Weak interactions, P, C and CP

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Weak interactions, P, C and CP

• Introduction
• Need of neutral currents
• Electroweak and Higgs
• Parity in weak interactions
• Helicity of the neutrino, C and CP
• Pion decay
• The K0K0 system
• KS regeneration
• Strangeness oscillation
• CP violation
• neutrino oscillations
• mixing, GIM mechanism and CKM matrix

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Introduction
Weak interaction governs radioactive decays,
decays which dont conserve strangeness, charm,
bottom or top, and reactions where neutrinos are
present.
Weak interactions are described by the exchange
of vector bosons who are the carriers of the weak
force. They were discovered in 1983 the W, W-
and Z0. Contrary to the massless photon and
gluon, these vector mesons are very massive
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The need for neutral currents
Weak interactions were thought to be only of the
charged-current type.
These reactions were mediated by W. This caused
a problem
This process has a divergent cross section
unless a neutral vector boson Z0 also exists.
g weak coupling
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Electroweak and Higgs
Another divergent process is
unless Z0 exists, and the weak coupling g is
approximately equal to the electromagnetic
coupling e
Exact cancellation is true only for massless
electron. For finite electron mass, need to
introduce a new scalar particle the Higgs
particle.
5
Mass estimate of the Higgs
6
This is where we are today
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Neutrino interactions
W exchange gives Charged-Current (CC) events and
Z0 exchange gives Neutral-Current (NC) events.
In CC events, the outgoing lepton determines if
neutrino or antineutrino in initial state.
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Weinberg-Salam model
Electroweak interactions are mediated by four
massless bosons, arranged in a triplet and a
singlet, in multiplets of weak isospin and
weak hypercharge. The triplet belongs to the
group SU(2) and the singlet to the group U(1) ?
model of Weinberg Salam referred to as SU(2) x
U(1). By a mechanism introduced by
Englert-Brout-Higgs, a scalar boson (Higgs)
generates through spontaneous symmetry breaking
(see ferromagnet) three very massive vector
bosons, W and Z0, while the fourth particle, the
photon, remains massless. The whole Lagrangian
can be expressed as follows
This gives that e g sin ?W, where ?W is the
Weinberg mixing angle.
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The weak isospin triplet is composed of three
massless gauge bosons W, W- and W0. In addition
there is a weak iso-singlet B0. In the theory of
Weinberg-Salam, the particles observed in nature
are mixtures of B0 and W0
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Spontaneous Breakdown of Rotational Symmetry
before dinner
once dinner starts
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Number of generations
Measurement of Z0 and evidence for 3 generations
First signs for existence of Z0
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Parity in weak interaction
Parity operator was introduced by Wigner in 1927
in context with atomic physics, and was believed
to be a universal law. The ? - ? puzzle was the
first indication that P conservation is not
universal.
The following decays were known of particles
around 500 MeV
Experimental data indicated J(?) J(?) 0.
The ? - ? puzzle
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Parity non-conservation
Lee and Young pointed out that all the evidence
for P conservation came from strong and
electromagnetic interactions. They hypothesized
that P is not conserved in weak interactions. The
decay times of ? and ? were consistent with the
decay being a weak one ? ? and ? are the same
particle, K meson, but do not conserve parity in
the decay. They are eigenstates of Parity in
strong and em interactions, but not in weak ones.
predicted that P will not be conserved in
radioactive decays. Was confirmed by Wu in 1957
and Lee (31) and Young (35) were awarded the
Nobel prize in Physics in 1957.
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The Wu experiment
Wu performed the parity-conservation test,
immediately after it was suggested by Lee and
Young.
She studied ?-decay of polarized 60Co.
Parity operation on the ? decay changes momentum
direction of electrons but does not change spin
direction.
If P conserved, no forward-backward asymmetry
expected.
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Wu experiment (2)
Cooled the sample of 60Co nuclei to 0.01 K in
presence of external magnetic field ? obtained
polarized nuclei with spins aligned in magnetic
field direction.
A and B measure the two photons, and the
anthracene scintillation counter measure the
intensity of the ? emission. The magnetic field
direction is changed from up (full dots) to down
(open circles). A clear asymmetry is observed,
which disappears as the system warms up and the
polarization stops.
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Helicity and P, C
Helicity of a particle is defined as its spin
projection along its direction of motion.
A particle is called right handed if its helicity
is positive, ? gt 0, and left handed if it is
negative, ? lt 0. An electron can exist in two
states eR and eL.
The parity operation P turns a right handed
particle into a left handed one because the
parity operation reverses the momentum vector but
not the spin one. The operation of charge
conjugation C does not change the handiness of
the particle but changes it to its antiparticle.
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Helicity of the neutrino
M. Goldhaber (PR 109(1958)1015) measured the
helicity of the neutrino in a K-capture of
Europium-152
The excited state of Samarium with total angular
momentum J1 decays to its ground state with the
emission of a photon
Select photons which were emitted in the
direction of the decaying 152Sm. The helicity of
the neutrino is the same as that of the photon ?
measuring the helicity of the photon measures the
helicity of the neutrino.
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Helicity of neutrino (2)
photon emission
Electron capture K shell, l0

