PHYS 3446 – Lecture #22
Wednesday, Nov. 29, 2006
Dr. Jae Yu
1. The Standard Model
Symmetry Breaking and the Higgs particle
Higgs Search Strategy
Neutrino Oscillations
Issues in the Standard Model
2. Feynmann Diagrams
Wednesday, Nov. 29, 2006
PHYS 3446, Fall 2006
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Spontaneous Symmetry Breaking
While the collection of ground states does preserve the
symmetry in L, the Feynman formalism allows to work
with only one of the ground states through the local
gauge symmetry  Causes the symmetry to break.
This is called “spontaneous” symmetry breaking,
because symmetry breaking is not externally caused.
The true symmetry of the system is hidden by an
arbitrary choice of a particular ground state. This is
the case of discrete symmetry w/ 2 ground states.
Wednesday, Nov. 29, 2006
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EW Potential and Symmetry Breaking
Not symmetric
about this axis
1
1
   2 2  2 4
2
4
Symmetric
about this axis
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The Higgs Mechanism
• Recovery from a spontaneously broken
electroweak symmetry gives masses to gauge
fields (W and Z) and produce a massive scalar
boson
– The gauge vector bosons become massive (W and Z)
– The massive scalar boson produced through this
spontaneous EW symmetry breaking is the Higgs
particle
• In SM, the Higgs boson is a ramification of the
mechanism that gives masses to weak vector
bosons, leptons and quarks
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Higgs Production Processes at
Hadron Colliders
Gluon fusion:
gg  H


WW, ZZ Fusion:
W W , ZZ  H
Higgs-strahlung
off W,Z:
qq  W , Z  W , Z  H
*
*
Higgs Bremsstrahlung
q q, gg  t t  H
off top:
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Hadron Collider SM Higgs Production s
LHC
We use WHen+b`b
channel for search for Higgs
at Tevatron
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Tevatron
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SM Higgs Branching Ratio
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We use WHen+b`b
140GeV/cPHYS
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Jae Yu
channel for search for Higgs
How do we find the Higgs particle?
• Look for WHl+n+b b-bar
• Use the finite lifetime of mesons containing b-quarks
within a particle jets.
Silicon
Detectors
b
vertex
Wednesday, Nov. 29, 2006
1”
Beampipe
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What do we know as of Winter 06?
29, 2006
PHYS 3446, Fall 2006
LEPWednesday,
EWWG:Nov.http://www.cern.ch/LEPEWWG
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114.4<MH<199GeV
How do we make a Neutrino Beam?
Good
target
Good beam
focusing
Sufficient dump
p
Long decay
region
• Use large number of protons on target to produce many
secondary hadrons (p, K, D, etc) and focus as many of
them as possible
• Let p and K decay in-flight for n beam in the decay pipe
– p+n (99.99%), Kn (63.5%)
• Let the beam go through shield and dirt to filter out  and
the remaining hadrons, except for n
– Dominated by n
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How can we select sign of neutrinos?
• Neutrinos are electrically neutral
• Need to select the charge of the secondary hadrons
from the proton interaction on target
• Sets of Dipoles are used to select desired charges of
the secondary hadrons
di-poles
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How can there be wrong sign of
neutrinos in a sign selected beam?
• Interaction of correct sign secondary hadrons
with beamline elements, including dump and
shields
– Act as if a fixed target is hit by hadron beam
• Back-scatter of unused protons into the
beamline
• CP violating neutrino oscillations
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4. QCD Factorization Theorem
Factor the whole interaction
into two independent parts!!
s=f*sp
n,(`n)
k
k’
, ()
p, q
Allow QCD perturbation
theory to work and physical
observables calculable.
W+(W-)
q=k-k’
Partonic hard scatter sp
q, (`q)
xP
P
}
EHad
Non-perturbative, infra-red part f
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How is sin2qW measured?
( 3)
coupling  I weak
Cross section ratios between NC and CC proportional to sin2qW
Llewellyn Smith Formula:
•
•
n (n )
R
•
•
( 3)
coupling  I weak
 QEM sin 2 qW

σnNC(n )
σnCC(n )
n (n )


σ
1
5
 ρ 2   sin2 θ W  sin4 θ W  1  nCC(n )
2
9
σ CC


Define experimental variable to distinguish NC and CC
Compare the measured ratio with MC prediction
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



How Can Events be Separated?
Event Length
Charged
Current
Events
Neutral
Current
Events
Wednesday, Nov. 29, 2006
y-view
Nothing is
coming in!!!

x-view

y-view
Nothing is
coming in!!!
x-view
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Nothing is
going out!!!
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Neutrino Oscillation
• First suggestion of neutrino mixing by B. Pontecorvo at the
K0, K0-bar mixing in 1957
• Solar neutrino deficit in 1969 by Ray Davis in Homestake
Mine in SD.  Called MSW effect
• Caused by the two different eigenstates for mass and weak
• Neutrinos change their flavor as they travel  Neutrino
flavor mixing
• SM based on massless neutrinos
• SM inconsistent
• Oscillation probability depends on
– Distance between the source and the observation point
– Energy of the neutrinos
– Difference in square of the masses
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Neutrino Oscillation Formalism
• Two neutrino mixing case:
n e   cosq
  
n     sin q
sin q  n 1 
   OR
cosq  n 2 
n e  cosq n1  sinq n 2
n    sin q n 1  cosq n 2
where n e and n  are weak eigenstates, while
n 1 and n 2 are mass eigenstates, and q is the
mixing angle that give the extent of mass
eigenstate mixture, analogous to Cabbio angle
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Oscillation Probability
• Substituting the energies in the wave functions:
2
2
 
 
m


i

m
t
1
n  (t )  exp  it  p  2 E   sin q n 1  cosq n 2 exp 
2 En  
n  

 
where m2  m12  m22 and En  p.
• Since the n’s move at the speed of light, t=x/c, where x
is the distance to the source of n.
• The probability for n with energy En oscillates to ne at
the distance L from the source becomes
 1.27m 2 L 

