Overview of Neutrinos
Where do they come from
Interaction types
How do we detect them
Types of detectors
First Observation
Historical Measurements and Mysteries
Measurement types and significance
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Florida
1
Why were neutrinos first postulated?
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Florida
2
Alpha Decay
Alpha Decay
Nucleus – 2 protons & 2 neutrons
Alpha particle: 2 protons + 2 neutrons
Classic 2-body decay at rest
Energy of decay products
always the same
3
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Beta Decay
Emitted beta particle has a continuous spectrum of E
n
νe
n
Niels Bohr proposed restricted
validity of energy conservation
p
3H
e-
1930: Pauli proposes (electrically
neutral) particle also emitted
during beta decay
(Dec 4th, 2010 = 80th anniversary!)
p
n
3He
p
1934: Fermi ran with it, developed
theory of beta decay
I have done something very bad today by proposing a particle
that cannot be detected; it is something no theorist should
ever do.
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Florida
4
Neutrino Sources
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Neutrino Sources
Solar: ~ 0.1 - 15 MeV
Nuclear Reactors: few MeV
Accelerators: ~0.1 MeV – 100 GeV
Atmospheric : 1 - 10 GeV
also SN, geo-neutrinos
Energy in eV
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106
MeV
109
GeV
1012
TeV
6
Solar Neutrinos
ppI
ppII
ppIII
Theoretical uncertainties
7
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Nuclear Reactor Neutrinos
Rb-92
ee
Reactors = only source of a pure anti-neutrino beam, pure
electron-flavor beam!
Anti-neutrinos are emitted by the radioactive fissile products
when they disintegrate via beta decay
~few MeV Energy
8
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Accelerator-Based Neutrinos
Beam of protons + a target material = mesons (, K)
Mesons decay into the neutrino beam seen by a detector
K+ / +  + + 
+  e+ +  + e
K0L  ++ - + 
Create neutrinos via meson Decay at Rest, Decay in Flight
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Accelerator-Based Neutrinos: DAR
-
Accelerator based Decay at Rest
absorbed by target
E
range
up to
52.8
MeV
+ DAR
Target Area
Mono-Energetic!
= 29.8 MeV
Liquid Mercury (Hg+) target
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Florida
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Accelerator-Based Neutrinos: DAR
+  + + 
 = 26 ns
+  e+ + anti- + e
 = 2.2 s
• Pulse timing, beam width,
lifetime of particles =
excellent separation of
neutrino types
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Simple cut on beam
timing = 72% pure 
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Accelerator-Based Neutrinos: DAR
+  + + 
 = 26 ns
+  e+ + anti- + e
 = 2.2 s
• Mono-energetic 
– E = 29.8 MeV
• anti-, e = known
distributions
– end-point E = 52.8 MeV
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12
Accelerator-Based Neutrinos: DAR
Advantage = Know timing of
beam, lifetime of particles, use
to greatly suppress cosmic ray
background
Advantage = extremely well
defined flux
Disadvantage = Low E limits
choices of neutrino interaction
signal
Disadvantage = Beam is
isotropic - no directionality
Hard to make an intense
isotropic beam
13
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Accelerator-Based Neutrinos: DIF
• Advantage : more intense beam because mesons are
focused (not isotropic)
• Advantage : can select neutrino, anti-nu beam
• Disadvantage : difficult to understand the flux (in content
and in E – have wrong sign contributions)!
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Florida
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Atmospheric Neutrinos
High energy protons + nuclei
collide in the upper
atmosphere = high energy
pions
Pions  muons + neutrinos
Muons  neutrinos
( + ) : (e + e) = 2 : 1


