Particle Physics
Physics 735: Fall 2008
Sridhara Dasu
http://www.hep.wisc.edu/~dasu/physics735
Physics 735: Goals
• Gain sufficient proficiency in particle physics
phenomena and phenomenology, so that
– experimentalists can begin research
• Tevatron or LHC
• Neutrino physics
– theorists can build on the foundation provided
• Phenomenology
• Cosmology
• String theory
April 13, 2015
Course Structure
• Lectures
– Provide introduction to the subject
– Provide motivation for you to read further
– Provide opportunity to discuss the subject with
your fellow students and me
• Please feel free to stop me and ask questions
• Hopefully, the answers provided will improve your
understanding of the subject and your colleagues’
• Homework (3 hours per week)
– Read text books
– Work out problems
April 13, 2015
Lecture Logistics
• Particle physicists are by necessity globe
trotters – my labs are in Stanford & Geneva
– I will be away for 6 of 29 lectures
– I would like to compensate by longer lectures
• Say, 12:30 – 14:15, Tue/Thu
• I will provide some refreshments so you can stand the
long lecture 
– Let me know if it does NOT work and I will try to
find some other way
April 13, 2015
Other Details
• Office hours
– Tue and Wed afternoons
– Call me 608-262-3678 or 408-829-6625 to ensure
I am in my room
• Grading
– Homework (75%)
• You may work in groups
• You may consult me in my office hours
– Final paper (25%)
• You must chose and complete a project independently
– Example projects will be provided later
– http://www.hep.wisc.edu/~dasu/physics735
April 13, 2015
The Quantum Universe
• The big questions
– What is the nature of the universe and what is it made of?
– What are matter, energy, space and time?
– How did we get here and where are we going?
• “In the last 30 years, physicists have achieved a
profound understanding of the fundamental particles
and the physical laws that govern matter, energy,
space and time … the Standard Model can truly be
celebrated as one of the great scientific triumphs of
the 20th century.”
• http://www.interactions.org/pdf/Quantum_Universe.pdf
• In Physics 735 we will study the Standard Model
April 13, 2015
Quantum Universe
Unified Forces
http://interactions.org/quantumuniverse/
– Are there undiscovered principles of nature:
new symmetries, new physical laws?
– How can we solve the mystery of dark energy?
– Are there extra dimensions of space?
– Do all forces become one?
The Particle World
– Why are there so many kinds of particles?
– What is dark matter? How can we make it?
– What are neutrinos telling us?
The Birth of the Universe
– How did the Universe come to be?
– What happened to the antimatter?
April 13, 2015
From Quarks to Cosmos
•
Connecting Quarks with the Cosmos, Eleven Science Questions for the New Century
– National Research Council of the National Academies
– ISBN 0-309-07406-1, www.national-academies.org and http://www.nap.edu
April 13, 2015
Reverse Engineering the Universe
•
•
•
•
http://pancake.uchicago.edu/~carroll/universelab05/
A great achievement of the 20th century physics
– Unification of the theory of microcosm and the macrocosm
– Cosmology: The Big Bang and The Standard Model of elementary particles.
Observations
– Our Universe is expanding
• The relic radiation now at microwave energies observed - being studied
– Our Universe is made of matter (as opposed to anti-matter!)
• The Standard Model does allow matter-antimatter asymmetry
– Our Universe is predominantly made of dark matter
• Not enough matter in the universe to account for the rate of expansion
In the early universe just after the Big Bang the temperatures were high and matterantimatterradiation field transitions were predominant
– As the Universe cooled to below 2Melectron these transitions stopped
– There must have been some asymmetry that led to matter domination
– There must have been some process that caused high mass particles to decay into
very weakly interacting particles (dark matter)
High energy experiments can probe phenomena relevant for cosmology
– Study the physics of the early universe  Study particles predominant at ~t0.
– Reasons for matter-antimatter asymmetry (quark mixing and neutrino mixing)
– Discover the dark matter
April 13, 2015
Particle Physics
• Theoretical Framework
– The Standard Model of Particle Physics
• Relativistic Quantum Gauge Field Theories of microscopic frontier that
is accessible to the experiments
– Relativity and Quantum Mechanics folded together
– But, SM cannot be complete, what is the new physics that lies
beyond the SM (BSM)?
• Laboratory Experimental Probes
– Electro-weak Physics
– Heavy quark Physics
– Neutrino Physics
April 13, 2015
The smallness of the electron
• At the end of 19th century
– Physicists pondered about the electron
• Electron is point-like
• At least smaller than 10-17 cm
• Like charges repel
– Hard to keep electric charge in a small pack
• Need a lot of energy to keep it small!
April 13, 2015
2
E=mc
• Energy and matter are related
– Energy can be transformed to mass
and vice versa
• Conservation of mass-energy
• Measured energy of the electron is only 0.5 MeV
– Can explain a size of 10-10 to 10-13 cm
– Cannot explain < 10-17 cm as measured
• Need LOTS of energy to pack charge tightly inside the
electron
– Breakdown of theory of electromagnetism
April 13, 2015
Uncertainty Principle
• Uncertainty Principle:
You can violate energy
conservation but only for a
short time
Werner Heisenberg
April 13, 2015
Relativistic Quantum world
• Dirac formulated Relativistic Quantum
Mechanics
– Schrodinger equation
• Not relativistic (space2 but time1)
• Predicted antimatter
– Anderson discovered positron
• You can create more massive objects than you
have energy - but they are virtual - i.e., they
disappear promptly and rematerialize in particle
states that conserve mass-energy
• Vacuum is full of quantum bubbles!
Paul Adrian Maurice Dirac
April 13, 2015
Electron Stability Requires Anti-Matter
• Electron creates a force to
repel itself
• Vacuum bubble of matter antimatter creation/annihilation
• Electron annihilates the positron
in the bubble
 Size of the electron is no longer a
relevant parameter - the closer
you probe, the more you see the
structure of vacuum … matter
and antimatter pairs
April 13, 2015
Structure of Matter
• Rutherford Scattering: Discovery of nucleus
April 13, 2015
Finite Sized Nucleons
• Hofstadter
– Elastic electron scattering
– At Stanford
April 13, 2015
Yukawa’s Prediction of Mesons
• What is responsible for strong binding
between nucleons?
• Yukawa (1935) postulated a new potential
which is large at short distances and decreases
rapidly at distances larger than about 2 fm.
– Treated the problem in a relativistic quantum theory
– He clearly showed that in the relativistic quantum world
particles interact by exchanging virtual quanta which
mediate the force
– He predicted the mass of pions
gs2 er /a
Yukawa Potential, U(r) 
4 r
April 13, 2015
Yukawa’s Prediction
• Following electromagnetism for new potential
Electrostatics, Poission Equation: 2V(r) 
 (r)
0
gs2 er /a
1

