Enrique Fern

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Neutrino Oscillations a km-scale Quantum
Phenomenon

• Enrique Fernández
• Univ. Autónoma Barcelona/IFAE

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The Neutrino Hypothesis
circa-1930 If nuclear b-decay is a two-body
decay ? energy cannot be conserved ? the
spin-statistics connection does not hold
e.g. energy conservation implies that the
electron should have a fixed energy. Observation
tells us that the spectrum of the electron is
continuous.
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The Neutrino Hypothesis
These two problems lead W. Pauli to postulate
the existence of a particle that escaped
detection
(4 December 1930, Zürich) Dear radioactive ladies
and gentlemen ...I have hit upon a desperate
remedy to save the exchange theorem and the
energy theorem. Namely there is the possibility
that there could exist in the nuclei electrically
neutral particles that I wish to call neutrons...
But I dont feel secure enough to publish
anything about this idea I admit that my
remedy may appear to have a small a priori
probability because neutrons, if they exist,
would probably long ago have been seen. However,
only those who wager can win
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The Neutrino Hypothesis
What Pauli was saying
for 2-body decay
End point and shape of the spectrum depend on
neutrino mass. This method of measuring the mass,
still in use, gives mnlt 2.2 eV/c2.
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Fermis Theory of Weak-Interactions
Pauli invented the neutrino and Fermi (in 1934)
made an extremely successful theory of weak
interactions based on it

• are Dirac spinors Gi are 4X4 complex matrices
  currents can be Scalar, Vector, Axial Vector,
  Pseudoscalar o Tensor.

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Fermis Theory of Weak-Interactions
Fermis theory lead to some predictions
b decay
Observed by Jolliot-Curie in 1934.
electron capture
Observed by Alvarez in 1938.
inverse b-decay
Predicted by Bethe and Peierls.
Bethe and Bacher (1936) there is only one
process which neutrinos can certainly cause. That
is the inverse beta process, consisting of the
capture of a neutrino by a nucleus together with
the emission of an electron (positron). It
seems practically impossible to detect neutrinos
in the free state
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Neutrino discovery
Remember inverse-beta-decay
Is it possible to detect neutrinos by means of
this reaction? Neutrino cross-sections are small,
very small. Today we know that the cross-section
for the above reaction is of the order of
10-40cm2. The mean free path of such neutrinos
in, say in a block of Lead, is of the order of 1
light year!. Detecting neutrinos is next to
impossible.
Or may be not
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Neutrino discovery
The atomic age made available very intense
sources of neutrinos nuclear bombs and nuclear
reactors.
Typical nuclear bomb
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Neutrino discovery
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Neutrino discovery

The project was actually approved at Los Alamos!
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Neutrino discovery

A much better idea Put a detector at some
distance from the core of a nuclear reactor.
Use delayed coincidence between e annihilation
and neutron capture
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Neutrino discovery