e
15
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Neutrino Interactions
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Florida
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Neutrino Interactions
Picture © Ben Still
http://neutrinoscience.blogspot.com/
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Florida
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Neutrino Interactions
Z: Neutral Current
Elastic Scattering (NC)
NEUTRINO
NEUTRINO
TARGET
NUCLEUS
TARGET
NUCLEUS
Target left intact
Neutrinos elastic scatter from any particle
Observe recoil energy of target
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Florida
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Neutral Current Interactions
1973: First observation of a NC neutrino event
Gargamelle bubble
chamber at CERN
Confirmed shortly
after at FNAL
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Florida
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First Neutral Current Observation
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Neutrinos
Scattered off of an electron
20
Neutrino Interactions
W: Charged Current
Quasi-Elastic Scattering
LEPTON
NEUTRINO
TARGET
NUCLEUS
CONVERTED
NUCLEUS
Neutrino in, charged lepton out
Target changes type
Need minimum neutrino E to make the
two outgoing particles
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Florida
G. Zeller
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Neutrino Interactions
W: Charged Current
Pion Production
LEPTON
CHARGED PION
NEUTRINO
TARGET
NUCLEUS
CONVERTED
NUCLEUS
Neutrino in, charged lepton out
Target changes type
Interacts with whole nucleus (coherent production)
Target passes through Δ(1232) resonance (resonant
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production)
G. Zeller
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Neutrino Interactions
W: Charged Current
Deep Inelastic Scattering
LEPTON
NEUTRINO
TARGET
NUCLEUS
HADRON
SHOWER
Neutrino in, charged lepton out
Target blows up, produces
hadron shower
G. Zeller
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Florida
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Detecting Neutrinos
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Florida
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Detecting Neutrino Interactions
Passage of particles through matter leaves a
distinct mark (energy deposition)
Cerenkov effect / light
Scintillation light
Radiochemical reactions
e + 37Cl = 37Ar + eMeasure neutrino flux by counting number of
produced Ar atoms
* Used by Ray Davis in first solar deficit measurement
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Florida
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Cerenkov and Scintillation Light
In media, light travels slower than in vacuum:
In vacuum: vlight = c
In material: vlight = c/n
where n = index of refraction, n ≥ 1
Particles still subject to the absolute “speed limit” (vparticle < c )
So in a medium, particles can travel
faster than the speed of light (in the
medium)!
Similar to sonic boom
phenomenon, where an aircraft
travels faster than the
speed of sound
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Florida
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Cerenkov and Scintillation Light
Some Details…
Light in a medium: vlight = c/n;
distance traveled in time t is
(c/n) * t
Particle speed:
as always, travels at
vparticle = βc;
distance traveled in
time t is βct
Particle direction
Simple trig: cos θC =
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=
; nBooNE oil ~ 3/2
Requiring cos θC < 1 gives βcerenkov > 2/3
27
Cerenkov and Scintillation Light
• Particles with a velocity greater than the
speed of light * in the medium* produce an
E-M shock wave
– v > c/n
– Similar to a sonic boom
• Prompt light signature
• Particles deposit energy in the medium
• Isotropic, delayed
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Florida
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Using Light to Identify Particles
The pattern the Cherenkov radiation makes on PMTs differs based
on particle type (this is primarily due to different masses)
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Neutrino Detectors
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Florida
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Neutrino Detectors : Large Vats o’ Liquid
Detect Cerenkov light from  interacting with water in
Kamiokande
– Electron neutrino scatters elastically from an atomic
electron
– Scattered ele follow the
direction of the incoming
 (~15 deg. max
deviation)
– Threshold E for
interaction = 4 to 5 MeV
31
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Neutrino Detectors : Large Vats o’ Liquid
Detect Cerenkov light from  interacting with heavy water
Deuterium nuclei in water = distinguish electron neutrinos from other types
Neutrino interaction rates are higher in heavy water than ordinary water =
uses less water, less collection time to have same statistics as
Kamiokande
NC : D +  = p + n + 
CC : D + e = p + p + e
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Florida
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Neutrino Detectors : Large Vats o’ Liquid
Detect Cerenkov light from  interacting with
ocean water (Antares)
33
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Ex: Detecting Reactor Neutrinos
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Florida
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Ex: Detecting Accelerator Neutrinos
Mainly a
Cerenkov detector
35
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Neutrino Detectors : Large Vats o’ Liquid
Detect transformation of atoms under neutrino
interaction
e + 37Cl = 37Ar + e- : Homestake
Only sensitive to  from 7Be, 8B branches (>0.8 MeV)
e + 71Ga = 71Ge + e- : Gallex
Sensitive to  from
initial proton fusion
reaction (>233 keV)
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Florida
36
Segmented Neutrino Detectors
MINERvA
Elevation View
LHe
0.25t
2.14 m
3.45 m
coming this
