PHYS 5326 – Lecture #11
Monday, Feb. 24, 2003
Dr. Jae Yu
1. Brief Review of sin2qW measurement
2. Neutrino Oscillation Measurements
1. Solar neutrinos
2. Atmospheric neutrinos
3. A lecture on neutrino mass (Dr. Sydney
Meshkov from CalTech)
•Next makeup class is Friday, Mar. 14, 1-2:30pm, rm 200.
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
Jae Yu
1
How is sin2qW measured?
( 3)
coupling  I weak
( 3)
coupling  I weak
 QEM sin 2 qW
• Cross section ratios between NC and CC proportional to sin2qW
• Llewellyn Smith Formula:
 ( )
R

σNC( )
σCC( )
Monday, Feb. 24, 2003
 ( )


σ
1
5
 ρ 2   sin2 θ W  sin4 θ W  1  CC( )
2
9
σ CC


PHYS 5326, Spring 2003
Jae Yu
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



SM Global Fits with New Results
Without NuTeV
c2/dof=20.5/14: P=11.4%
With NuTeV
c2/dof=29.7/15: P=1.3%
Confidence level in upper
Mhiggs limit weakens slightly.
LEP EWWG: http://www.cern.ch/LEPEWWG
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
Jae Yu
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Tree-level Parameters: r0 and sin2qW(on-shell)
sin2 θ W  0.2265  0.0031
ρ 0  0.9983  0.040
2 (On  shell)
W
δsin θ
 M 2t  175GeV 2 

 0.00022  
2



50GeV


 MH 
 0.00032  ln

 150GeV 
• Either sin2qW(on-shell) or r0 could agree with SM but both agreeing
simultaneously is unlikely
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
Jae Yu
4
Model Independent Analysis
• R` can be expressed in terms of quark couplings:
- 
 - 

  N   X 
  g2  r 1g2
R    - 
L
R


  N      X 


σ νN    X
1
r


Where
σ νN     X
2




Paschos-Wolfenstein formula can be expressed as
R 
ν
ν
σNC
 σNC
ν
ν
σ CC
 σ CC
Monday, Feb. 24, 2003
ν
ν
1
R

rR


 ρ2   sin2θ W  
 gL2  gR2
1 r
2

PHYS 5326, Spring 2003
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Model Independent Analysis
Difficult to explain the
disagreement with SM by:
Parton Distribution Function or
LO vs NLO or Electroweak
Radiative Correction: large
MHiggs
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
Jae Yu
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Linking sin2qW with Higgs through Mtop vs MW
One-loop
correction to
sin2qW
 shell)
δsin2 θ(On
W
Monday, Feb. 24, 2003
 M 2t  175GeV 2 
 MH 

 0.00022  

0.00032

ln


2

 150GeV 
 50GeV 

PHYS 5326, Spring 2003
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Oscillation Probability
• Substituting the energies into the wave function:
2
2
 
 
m


i

m
t
1
  t   exp  it  p  2 E   sin q  1  cosq  2 exp 
2 E  
  

 
where m2  m12  m22 and E  p.
• Since the ’s move at the speed of light, t=x/c, where x
is the distance to the source of .
• The probability for  with energy E oscillates to e at
the distance L from the source becomes
 1.27m 2 L 

P    e   sin 2q sin 
E


2
Monday, Feb. 24, 2003
2
PHYS 5326, Spring 2003
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Why is Neutrino Oscillation Important?
• Neutrinos are one of the fundamental constituents in nature
– Three weak eigenstates based on SM
• Left handed particles and right handed anti-particles only
– Violates parity  Why only neutrinos?
– Is it because of its masslessness?
•
•
•
•
SM based on massless neutrinos
Mass eigenstates of neutrinos makes flavors to mix
SM in trouble…
Many experimental results showing definitive evidences of
neutrino oscillation
– SNO giving 5 sigma results
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
Jae Yu
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 Sources for Oscillation Experiments
• Must have some way of knowing the flux
– Why?
• Natural Sources
– Solar neutrinos
– Atmospheric neutrinos
• Manmade Sources
– Nuclear Reactor
– Accelerator
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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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
 e + e  e+X: electron gives out Cerenkov light
  CC interactions, resulting in muons with Cerenkov light
• Detectors using accelerator made neutrinos
– Look very much like normal neutrino detectors
• Need to increase statistics
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
Jae Yu
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Solar Neutrinos
• Result from nuclear fusion process in the Sun
• Primary reactions and the neutrino energy from
them are:
Name
Reaction
E End point (MeV)
pp
p  p  D  e  e
0.42
pep
p  e  p  D  e
1.44
7Be
7
Be  e  7 Li   e
0.86
B  2 4 He  e    e
15
8B
Monday, Feb. 24, 2003

8
 
PHYS 5326, Spring 2003
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Solar Neutrino Energy Spectrum
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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Comparison of Theory and Experiments
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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Sudbery Neutrino Observatory (SNO)
•Sudbery mine, Canada
•6800 ft underground
•12 m diameter acrylic vessel
•1000 tons of D2O
•9600 PMT’s
Elastic
Scattering
Neutral
Current
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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SNO e Event Display
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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Solar Neutrino Flux
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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SNO First Results
0.35
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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Atmospheric Neutrinos
• Neutrinos resulting from the atmospheric
interactions of cosmic ray particles
  to e is about 2 to 1
– He, p, etc + N  p,K, etc
 p  
  e+e+
– This reaction gives 2  and 1 e
• Expected flux ratio between  and e is 2 to 1
• Form a double ratio for the measurement
Monday, Feb. 24, 2003
 N e


N 
R  
 N e


N 
PHYS 5326, Spring 2003

Jae Yu
Exp




The




19
Super Kamiokande
•Kamioka zinc mine, Japan
• 1000m underground
•40 m (d) x 40m(h) SS
•50,000 tons of ultra pure H2O
•11200(inner)+1800(outer)
50cm PMT’s
•Originally for proton decay
experiment
•Accident in Nov. 2001,
destroyed 7000 PMT’s
•Dec. 2002 resume data taking
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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Atmospheric Neutrino Oscillations
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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Super-K Atmospheric Neutrino Results
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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Super-K Event Displays
Stopping 
Monday, Feb. 24, 2003
3
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Other Experimental Results
Macro experiment
Soudan 2 experiment
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
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Accelerator Based Experiments
• Mostly  from accelerators
• 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 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
Monday, Feb. 24, 2003
PHYS 5326, Spring 2003
Jae Yu
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