P(n   n e )  sin 2q sin 
En


2
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n Sources for Oscillation Experiments
• Natural Sources
– Solar neutrinos
– Atmospheric neutrinos
• Manmade Sources
– Nuclear Reactor
– Accelerator
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Oscillation Detectors
• The most important factor is the energy of neutrinos
and its products from interactions
• Good particle ID is crucial
• Detectors using natural sources
– Deep under ground to minimize cosmic ray background
– Use Cerenkov light from secondary interactions of
neutrinos
• ne + e  e+X: electron gives out Čerenkov light
• n CC interactions, resulting in muons with Čerenkov light
• Detectors using accelerator made neutrinos
– Look very much like normal neutrino detectors
• Need to increase statistics
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Atmospheric Neutrinos & Their Flux
• Neutrinos resulting from the atmospheric
interactions of cosmic ray particles
– He, p, etc + N  p,K, etc
• p  n
•  e+ne+n
– This reaction gives 2 n and 1 ne
• Expected flux ratio between n and ne is 2 to 1
• Give a predicted ratio of 

N
 ne   1
 Nn 
2
 

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SNO Experiment Results
0.35
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Importance of the Zenith Angle
• The Zenith angle represents the different distance the neutrinos
traveled through the earth
• The dependence to the angle is a direct proof of the oscillation
 1.27m L 
probability

P(n  n )  sin 2q sin 
2

Wednesday, Nov. 29, 2006
2
e
2


En


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Super-K Atmospheric Neutrino Results
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Accelerator Based Experiments
• Mostly n from accelerators
• Far better control for the beam than natural or
reactor sources
• Long and Short baseline experiments
– Long baseline: Detectors located far away from the
source, assisted by a similar detector at a very short
distance (eg. MINOS: 370km, K2K: 250km, etc)
• Compare kinematic quantities measured at the near detector
with the far detector, taking into account angular dispersion
– Short baseline: Detectors located at a close distance to
the source
• Need to know flux well
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Long Baseline Experiment Concept (K2K)
Compare kinematic distributions between near and far detectors
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Different Neutrino Oscillation Strategies
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Exclusion Plots
n disappearance
`ne appearance
ne appearance
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Future: Neutrino Factory
• Spin-off of a muon collider research
– One a hot, summer day at BNL, the idea of neutrino storage
ring popped up
• Future facility using muon storage ring, providing well
understood neutrino beam (n and ne) at about 106
times higher intensity
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What do we know now?
• We clearly know neutrinos oscillate  Neutrinos have
masses
• It seems that there are three allowed regions of
parameters (sin22q and m2) that the current data
seem to point
–
–
–
–
–
–
–
LSND ~1eV2; Super-K ~ 10-3 eV2, Solar (LMA) ~ 10-5 eV2
There are at least three flavors participating in oscillation
Sin22q23 ~ 1 at 90% confidence level
|m322| ~ 2x10-3 eV2
m212 ~ 2x10-3 eV2 (If LMA confirmed)
Sin22q12 ~ 0.87 at 90% confidence level (if LMA confirmed)
Sin22q13 < O(0.1)
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What do we not know?
• Does 3-flavor mixing provide the right framework?
– For CP–violating oscillation, additional neutrino flavors,
neutrino decay, etc?
• How many flavors of neutrinos do we have?
• Is sin22q13 0 or small?
• What is the sign of m32?
– What are the configuration of neutrino masses?
– What are the actual masses of neutrinos mass eigenstates?
• What are the matter effects?
• Is sin22q23 = 1?
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Issues in SM
• Why are the masses of quarks, leptons and vector bosons the
way they are?
• Why are there three families of fundamental particles?
• What gives the particle their masses?
• Do the neutrinos have mass?
• Why is the universe dominated by particles?
– What happened to anti-particles?
•
•
•
•
•
•
What are the dark matter and dark energy?
Are quarks and leptons the “real” fundamental particles?
Other there other particles that we don’t know of?
Why are there only four forces?
How is the universe created?
Where are we from?
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Feynman Rules
• The rules for any process are:
• Draw all possible diagrams
– Different time-orderings of a given process are represented by the same
diagram.
• Given the initial momentum and energy, define how momentum
and energy flow for each line in the diagram.
– Where each diagram has a closed loop, there is an arbitrary momentum
and energy flow around the loop and we must integrate over all possible
choices for these quantities.
– Each intermediate line in the diagram contributes a factor to the amplitude
of 1/(E2-p2c2-m2c4) where m is the appropriate mass for the particle
type represented by the line. Note that this says that the more "virtual" the
particle represented by a line is, the smaller the contribution of the
diagram.
• Add the amplitude factors from all possible diagrams to get the
total amplitude for the process.
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Feynman Diagram Components
Image
Description
Particle Represented
straight line, arrow to
the right
straight line, arrow to
the left
wavy line
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electron
positron
photon
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Feynman Diagram Rules
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A Few Example Feynman Diagrams
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A Few Feynman Diagram Exercises
•
•
•
•
•
Leptonic decays of W+, W- and Z0
Leptonic decay of p-, p+ and p0
Top quark decay (tbW) possibilities
P and `P collisions
WH production and final states from P and `P
collisions
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