Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14,...
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Transcript of Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14,...
![Page 1: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/1.jpg)
Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae Yu
1
PHYS 5326 – Lecture #6
Wednesday, Feb. 14, 2007Dr. Jae Yu
1. Neutrino Oscillation Formalism 2. Neutrino Oscillation Measurements
1. Solar Neutrinos2. Atmospheric neutrinos3. Accelerator Based Oscillation Experiments
![Page 2: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/2.jpg)
Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae Yu
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Neutrino Oscillation• First suggestion of neutrino mixing by B. Pontecorvo to
explain K0, K0-bar mixing in 1957• Solar neutrino deficit in 1969 by Ray Davis in Homestake
Mine in SD. Called MSW (Mikheyev-Smirnov-Wolfenstein) effect – Describes neutrino flavor conversion in medium
• Caused by the two different eigenstates for mass and weak• Neutrinos change their flavor as they travel Neutrino flavor
mixing• Oscillation probability depends on
– The distance between the source and the observation point– The energy of the neutrinos– The difference in square of the masses
![Page 3: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/3.jpg)
Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae Yu
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Neutrino Oscillation Formalism• Two neutrino mixing case:
cos sin e 1 2
where and are weak eigenstates, while and are mass eigenstates, and is the mixing angle that gives the extent of mass eigenstate mixture, analogous to Cabbio angle
e
1 2
e
ORcos sin
sin cos
1
2
sin cos 1 2
![Page 4: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/4.jpg)
Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae Yu
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Oscillation Probability• Let at time t=0 be the linear combination of 1 and 2
with masses m1 and m2, the wave function becomes:
0 sin cost 1 2
1 2sin exp cos expE Et i t i t 1 2
• Then later time t the wave function becomes:
• For relativistic neutrinos (E>>mi), the energies of the mass eigenstates are:
22 2
2k
k k
mE p m p
p
![Page 5: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/5.jpg)
Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae Yu
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Oscillation Probability• Substituting the energies into the wave function:
2 21exp sin cos exp2 2m i m tt it p E E
1 2
where and .2 2 21 2m m m 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
2
2 2 1.27sin 2 sine
m LP
E
![Page 6: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/6.jpg)
Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae Yu
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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
![Page 7: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/7.jpg)
Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae Yu
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Sources for Oscillation Experiments• Must have know the flux by the species
– Why?• Natural Sources
– Solar neutrinos– Atmospheric neutrinos
• Manmade Sources– Nuclear Reactor– Accelerator
![Page 8: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/8.jpg)
Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae Yu
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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 underground to minimize cosmic ray background– Use Čerenkov light from secondary interactions of
neutrinos• e + N e+X: electron gives out Čerenkov light• CC interactions, resulting in muons with Čerenkov light
• Detectors using accelerator made neutrinos– Look very much like normal neutrino detectors
• Need to increase statistics
![Page 9: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/9.jpg)
Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae 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)
8B
7Be
pep
pp
7 7eBe e Li
ep p D e
ep e p D
8 42 eB He e 15
0.86
1.44
0.42
![Page 10: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/10.jpg)
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Solar Neutrino Energy Spectrum
![Page 11: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/11.jpg)
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Comparison of Theory and Experiments
![Page 12: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/12.jpg)
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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
Inelastic Scattering
![Page 13: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/13.jpg)
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SNO e Event Display
![Page 14: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/14.jpg)
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Solar Neutrino Flux
![Page 15: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/15.jpg)
Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae Yu
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SNO First Results
0.35
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Wednesday, Feb. 14, 2007 PHYS 5326, Spring 2007Jae Yu
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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 ,K, etc
•
• 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 measuremente
e
Exp
The
NN
RNN
![Page 17: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/17.jpg)
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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
•Virtually all PMT’s below the surface of the water
•Dec. 2002 resumed data taking
![Page 18: Wednesday, Feb. 14, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #6 Wednesday, Feb. 14, 2007 Dr. Jae Yu 1.Neutrino Oscillation Formalism 2.Neutrino.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f185503460f94c2f5bc/html5/thumbnails/18.jpg)
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• The dynodes accelerate the electrons to the next stage, amplifying the signal to a factor of 104 – 107
• Quantum conversion efficiency of photocathode is typically on the order of 0.25
• Output signal is proportional to the amount of the incident light except for the statistical fluctuation
• Takes only a few nano-seconds for signal processing• Used in as trigger or in an environment that requires fast response• Scintillator+PMT good detector for charged particles or photons or neutrons
Photo-multiplier Tube
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Some PMT’sSuper-Kamiokande detector
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Homework Assignments• Complete the derivation of the probability for of
energy E to oscillate to e at the distance L away from the source of .
• Draw the oscillation probability distributions as a function of– Distance L for a fixed neutrino beam energy E (=5, 50,
150 GeV)– E for a detector at a distance L (=1.5, 735, 2200km)
away from the source• Due Wednesday, Feb. 21