Yukawa Potential, U(r) 
  2  2  U(r)  gs2 (r)

4 r
a 
 2
2
1
Yukawa Generalization:    2 2  2  U(r,t)  0
c t
a 

Propagating wave solution, U  exp(ip.r / h  iEt / h)
E2
p2 1
c 2 h2
2 2
yields: 2 2  2  2  E  c p  2
ch
h
a
a
h
i.e., a particle of mass, mU 
: 100 MeV for a  2 fm
ac
April 13, 2015
Who ordered the muon?
• In 1937 a new particle of mass
105.7 MeV was discovered
– However, it interacted with matter
very weakly, a heavy lepton
– Created in upper reaches of the
atmosphere many of them were
able to reach the ground level
traversing a large amount of matter
– Muon - I. Rabi asked,
“Who ordered the muon?”
– Yukawa’s mesons (pions) were
eventually discovered in 1947
April 13, 2015
Discrete Symmetries
Discrete operations
Parity:
P(x)  (x)
Parity is violated - i.e., mirror image processes do not have identical rates
When e +  e       , at high energies when weak interactions are
important, there is a forward backward asymmetry
Charge Conjugation:
C(x)  (x)
The combined operation CP transforms particle to antiparticle moving in
opposite direction
CP symmetry is violated when matter and antimatter behave differently
April 13, 2015
Symmetries and Quantum Numbers
• Strong interactions seem to be independent of
nucleon flavor (proton or neutron)
• This symmetry for strong interaction implies a
conserved current or quantum number
(Noether’s theorem)
– Isospin
– Proton = +1/2 Iz, Neutron = -1/2 Iz
– Isospin follows spin angular momentum algebra
1  1  0