Spring
5m
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Florida
2m
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First Observations and Discovery
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Florida
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First Observation of Neutrinos
1955: Reines and Cowan
Savannah River nuclear reactor (South Carolina, USA)
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Florida
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First Observation of Neutrinos
Used inverse beta decay reaction (e+p  n+e+)
Detect e+ via two 0.5 MeV back to back photons from e+e- annihilation
Detect neutron via (n + 108Cd 109Cd* 109Cd + ϒ), within 5 μsec of
gamma pair
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Florida
40
Discovery of the Muon Neutrino
1962: First accelerator nueutrino expt (BNL), proved existence of νμ
10 ton spark chamber, 90 Al plates filled with
Ne gas
νμ + Al = muon trails in spark chamber
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Florida
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Discovery of the Tau Neutrino
2000: DONUT first direct observation of ντ (FNAL)
800 GeV protons +
tungsten = Ds
Ds  τ + anti-ντ
ντ
ντ interacts with
nucelon in emulsion
target, produces tau
lepton seen by
spectrometer
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Florida
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Discovery of the Tau Neutrino
2000: DONUT first direct observation of ντ (FNAL)
Tau neutrino
enters detector
Tau lepton created … and decays
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Florida
43
History of Neutrino Discovery
2000: First direct
observation of 
(DONUT expt @ FNAL)
1962: Lederman,
Schwartz,
Steinberger
discover  @
BNL
1988 N.P.
1956: Reines and
Cowan discover e
@ Savannah
River Reactor
1995 N.P.
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Florida
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Three Flavors of Neutrinos
Flavor states, active states
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Why Only Three?
Precision studies of the Z-line
shape from LEP determined
the number of active light
neutrinos = 2.984 ±
0.008(before ντ was
discovered!)
Big-bang nucleosynthesis
also constrains number of
light neutrinos at 1 MeV scale
to between 1.2 and 3.3
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Florida
46
Distinctive Measurements and
Mysteries
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Florida
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Standard Model Neutrino Theory
1957: neutrinos found to be left-handed
Absence of RH neutrino or LH anti-neutrino
no Dirac mass term in the SM L
Lmass = m(ΨLΨR + ΨLΨR)
SM neutrinos by construction are massless
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Florida
48
First Observation of Solar Neutrinos
1965: First neutrino
found in nature
(sun)
Sellschop, Reines,
et al. @ gold mine
(ERPM) near
Boksburg
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Florida
South Africa
49
Solar Neutrino Problem
1968: Ray Davis et al
Homestake mine in South Dakota, USA
Saw far fewer νs than expected from the sun
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Florida
50
Homestake Neutrino Experiment
Tetrachloroethylene tank
νe + 37Cl  37Ar, half life 35 days
Isolate and count 37Ar
69% deficit
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Florida
51
Atmospheric Neutrino Deficit
1986: Measured ratio of νe to νμ finds deficit of atmospheric
νμ by Kamiokande (Mozumi Mine, Hida, Japan) and IMB (Fairport
Mine, Lake Erie, USA)
Different from solar deficit
Solar: missing νe
Atmospheric: missing νμ
E scale for solar vs
atmospheric neutrinos differ
by 3 orders of magnitude
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Florida
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First Neutrinos from Supernova (1987A)
1987: Kamiokande and IMB detect first nus from SN, 1987A
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Florida
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Oscillation Firsts: Solar Anomaly
2001: SNO showed solar deficit due to flavor oscillations.
Nuclear reactions in sun aren’t energetic enough to make νμ or ντ. Solar νs
clearly arrive at Earth in more than just νe flavors with a total flux consistent
with solar models
Detect Cerenkov light from  interacting with heavy water
Deuterium nuclei in water = distinguish electron neutrinos from other types
NC : D +  = p + n + 
CC : D + e = p + p + e
H. Ray, University of
Florida
54
Oscillation Firsts: Atmospheric Deficit
1998: Atmospheric deficit confirmed due to oscillations by Super Kamiokande.
Sensitivity to atmospheric νe, direction of νμ, lack sensitivity to ντ. Measured νe flux
consistent with theoretical prediction. No significant excess of νe, deficit interpreted as
νμ  ντ (Δm223)
2004: K2K confirms atmospheric νμ
disappearance using the proton accelerator at
KEK and the Super-K neutrino
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Florida
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Oscillation Firsts: OPERA
Pure νμ beam
Bricks of photographic films &
lead sheets
Scintillator counters
First observation
of ντ candidate
event!
Magnetic spectrometer
Phys. Lett. B 691, issue 3, pg 138-145 July 2010
Searching for νμντ
oscillations via appearance
analysis
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Florida
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Mass Firsts: ???
All mass experiments to date have only set upper limits on
the neutrino mass!
Many experiments underway/about to start
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Florida
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How do we perform our
measurements?
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Florida
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Cross Sections
Cross section = probability that an interaction will
take place
Volume of detector = V (m3)
Density of nucleons = n (1/m3)
Neutrino flux =  (1/m2s)