On June 14, 1956, Reines and Cowan sent a
telegram to Pauli We are happy to inform you
that we have definitely detected neutrinos from
fission fragments by observing inverse beta decay
of protons
1995 Nobel Prize to Reines (shared with M. Perl)
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Peculiar neutrino weak-interaction properties
Parity is not conserved in weak interactions.
T. D. Lee and C. N. Yang (1950) To decide
univocally whether parity is conserved in weak
interactions one must perform an experiment to
determine whether weak interactions differentiate
the right from the left.
A relatively simple possibility is to measure the
angular distribution of the electrons coming from
beta decays of oriented nucleian asymmetry of
the distributionconstitutes an unequivocal proof
that parity is not conserved in beta decays.
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Peculiar neutrino weak-interaction properties
Experiment of C.S. Wu et al (1956).
Measure electrons from b-decay of polarized Co
nuclei.
Polarization is obtained by aligning nuclear
spins with external magnetic field. What the
experiment measured was that
is, the correlation between nuclear spin and
electron momentum. The quantity
is a pseudoscalar, it changes sign under parity.
If parity is conserved should be
zero. The measured value was close to -1.
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Peculiar neutrino weak-interaction properties
Lee and Yang interpretation (1957)
The antineutrino is always emitted with helicity
1.
Lee and Yang formulated the 2-component neutrino
theory neutrinos ? left (negative)
helicity antineutrinos ? right
(positive) helicity Neutrinos should have zero
mass.
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Peculiar neutrino weak-interaction properties
The actual proof that the neutrino has negative
helicity was done by M. Goldhaber and
collaborators in 1958
The Sm nucleus recoils from the neutrino. It
decays to the ground state by emitting a g. The
polarization of the g measures the helicity of
the neutrino (in a non-trivial way!).
Neutrinos have negative helicity.
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Peculiar neutrino weak-interaction properties
BUT R. Feynman and M. Gell-Mann concluded that
the weak interaction is V-A (1958) Weak
interaction acts on the ? left-handed
component of particles. ? right-handed
component of antiparticles.
There could be right-handed neutrinos and
left-handed antineutrinos, but they would not
interact weakly!
For massless particles handeness and helicity are
equivalent. The Co and Eu experiments do not
necessarily imply that the neutrinos are
massless. But zero-mass neutrinos were
nevertheless incorporated into the SM, , since
there was no evidence to the contrary.
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Peculiar neutrino weak-interaction properties
We will see later that in fact neutrinos have
mass. Therefore there could be right-handed
neutrinos and left-handed antineutrinos. For a
neutral particle (all charges equal to zero)
there are two possibilities ? Dirac
neutrinos nR is a distinct state from nL The
neutrino field is a 4 component spinor ? Majorana
neutrinos nR is the antineutrino of nL The
neutrino is its own antiparticle! We still do not
know which is the case. The only hope to check
this is neutrinoless double-beta-decay.
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More than one neutrino
So far we have seen only electron-neutrinos, ne.
These neutrinos are produced together with
electrons in b-decay.

• But there was another particle, like the
  electron but heavier the muon. This particle
  should decay into an electron and a gamma
• m?eg
• through the diagram

But this decay did not occur.
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More than one neutrino
Furthermore in the late 40s it became clear that
the muon decayed into more than one particle.
Presumably the unseen particles were neutrinos
m? e n n
Were the neutrinos the same?
There was a particle that decayed into a muon and
a (presumably) neutrino the pion. p? m n
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More than one neutrino
With the new accelerators it became plausible to
make intense n beams. The idea occurred
independently to Schwartz and Pontecorvo.

• ? m n
• nN?e o m?