• Momenta, p

Eu at rest
Select photons in Sm dirn
Neutrino, Sm in opposite dirns

• spin

?
?
e-
S ½
S 1
right-handed
right-handed
OR
S- ½
S- 1
Left-handed
Left-handed

• Helicities of forward photon and neutrino same
• Measure photon helicity, find neutrino helicity

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Helicity of neutrino, P, C, CP
Neutrinos are close to massless. This means that
relativistic fermions which can be treated as
massless would exist also only as left-handed,
with the anti-fermion being right-handed.
(suppression of forbidden states m2/2E2)
The implication of having only left-handed
neutrino is breaking of P and C conservation
However, CP can be conserved
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P
Charge Inversion Particle-antiparticle mirror
C
Parity Inversion Spatial mirror
CP
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Pion decay
The pion decays with a puzzling branching ratio
Since the pion spin (and helicity) is 0, the
decay in its rest frame has the following
configuration
The neutrino is left-handed ? the lepton also has
to be left-handed, to conserve helicity.
In positron decay mode, the positron is
relativistic ? must behave like the antineutrino
? exists only as eR, which suppresses this decay
mode.
In muon decay mode, muon not relativistic ? can
exist both as right- handed and as left-handed.
In the decay it is always left-handed. Thus muons
from pion decay are polarized as left-handed, to
cancel the left-handed neutrino.
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The system
The two neutral Kaons are two distinct particles
in strong and em interactions, with definite
strangeness numbers. Their decay is however
through weak interactions, which does not
conserve strangeness. Thus the two states can
mix. One can have transitions between the two
states
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CP of the neutral K system
The mixing happens in such a way as to produce
eigenstates of operators which are conserved in
weak interactions. Since CP seems to be conserved
in weak interactions, we need to create
combinations which are eigenstates of CP.
Chose the arbitrary phases ? ? 1. Clearly
the K0s are not eigenstates of CP, but one can
form linear combination which are
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K1, K2, KS, KL
There are two components in the decay of the
neutral K a short lived state, which decays into
2? and is called KS, and a longer living K which
decays into 3?, denoted KL. Their life times are
Since ?0 has C, the CP of the ?0?0 system is
determined by their P, and the same is true for
the ?0?0?0 system. Thus
One therefore associates the experimentally
observed states KS and KL with K1 and K2.
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KS regeneration
Can verify experimentally the superposition
scheme of the neutral K. Start with a pure K0
beam, obtained from the reaction ?-p?K0?. The K0
beam moves in vacuum for length corresponding to
100?(KS). Only 50 beam intensity left,
consisting of KL. This beam interacts strongly
with a target (see figure).
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Regeneration (2)
The two components of KL which pass through
target are both reduced in intensity after
interacting with target. The reduction is not the
same for both components because
The reason for this there are no S1 baryons.
What do we find after KL passes the target?
Denote
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Regeneration (3)
The strangeness content of the beam which emerges
from the block is therefore
In terms of
? the short lived K1 (KS) has been regenerated.
This was confirmed experimentally by detecting ??
decays.
Since
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Strangeness oscillation
K0 has a definite strangeness (S1) when
produced in a strong interaction
However, some time after the production, the
traveling K0 becomes a superposition of two
components with S1 and S-1. The intensities of
these two components are a function of time and
oscillate. This oscillation enable the
measurement of the small mass difference ?m
between K0S and K0L.
At t0
At time t, the two components evolve differently
with time
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Strangeness oscillation (2)
For unstable particles with mass m and lifetime ?
1/?, the time dependent wavefunction, in the
particle rest system, is expressed
Therefore we can write
which started as a pure K0
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Strangeness oscillation (3)
The intensities of the two components, after time
t, is
Only they can produce S-1 baryons (?hyperons).
Measuring number of hyperons as function of the
distance gives
Although K1 and K2 are mixtures of K0 and ,
which have identical masses, they have a small
mass difference.
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CP violation
Are K1 and K2 the particles appropriate for the
weak force? This is true if CP is conserved, as
they are eigenstates of CP.
A test of CP conservation in weak interactions
would be to look for a 2? decay of K2. If CP is
conserved, this decay is forbidden.
Used the AGS accelerator at Brookhaven. 30 GeV
proton beam. Be target. K? were produced in pBe
collisions. Collimator at 4.5 m from the target,
magnet at 6.5 m, 2nd collimator at 18 m. K1
decayed before reaching the 2nd collimator.
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Observation of K2?2p