2
2
Pions are isospin 1 states, there should three of
1
them with about the same mass as was observed.
• Weak interactions do not conserve isospin
• Neutron beta decay, np e e
April 13, 2015
Many mesons and baryons
• Pions, (0, ±)
– Strong binding is independent of proton/neutron numbers
• Isospin symmetry implied three I=1 Yukawa pions
– Angular excitations, vector mesons (, , …)
• Kaons, (KS, KL, K±)
– Strange particles produced in pairs
– Strong and EM interactions conserve strangeness a new quantum
number
• But weak interactions violate strangeness
• Kaons decay to pions and leptons
• Organizing the mesons and baryons
– Flavor (softly broken) symmetries
– Gellman’s eight fold way  substructure (quarks)
• SU(3) symmetry invoked to explain octet of pseudo scalar mesons
• Predicted missing member of decuplet of baryons, which was discovered
– However, predicted fractionally charged quarks were not observed
April 13, 2015
Down to Quarks
Rutherford Scattering with
high energy electrons
Stanford Linear
Accelerator Center
April 13, 2015
Proton Structure Revealed
April 13, 2015
Discovery of Charm
 (e e  hadrons)
R
revealed a sharp peak at about 3 GeV mass
 (e e      )
A new heavy quark-anti-quark bound-state (J/ ) production
April 13, 2015
Quark Model
• With u, d, s and c quarks
April 13, 2015
Mesons
• Many types
• Many decay modes
• Some are long lived,
i.e., > 10–8 s
• Massive  short life
• Detection
– Long lived
• Interactions with
detector matter
– Short lived
• Calculating
combined
masses using
detected particles
April 13, 2015
Quarks and Color
• Overwhelming evidence for nucleon and meson
substructure in terms of quarks
– Quarks are spin-1/2 and fractionally charged
• However, quarks were never observed directly
• Some thing confines them into mesons (qq) and baryons (qqq)
– Baryons should have antisymmetric wave function
• Proton, p = uud, neutron, n=udd are OK
• How about, ++=uuu?
– Solve both problems
•
•
•
•
April 13, 2015
Invent a new quantum number color
All particles are color less: q, qq, … cannot exist
Overcome statistics problem by choosing p=uRuGdB, ++=uRuGuB
This seemingly contrived solution is actually the scheme chosen
by nature! Rather than Yukawa’s theory, the color dynamics works
Screening of Electric & Color Charge
April 13, 2015
Weak Interactions: Mass
• Why are weak interactions (-decay) weak?
– Massive mediating bosons (W± and Z0) unlike the case of photons
(80, 90 GeV) - these bosons were discovered at CERN in 80s
• Weak interactions change flavor
– There are no large flavor changing neutral currents, i.e., not Z
– Mediating bosons that change flavor are charged, W±
– Flavor changing weak interactions allow decay of heavier generation
quarks and leptons to lighter generations
• Flavor changing neutral current transitions indicate new physics
• Electroweak unification at high mass scales
– Electroweak theory predicts existence of a fundamental scalar higgs
and neutral currents
– Interactions of W and Z with higgs field give them mass
• Secondary benefit: Yukawa like couplings of matter particles to
higgs field give them mass
• But, Higgs boson is yet to be found (LHC)
April 13, 2015
The Last Generation
•
•
Another generation of quark, bottom or beauty, was found
– Symmetry implied existence of a top quark which was eventually found few
years ago
– Bottom forms mesons but top is so heavy that it decays before QCD can
confine it to a meson
Are there more generations?
– Leptons also form doublets, (e, e), (, ), (, )
– Neutrinos are almost massless
– Neutrinos couple to Z boson weakly
– Z decay width can predict how many neutrinos are allowed if they are less
than half the mass of Z (MZ=91GeV)
– Measurements indicated only 3 allowed light neutrinos
• Therefore, assuming that any new neutrinos are light there are only three
lepton generations of the type we know
– The suggestive symmetry between lepton and quark content implies that we
probably arrived at the last generation, unless the fourth generation behaves
very differently from the other three
April 13, 2015
Matter Particles
As Dirac Predicted all of these matter particles also have
corresponding antimatter particles
April 13, 2015
Interactions Between Particles
CERN - Geneva
April 13, 2015
Particle Interactions
April 13, 2015
Elementary particles
Leptons:
  e0 
 e1 
Quarks:
 u2/3 
 d 1/ 3 
  0 
 1 
 0 