Cross Section  (m2) = # neutrino interactions per second
Flux * Density * Volume
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# of targets
59
Recipe for Detection
# neutrino = Cross Section  (m2) * Flux * Density * Volume
Interactions per sec
# of targets
Want a large # of interactions/second - the larger
your sample, the more precise your measurement
Need large-scale detectors (large # of targets)
Need high rate of neutrinos entering your detector
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Florida
60
Cross Section Measurements
Mandelstam
variables: square of
Isolate your selection of events
COM energy and
Fermi
Compare
dataconstant
to Monte Carlo in interesting variables
square of momentum
Fit final distribution to extract cross section parameters
transferlike form
factors, axial mass, etc.
Energy of neutrino
Nucleon mass
1.
2.
3.
Mixing matrix element
Q2
B(Q ) = 2 FA ( F1 + F2 )
M
4-momentum
gA
transfer
FA =
2
2
æ
Q2 ö
ç1+ 2 ÷
è MA ø
Measured in β decay
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Florida
MiniBooNE, νμ CCQE Events
61
Oscillation Measurements
Look for neutrino beam to disappear
Look for neutrino not present in the beam to appear
Both use CCQE typically because charged lepton is easy to tag
Charged Current
Quasi-Elastic
(CCQE)
MiniBooNE Anti-neutrino
5.66e20 POT
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Florida
62
Mass Measurements
Look for small fluctuations/bumps in beta, double-beta endpoint spectrum
http://www.mpi-hd.mpg.de/blaum/high-precision-ms/ptms/neutrino-mass.en.html
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Florida
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What is Significance?
What is the probability that you would find a result
due to chance?
Significant = probably not due to chance
Significance in sigma =
Observed – Expected
Total Error
σtot = √(σstat2 + σsys2)
In HEP, need 4-5 sigma to claim
observation/discovery, 3 sigma for verification of
previous claim
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Florida
64
CP and CPT Violation
Giunti and Kim, Fundamentals of Neutrino Physics and Astrophysics
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Florida
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Summary
Neutrinos created from a variety of sources, wide range of
energies
Engage in weak interactions only
Look for Cerenkov and scintillation light from created charged
lepton
Detect neutrinos using large vats of liquid, highly segmented
collider-like detectors
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Florida
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Summary
Observed deficit in solar, atmospheric neutrinos
proven to be due to flavor oscillations
therefore, neutrinos have mass!
Haven’t yet directly measured masses, only set limits
Experiments to perform first measurement of νμτ
oscillations, measure mass, underway
Primarily use CCQE to detect neutrinos in oscillation
experiments
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Florida
67
Neutrino Oscillation Theory
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68
History of Oscillation Theory
1957: Pontecorvo proposed oscillations, analogous
to neutral kaons (ν - ν)
1962: Maki, Nakagawa, Sakata suggested
transitions between different flavors
1967: fully developed theory of oscillations
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Florida
69
Oscillation Theory
The flavor (weak) neutrino states (νe, νμ, ντ) are really
comprised of three different mass states, ν1, ν2, ν3
3
| n a = åUa* i | n i
i=1
Where Uαi are elements of the PMNS matrix
(Pontecorvo-Maki-Nakagawa-Sakata)
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70
Oscillation Theory
In the quark sector, flavor eigenstates are
superpositions of weak eigenstates
allows generation-mixing decays
In the neutrino sector, flavor eigenstates are
superpositions of mass eigenstates
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Florida