• Two spectrometers
• Spark chamber
• Magnet
• Scintillator
• Water Cherenkov counter
• Spark chambers were triggered on a coincidence
  between water Cherenkov (vgt0.75 c - pions) and
  scintillation counters. This removed most slow
  particles produced in collisions of neutrons

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Results
Observed about 50 events out of 23,000 decays
where K2? ? ?- ? CP is violated ? the particles
seen by the weak interactions are KS and KL,
which are superpositions of the CP eigenstates K1
and K2
Why is CP violated? One possible explanation CP
is conserved in weak interactions, and the
violation is due to some superweak force. CP
violation should also be seen in case of D0 and
B0. There is a special B-factory at SLAC, where
the BaBar collaboration is seeing some
encouraging signals for this effect. Another
experiment in KEK, BELLE, is also seeing the same
results. Both results are still preliminary.
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Implications of CP violation
Can convey to intelligent alien the absolute
distinction between left and right CP violation
is also demonstrated in the leptonic decay of KL
Can communicate that we define the neutrino as
the one associated with the more abundant
leptonic decay mode of the long-lived
KL-particle. This establishes a common
matter-antimatter convention which allows the
alien to identify uniquely our handedness
convention.
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Matter-antimatter asymmetry

• Combining GUT with CP violation can explain the
  net baryon number in the universe (Andrei
  Sakharov, 1967, baryogenesis)
• at times less then 10-35s after the Big Bang,
  temp still higher than 1028K, superheavy gauge
  bosons X and anti-X (MX1015GeV) equally produced
  and remained in thermal equilibrium

• universe expended and cooled. X and anti-X can
  no longer be produced. Expansion of universe
  destroyed equilibrium expansion faster than the
  bosons could interact ? large numbers of bosons
  began to decay.
• because of CP violation, decay rate of X to
  quark is slightly more rapid than that of anti-X
  to anti-quark ? the average value of the baryon
  number states bigger than antibaryons, creating a
  net baryon number in the present universe.