electroweak
interactions
(

,Z,W
)
  1 
 c2 / 3 
 s 1/ 3 
 t 2/3 
 b 1/ 3  electroweak and strong (g) interaction
Each of these have a corresponding anti-particle
An additional fundamental scalar (Higgs) needed to complete the SM picture
We are awaiting the discovery of Higgs
ee+
,Z
t
b
b
c
eW+
W-

Heavier elementary particles decay - only the first
generation (e,u,d), photons () and neutrinos () are stable.
April 13, 2015
Flavor Changing Interactions
• Charged W± particles (like photons but massive - 80 GeV)
change flavor of quarks
– For short period energy conservation can be violated to create
virtual heavy W± particles
• Heavier quarks, leptons decay to lighter generations
– Only u, d, electron, neutrinos remain
– But, why not positrons, …?
• Cross generational coupling exists
– b quark decays to c quark + X
– The down-type quarks mix together
b
c
• Quantum mechanical superposition of states
eW
April 13, 2015
Quark Mixing Matrix
Cabibbo - Kobayashi- Maskawa (CKM)
d  Vud Vus Vub  d 
  
  
s Vcd Vcs Vcb  s 
  
  
b Vtd Vts Vtb  b 
T his complex mixing matrix is unitary
Four unique parameters- three mixing angles
one complex phase (measured experimentally)
If complex phase is nonzero mat ter and ant imatter
can behave differently (decays will involve different
combinations of CKM matrix elements)
April 13, 2015
Baryon Number
Protons are stable (Lifetime greater than life of the Universe)
Some conservation law should protect this decay: Baryon number
Quarks have Baryon number = 1/3
Mesons: quark-antiquark bound states (Baryon Number = 0)
B meson (bd )
B meson (bd)
Free quarks cannot exist - they are
confined to mesons or baryons.
Baryons: 3 quark states (Baryon Number  0)
proton (uud) ; B=1
anti-proton (uud) ; B=-1
neutron (ddu) ; B=1
All mesons decay (Lifetime  10 -8 s)
Anti-protons should be stable too (annihilate when p-p meet)
(neutrons are unstable when free - survive only in bound nuclei)
April 13, 2015
Neutrino Mixing
• Measure neutrinos from Sun (low energy) and those
produced by meson decays in atmosphere (higher energy)
• Well predicted flux and ratios
April 13, 2015
Neutrino Mixing Matrix
• Experiments are on to measure neutrino mixing matrix and
absolute mass scale for neutrinos
• Is there CP violation in neutrino sector?
April 13, 2015
Mixing Solutions
Two mass difference squares measured with large mixing angles
Quark mixing is much smaller but it violates CP
What is the level of 1-3 mixing in neutrino sector?
Is CP violated in the neutrino sector?
April 13, 2015
More on higgs
• The Standard Model is not complete
– In higher orders of perturbation theory QFT result in divergences,
which are tamed by renormalization
– Higher order corrections to higgs results in a divergence that requires
high degree of tuning
– One can avoid fine tuning if there are cancellations
• Note corrections due to fermion-higgs and boson-higgs couplings
are opposite in sign
• If the particle content of SM is duplicated by including a boson
partner for each fermion and a fermion partner for each boson, the
cancellations will result in stable higgs mass
• SUPERSYMMETRY
– Super partners are not found yet - they must be massive
– Side effect: if there is a conserved quantum number associated with
SUSY (R-parity), then lightest SUSY particle must be stable
• A candidate for dark matter
– Massive stable weakly interacting neutral particle
April 13, 2015
The Big Picture
Content of the Universe
5%
25%
70%
Ordinary Matter (No anti-matter)
Dark Matter (Gravity felt)
Dark Energy (Acclerating expansion)
• Particle Physics, that can be explored in the coming decade,
holds the key to at least the first two items
April 13, 2015