71
The PMNS Matrix
Atmospheric
Short baseline reactor
Solar
0νββ Decay
Uαi
c = cos ϑ
s = sin ϑ
phase factor δ non-zero
only if CP violating
α1, α2 are only physical if neutrinos are
their own anti-particles (Majorana)
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Florida
72
The PMNS Matrix
Atmospheric
Short baseline reactor
Solar
0νββ Decay
Uαi
θ23 ≈ π/4
Maximal mixing
θ13 < π/20
θ12 ≈ π/6
Small, quark-like
Large, nonmixing
maximal mixing
Compare to the CKM matrix
θ23 ≈ π/76
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θ23 ≈ π/870
θ23 ≈ π/14
73
Two-Neutrino Approximation
Start with our definition of flavor states:
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D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
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Two-Neutrino Approximation
Look at the νμ state over time:
H. Ray, University of
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D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
75
Two-Neutrino Approximation
Question: Is it correct to assume that both mass
eigenstates have the same momentum (or same
energy)?
NO! But it turns out 2 wrongs DO make a right!
See “Paradoxes of neutrino oscillations”, Akhmedov and Smirnov, 2009
http://www.ictp.trieste.it/~smirnov/Akhmedov_n.pdf
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76
Two-Neutrino Approximation
Now assume the neutrinos are relativistic:
Work in “natural” units, where
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D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
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Two-Neutrino Approximation
Use binomial expansion!
2
x
(1+ x)a =1+ a x + a (a -1) .....
2!
Let p >> mo, and
Now rewrite the energy of the two mass states as:
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D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
78
Two-Neutrino Approximation
How does the νμ evolve in time?
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D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
79
Two-Neutrino Approximation
Now, let’s make some substitutions:
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D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
80
Two-Neutrino Approximation
That lets us go from here:
To here:
H. Ray, University of
Florida
D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
81
Two-Neutrino Approximation
Now, what’s the probability that a νμ will oscillate into a νe?
H. Ray, University of
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D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
82
Two-Neutrino Approximation
Now, what’s the probability that a νμ will oscillate into a νe?
H. Ray, University of
Florida
D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
83
Two-Neutrino Approximation
e e sin q cos q [1- (e
+iz -iz
2
2
iDm2 x
2p
1´ sin q cos q [1- (e
2
2
+e
iDm2 x
2p
-iDm2 x
2p
+e
)+e
-iDm2 x
2p
iDm2 x -iDm2 x
2p
2p
e
)+1]
Dm x
(sin q cosq ) [2 - 2cos(
)]
2p
2
2
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84
]
Two-Neutrino Approximation
2
Dm
x
2
(sin q cosq ) [2 - 2cos(
)]
2p
2
1
Dm
x
2
( sin 2q ) 2 ´[1- cos(
)]
2
2p
1 2
Dm 2 x
sin 2q [1- cos(
)]
2
2p
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85
Two-Neutrino Approximation
The neutrino is relativistic, so we can make another substitution:
and similarly,
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D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
86
Two-Neutrino Approximation
Use the trig identity
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to get:
D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
87
Two-Neutrino Approximation
Now make the argument of the sine be dimensionless!
Substitute ħc = 197 eV nm to get:
H. Ray, University of
Florida
D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
88
Two-Neutrino Approximation
The probability for oscillations between states (no CP
violation) is:
Δm2ab = m2a – m2b
L ( m) 