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Highlights of neutrino history

• 1930 Pauli postulates neutrino existence
• 1953 Clyde Cowan and Fred Reines discover
  electron neutrino (Nobel 1995)
• 1957 Neutrino oscillations predicted by
  Pontecorvo
• 1962 discover the muon neutrino (Nobel 1988)
• 1973 Neutral current neutrino interactions
  observed
• 1974 discover tau particle (Nobel 1995) and
  assumed existence of tau neutrino (experimental
  evidence 2000)
• 1989 Only 3 light neutrino families
• 1998 the Super-Kamiokande collaboration announce
  evidence of non-zero neutrino mass (Nobel 2002)

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Quark mixing
In the SM, there is symmetry between leptons and
quarks. There is lepton universality (unless
there is a reason to break it see ? decay), so
expect also existence of quark universality. Does
it work?
For simplicity, assume 3 leptons and 3 quarks.
The weak decays can be classified into two
categories those which do not change
strangeness, ?S0, and those where strangeness is
changed by one unit, ?S1. The ? decay of the
neutron, and that of the ? are the respective
examples
On the quark level, in the decay a d (s)? u with
the emission of W-
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Cabibbo model
Quark universality would require that n and ?
?-decays should occur with about equal strength
(apart from phase space factors). Experimentally
the ?S0 decay is about 20 times stronger than
the ?S1 decay.
Cabibbo suggested the following solution (1963)
the eigenstates of the quarks in weak
interactions are different from those in strong
interactions.
Cabibbos conjecture was that the quarks that
participate in the weak interaction are a mixture
of the quarks that participate in the strong
interaction.
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Cabibbo angle
  This mixing was originally postulated by
Cabibbo (1963) to explain certain decay patterns
in the weak interactions and originally had only
to do with the d and s quarks. d d cosq s
sinq Thus the form of the interaction (charged
current) has an extra factor for d and s quarks
Purely leptonic decays (e.g. muon decay) do
not contain the Cabibbo factor
The Cabibbo angle can be measured using data from
the following reactions
From the above branching ratios we find qc
0.27 radians
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Extension to 4 quarks (GIM)
In 1969-70 Glashow, Iliopoulos, and Maiani (GIM)
proposed to extend the model of Cabibbo by
postulating the existence of a fourth quark
charm.
Adding a fourth quark actually solved a long
standing puzzle in weak interactions, the
absence (i.e. very small BR) of decays
involving a flavor (e.g. strangeness) changing
neutral current
However, Cabibbos model could NOT incorporate CP
violation and by 1977 there was evidence for 5
quarks!
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The Cabibbo-Kobayashi-Maskawa (CKM) model

• In 1972 (2 years before discovery of charm!)
  Kobayashi and Maskawa extended Cabibbos idea to
  six quarks
• 6 quarks (3 generations or families)
• 3x3 matrix that mixes the weak quarks and the
  strong quarks (instead of 2x2)
• The matrix is unitary ?3 angles (generalized
  Cabibbo angles), 1 phase (instead of 1 parameter)
• The phase allows for CP violation

Just like ?c had to be determined from
experiment, the matrix elements of the CKM matrix
must also be obtained from experiment.
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CKM Matrix
The CKM matrix can be written in many forms 1)
In terms of three angles and phase
This matrix is not unique, many other 3X3 forms
in the literature. This one is from PDG2000.
The four real parameters are d, q12, q23, and
q13. Here ssin, ccos, and the numbers refer to
the quark generations, e.g. s12sinq12.
2) In terms of coupling to charge 2/3 quarks
(best for illustrating physics!)
3) In terms of the sine of the Cabibbo angle
(q12). This representation uses the fact that
s12gtgts23gtgts13.
Wolfenstein representaton
Here lsinq12, and A, r, h are all real and
approximately one. This representation is very
good for relating CP violation to specific decay
rates.
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CKM Matrix
The magnitudes of the CKM elements, from
experiment are (PDG2008)

• There are several interesting patterns here
• The CKM matrix is almost diagonal (off diagonal
  elements are small).
• The further away from a family, the smaller the
  matrix element (e.g. VubltltVud).
• Using 1) and 2), we see that certain decay chains
  are preferred
• c s over c d D0 K-p over D0 p-p (exp.
  find 3.8 vs 0.15)
• b c over b u B0 D-p over B0 p-p (exp.
  find 3x10-3 vs 1x10-5)
• Since the matrix is supposed to be unitary there
  are lots of constraints among
• the matrix elements

