the amplitudes from all possible diagrams to get the total amplitude, M, for a process transition probability.
Fermi’s Golden Rule
4 Born Diagrams (Electroweak)
Higher Order Quantum Loop Diagrams (QED only)
3rd order corrections
Dirac theory predicts g=2, but this is modified
by quantum fluctuations.
Radiation and re-absorption of virtual photons contributes an anomalous magnetic moment.
Lowest order correction
Hundreds of diagrams!
measurements of aμ
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
1900Planck Black Body Radiation explained in terms of light quanta
1905Einstein explained the
Photoelectric Effectin terms of quanta of energy
1925G.N. Lewisproposed the name Photon for quanta of light.
1925Compton showed quantum (particle) nature of X-rays
Gargamelle Bubble Chamber
Carlo Rubbia (UA1)
Simon van der Meer
UA1 and UA2.
Rubbia came up with idea and led UA1.
Super Proton Synchrotron turned into proton-antiproton collider. Stochastic cooling technique.
“Missing Energy” = neutrino
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, MARK-J, PLUTO
Third jet produced by
There are 3 “valence”quarks
inside the proton bound together
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…..
Some particles apparently contain quarks in the same state
violates Pauli Exclusion Principle(e.g. ++ = uuu).
Proposed that quarks carry an extra quantum number
All physical particles are colour neutral or “white”.
Expect 9 gluons from all combinations (3 colours x 3 anti-colours):
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+anti-colour
charge, e.g. red-anti 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!
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 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.
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
Bosons = Spin 1
ForceParticle Charge Mass Relative Range
(GeV) Strength (m)
Bosons = Spin 2
(not observed yet!)
Summary of how different particles feel the different forces:
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 non-re-normalisable. Graviton has not been discovered!
Length1.62 x 10-35 m
Time5.39 x 10-44 s
Energy1.22 x 1019 GeV/c2
Temp1.42 x 1032 K
or EW symmetry breaking
EM coupling constant
= 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 become equal.
Standard Model + GUT
LEP, Amaldi et al, 1991
SUSY at 1 TeV + GUT
not yet found
The masses of composite
particles like protons and neutrons are mainly given by the motion of the constituents.
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.
Why do some particles
have large masses
whilst others have little
or no mass?
Mass = 511 eV
Mass < 10-18 eV
Mass = 80 x 109 eV
Mass < 2eV
M(top) = 172 GeV ± 0.9 ± 1.3 GeV
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
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!
State in which the Higgs field is zero is not the lowest energy state.
EW - Higgs Field
EM - Electric & Magnetic Fields
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.
Fit to LEP EW Measurements
at LEP Collider
Also, limits from Tevatron
4 Jul 2012, CERN
Francois Englert & Peter Higgs
Higgs does not couple to zero mass photon.
Possible via a top quark loop.
Phys. Lett. B 716 (17 Sept 2012), Issue 1
Phys. Lett. B 716 (17 Sept 2012), Issue 1
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, … +S-1, +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.
Professor Glenn Patrick
email: [email protected]