2
2
P e ( L / E )  sin 2 sin 1.27 m (eV )

E ( MeV ) 

2
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2
89
Visualizing Neutrino Oscillations
Neutrino oscillation is an interference experiment (double slit
experiment)

light source
slit
screen

If 2 neutrino mass states, 1 and 2, have different phases, they
cause quantum interference.
H. Ray, University of
Florida
90
Visualizing Neutrino Oscillations
Neutrino oscillation is an interference experiment (double slit
experiment)
light source
U1

 2
slit
Ue1*
screen
e
1 e
If 2 is heavier than 1 they have different group velocities hence
different phases, thus the superposition of those 2 wave packets
no longer makes the same state
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91
The Sweet Spot for Observation
For a mono-energetic neutrino beam
Maximum chance of observing
if detector is situated these
distances from the point of
creation of the neutrino beam
H. Ray, University of
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D. Smith, http://physicsx.pr.erau.edu/Office/oscillations.pdf
92
Understanding Oscillation Fits
æ
L(m) ö
2
2
2
2
Pm®e (L / E) = sin 2q sin ç1.27Dm (eV )
÷
E(MeV ) ø
è
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93
Other Neutrino Properties
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Florida
94
Mass hierarchy problem
L ( m) 

2
2
P e ( L / E )  sin 2 sin 1.27 m (eV )

E ( MeV ) 

2
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2
http://francisthemulenews.wordpress.com/tag/fisica-teorica/
95
Neutrino Properties
How do neutrinos acquire mass?
Dirac vs Majorana particle?
Absolute masses of neutrinos
Mass hierarchy
Mixing angles, why so different from quarks?
CP violating?
Why are ν masses so small wrt other SM
fermions?
• Interaction rates
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Summary of Today
Neutrinos are a fundamental particle of the SM
They come from a wide variety of sources
Only engage in weak interactions, interact very rarely
Detect using light signatures, radiochemical means
Use big vats of liquid and highly segmented detectors
They oscillate, or change flavor
Oscillation probability can be altered depending on neutrino flavor, if neutrinos are traveling
through dense matter
We don’t know their mass
Many mysteries regarding neutrino properties, very rich field for exploration
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BACKUP
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Florida
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What about Matter Effects?
Neutrinos interact with matter – so what happens when
neutrinos travel through the Earth to get to your detector?
How does that affect oscillations?
Subject to a potential due to coherent forward elastic
scattering with the particles in medium (electrons
and nucleons)
Potential is equivalent to index of refraction, modifies
mixing of neutrinos
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Florida
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Matter Effects
1978: L. Wolfenstein found neutrino mixing angle in vacuum is replaced
by an effective mixing angle in matter
For some matter densities it can be large, even if the mixing angle in
vacuum is small
1985: Mikheev and Smirnov found it’s possible to have flavor transitions
when νs propagate in a medium with varying density, there exists a region
along neutrino path in which effective mixing angle passes through the
maximal mixing value of π/4
MSW effect: most important application is in solar neutrino flavor
transitions
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Matter Effects
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Matter Effects
Neutrinos in matter affected by coherent AND incoherent
scattering with particles in the medium
Incoherent scattering is extremely small in most situations
and can be safely neglected
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Incoherent Matter Effects
σ for neutrino weak interactions with a charged lepton or hadron in the
center of mass (COM) frame is
σCOM ~ GF s
s is the Lorentz invariant Mandelstam variable which represents the
square of the total energy in the COM frame
In the lab frame s = 2EM
E is the neutrino energy and M is the mass of the target particle (neutrino
mass is neglected)
σLAB ~ GFEM ~ 10-38 cm2 EM/GeV2
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Florida
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Incoherent Matter Effects
Mean free path due to incoherent scatterings in a medium
with number density N of target particles is
1
10 cm
l»
»
Ns (N cm3 )(E M / GeV 2 )
38
In normal matter, main target particles are nucleons with
mass M ~ 1 GeV, number density NA/cm3 ~ 1024 / cm3
10 cm
»
(E / Gev)
14
lmatter
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Incoherent Matter Effects
lmatter
1014 cm
»
(E / Gev)
Earth’s diameter ~109 cm
Incoherent effects relevant if E > 105 GeV, extremely high!
Increase nucleon density to 1012 NA/cm3, then νs with E ~ 1
MeV have mean free path of 1 km
This high density can be reached in neutron stars and
supernova cores where diameter ~1 km, opaque to low
energy neutrinos
Only in extreme cases do we need to take into account the
incoherent scatterings
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Coherent Matter Effects
Evolution of active flavors through matter is affected by
effective potentials due to coherent interactions via CC and
NC scattering
http://www.nu.to.infn.it/pap/0812.3646/img232.gif
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Florida
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Coherent Matter Effects
Matter potential is:
1
Va = VCCdae +VNC = 2GF (N edae - N n )
2
Identical for νμ and ντ, different for νe
See same effect for νμ  ντ oscillations,
different for νe  νμ
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