k p p
n
p
m n
protons
Target and Magnetic Horn
detector
shielding
Accelerator
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More than one neutrino
An experiment was done at the Brookhaven 30 GeV
accelerator in 1962. Out of 29 events none was
compatible with an electron in the final state.
1988 Nobel Prize
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3 neutrino families
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3 neutrino families
If neutrinos are massless there is no interaction
that will mix the 3 families. Lepton-family
number as well as global lepton number are
conserved. But if the neutrino had mass, there
could be mixing through the same Higgs mechanism
that gives mass to the particles. Mass
eigenstates and weak eigenstates do not need to
be the same, as it indeed happens with the quarks.
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Neutrino oscillations
In the early sixties, Pontecorvo suggested that
if neutrinos had mass they could
oscillate. Assume we start with a pure neutrino
of a given family at t0, and let it evolve
freely. After time t
Lets assume, for simplicity, that we have only
two families
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Neutrino oscillations
Suppose that we create a beam of pure nm at some
source at t0. Question what is the
probability of finding a ne in a detector
located at a distance x from the source of the nm
flux?
After some algebra
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The solar neutrino problem (s)
In 1960 R. Davies started with an experiment to
detect solar neutrinos. The original motivation
was to check the mechanism for producing energy
in the Sun
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The solar neutrino problem (s)
The total luminosity is very well measured L
3.846x1026 watts All fusion reaction amount
to 4p ? 4He 2e 2ne (Q24.68
MeV) Assuming that gs and kinetic energy
(except that of the ns) go to heat, the heat
production per reaction is W
Q4mec2-ltEnsgt 26.1 MeV The total number of
nes produced by the Sun is then Nn 2 L /W
1.8x3038 ne . s-1 Flux on Earth surface
6.4x1010 ne/cm2s-1 (day and night)
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The solar neutrino problem (s)
The flux of solar neutrinos is very large but
their detection is very difficult. The pioneer
experiment of R.Davies took place at the
Homestake Mine in S. Dakota (at 1350m depth).
Large (600 tons) of Perchloroethylene (C2Cl4).
The detection method is radiochemical.
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The solar neutrino problem (s)
SSM Prediction 7.7 SNU (5.9 for 8B, 1.15 for
7Be, 0.65 others) 1 SNU10-36 captures/(atom
sec) Measurement2.56?0.16?0.16 SNU
The measurement was repeated by many experiments
with different techniques (e.g. Galium instead of
Clorine). All of them (except one) saw less
neutrinos than expected.
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The solar neutrino problem (s)
The problem was finally solved in 2002 with the
results of SNO, beautifully confirmed by KAMLAND
this year. But more later.
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The atmospheric connection.
A new era of detectors SuperKamiokande
50 ktons of pure H2O at 1000 m depth
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The atmospheric connection.
Detect Cherenkov light produced by charged lepton
l? from reacction nN? l? X (le,m), or e- from
ne-?ne- . Detector operates in real time and
has directional information.
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The atmospheric connection.
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The atmospheric connection.
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Superkamiokande Atmospheric Data
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Back to Solar Neutrinos
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The detected reaction is
ne

• ne X ? e- X

nm
.5
nt
0

• The reactions
• nm X ? m- X
• nt X ? t- X
• are not possible

En lt mm, mt ?
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In addition to charged-current reactions
there are neutral current reactions
The probles is to detect them
A special case is n e- ? n e- which is
that detected in SK. This reaction proceeds
through both CC and NC but they are
indistinguishable.
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One way to distinguish (proposed by H. H. Cheng
in 1984) is to use D2O (heavy water) as target,
instead of water.
In deuterium (D) ne D ? p p e- (CC) nl
D ? nl p n (NC) (l e,m,t) In the
last reaction the p and n break apart if the
energy is abobe 2.22 MeV. The free neutron is
captured, liberating 6.25 MeV. But its detection
is difficult... Another problem is how to get
tons of heavy-water.
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Sudbury Neutrino Observatory (S N O)
Detector located in Ni mine at 2000m depth.
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1kT of D20, surrounded by tank of 7.8 kT of
ultrapure H2O.
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In the SNO experiment there are 3 reactions
measured ne d ? p p e- CC nx e- ? nx
e- ES (as in SK) nx d ? p n nx NC
In D2O the events are selected statistically,
from characteristic variables for each reaction.
Derived from NC
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KAMLAND reactor experiment
Nuclear reactors are very intense sources of ne
from the b-decay of the neutron-reach fission
fragments.
Each fission results into 6 ne of various
energies.
Detection through inverse b-decay (as in
Reines-Cowan experiment).
KAMLAND liquid scintillator.
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KAMLAND reactor experiment
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Global fits to atmospheric and solar
sin2 q23 almost maximal sin2 q12 large sin2 q13
lt 0.05
Dm2atm 3x10-3 eV2 Dm2solar 3x10-5 eV2
But things could be more complicated.
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Future
In oscillations the big unknown now is q13.
CP violation?. Neutrino super-beams
Cosmic Neutrinos (from Super-Novae to
unexpected). Large projects underway.
The neutrino is a special particle and there is
still a lot of conventional physics to be done
with neutrinos.