So far experimental results are consistent with
expectations from a Unitary matrix. But as
precision of experiments increases, we might see
deviations from Unitarity.
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Measuring the CKM Matrix
No one knows how to calculate the values of the
CKM matrix. Experimentally, the cleanest way to
measure the CKM elements is by using interactions
or decays involving leptons. ? CKM factors are
only present at one vertex in decays with
leptons. Vud neutron decay n?pe? d ?
ue? Vus kaon decay K0 ? pe-?e s ?
ue? Vbu B-meson decay B- ? (? or ?)e-?e b ?
ue? Vbc B-meson decay B- ? D0e-?e b ?
ce? Vcs charm decay D0 ? K-e?e c ?
se? Vcd neutrino interactions ??d ? ?-c d
? c
D0 K-e?e
Amplitude ?Vcs Decay rate ?Vcs2
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Neutrino mass we will skip this chapter from
here to th3 end
Are neutrinos massless? Difficult to measure mass
of neutrino. Only upper limits were available.
The best came for the electron-neutrino from
study of Kurie plots from ? decay
One studies the momentum spectra of the electron,
the tail of which is sensitive to the
anti-neutrino mass. In addition to the simple
kinematics, one needs to apply nuclear
corrections, which are not always very
unambiguous.
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THE BETA-DECAY SPECTRUM OF TRITIUM
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Kurie Plot
? (E0 Ee) if m?0
pe Ee
Ee
coulomb correction
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RECENT MAINZ DATA 10 -YEARS OF
NEUTRINO
MASS FROM TRITIUM
EXPERIMENTS
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Neutrino oscillations
In a similar way to strangeness oscillations, one
can also have neutrino oscillations if the weak
eigenstate neutrinos are mixtures of neutrinos
of definite mass. Assuming only two massive
neutrinos (two-flavor oscillations)
One can calculate the probability of detecting a
neutrino of a certain flavor at a distance L from
the original neutrino source
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Neutrino sources for experimentation
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Super-Kamiokande and K2K
Super-Kamiokande Neutrino Observatory K2K (KEK to
Kamiokande) long baseline experiment Neutrino
beam generated at KEK (national HEP lab) 98 nm,
mean En 1.3 GeV Beam goes through the earth to
Super-K, 250 km away
Toyama
SK
KEK
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Super-Kamiokande
US-Japan collaboration (100 physicists) 50,000
ton ring-imaging water Cherenkov detector Inner
Detector 11,146 50cm PMTs, non-reflective liner

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Atmospheric Neutrinos

• Produced by cosmic rays in upper atmosphere
  (altitude Z1520 km)
• p? µ? nµ (anti- nµ)
• µ? e ? ne (anti- ne) anti- nµ (nµ)
• Expect 2 nµ 1 ne
• (Note Super-Kamiokande does not distinguish
  between
• n and anti-n)

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Type of Events

• Look for
• nµ n -gt µ p
• ne n -gt e p
• nµ p -gt µ p p
• ne p -gt e p p
• Atmospheric neutrinos GeV
• Use information from Cerenkov Rings from µ and e
  to reconstruct events

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Event Summary
We expected R1!
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Zenith Angle Distribution
Lost by oscillation of
?
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Atmospheric neutrino results
no-oscillations expectation
DATA
best-fit (Dm2 3x10-3 eV2)
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Solar neutrinos
Experiment Reaction Observed/ expected rate
SAGE 71Ga?e?71Gee- 0.560.07
GALLEX 71Ga?e?71Gee- 0.530.08
HOMESTAKE 37Cl ?e ?37Are- 0.270.04
KAMIOKA ?ee- ? ?ee- 0.390.06
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K2K accelerator neutrinos
Observed 108 events in Super-K, while the
expected number is 150.9 11.6-10.0 for the
no-oscillation hypothesis.
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Why build a detector at the South Pole?

• To look for the neutrinos interaction product
  (e,m,t)
• To use the earth as a filter
• To reject backgrounds

n
cosmic ray
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Location of Ice Cube
Ice Cube
AMANDA
South Pole
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Structure of Ice Cube

• 80 Strings
• 4800 Optical Modules
• 1 k? volume
• AMANDA within IceCube
• Energy Range 10E7eV 10E20eV

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AMANDA
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