Outline of lectures:

1

• Outline of lectures
• Status of the field What we know for sure and
  what we
• should try to find out in near future?
• 2) Is the total lepton number conserved? Are
  neutrinos Dirac
• or Majorana fermions?
• 3) Exploring the consequences of finite neutrino
  mass Neutrino
• magnetic moments, muon decay, beta decay.
  Scattered comments
• on particle physics models and the possible path
  to the nSM.
• 4) Neutrinos in astrophysics and cosmology.

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1) Prehistory birth of neutrino In nuclear a
and g decay discrete lines were observed,
however, the b spectrum of 210Bi looked
continuous (Chadwick 1914). The Q-value is 1161
keV, but the average b energy is only 337 keV
(Meitner1930). This violated energy conservation.
Also, the it was assumed that a nucleus, e.g.
14N, was made of 14 protons and 7 electrons. Yet
its statistics looked like BE, not FD. Way out
was suggested by Pauli (famous letter,
12/4/1930), when he proposed the existence of
neutrinos. Fermi (1934) formulated the theory
of b decay. Neutrinos and electrons were created
in the decay, not present beforehand. Bethe and
Peierls (1934) estimated neutrino cross section
as 10-44 cm2, hence unobservable. Discovery of
the neutron (Chadwick 32, Nobel Prize 1935))
solved the issue of statistics.
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Estimate of the cross section Take n -gt p e-
n and consider n p -gt n e At low (MeV)
energies the cross section can depend only on
E (the energy of the neutrino or positron). Hence
s GF2 E2 (hc)2. GF 1.17 x 10-11 MeV-2, hc
2x10-11MeV cm Thus s 10-44 cm2 (as in Bethe and
Peierls) Reminder Nuclei have R a few x
10-13 cm, nucleon Size is 10-13 cm ? 1 fm.
Hence typical cross sections are s p r2
10-24 cm2 ? barn. The low energy weak cross
sections are 20 orders of magnitude smaller.
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2) Early history In 1953-56 Reines and Cowan
detected electron antineutrinos from the nuclear
reactor using reaction n p -gt n e and
observing the annihilation radiation in delayed
coincidence with the neutron capture. The cross
section agreed with expectations. Thus
neutrinos became real particles. (Reines got the
Nobel Prize in 1995). In 1956 Lee and Yang
(Nobel Prize 1957) proposed that parity is not
conserved in weak interactions. They were
motivated by the study of K decays, which decayed
both into two and three pion states, of
opposite parity. The suggestion that parity is
not conserved was quickly verified
experimentally, by studies of b decay and m
decay. The two-component neutrino theory (Lee
Yang, Salam, Landau 1957) The observed maximum
parity violation in leptonic weak processes could
be accommodated if neutrinos are massless (and
hence helicity and chirality eigenstates). Only
lefthanded neutrinos (and righthanded antineutrino
s) would be needed. Lepton number would be
conserved.
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V-A theory A priori it was not clear which of
the possible Lorentz structures govern weak
interactions, in particular S-T or V-A. The
similarity of couplings in b and m decays lead to
the formulation of the V-A model (Feynman
Gell-Mann, 1958). Of particular interest was the
observation of the p -gt e ne decay. That
decay is forbidden in the limit me -gt 0 for
left-handed currents. Hence G(p -gt e n)/G(p -gt
m n) me2/mm2mp2 - me2/mp2 - mm2
1.284x10-4 in perfect agreement with the
experiment. Finally, the finding that the vector
coupling constants (but not the axial ones) are
the same (almost) in b and m decay lead to the
conserved vector current hypothesis. All that set
the stage for the Standard Electroweak Model of
Glashow, Weinberg and Salam (Nobel Prize 1979).
6
Proof that is nm different from ne Even earlier
(Lokanathan Steinberger 1955) the attempts to
observe m -gt e g gave a small upper limit
2x10-5 for the branch. That suggested that even
though the weak coupling appeared to be
universal, the nm may be different from ne. The
way to prove it is to show that the reaction nm
n -gt m p goes and nm n -gt e p does not
go. The proof was given by Danby et al. (1962,
Nobel Prize 1988) who found that the beam of
dominantly nm from pion decay makes muons, but
essentially no electrons (some were made from
contaminants in the beam).
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Discovery of neutral currents The Standard
Electroweak Model (Glashow 1961, Salam 1968,
Weinberg 1967) predicted (among other things) the
existence of neutral currents. They were observed
through nm e -gt nm e (observing recoiling
electrons) at CERN (1973). The third lepton
family (t lepton) was discovered in 1975 at
SLAC (Nobel Prize for Perl in 1995). An
experimental proof of the existence of nt was
made only in 1999 (DONUT experiment).

• Standard Model postulates that all neutrinos are
  exactly massless.
• Individual lepton flavors are conserved, i.e.
  processes not only
• like m -gt e g but also nm n -gt e- p etc.
  are strictly forbidden.
• However, more recent discoveries challenge this
  postulate and show
• that neutrinos are massive (albeit much lighter
  than other fermions)
• and that the individual lepton numbers are not
  conserved.
• Description of these phenomena will be the main
  topic of these
• lectures. It is hoped that the pattern of
  neutrino masses and
• mixing that is emerging will offer a glimpse
  into the fundamental
• source of particle masses and the role of flavor.

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Oscillation phenomenology-quantum mechanical
interference
States with a definite flavor, ne, nm, are
superpositions of states n1, n2 with definite
mass which propagate simply as plane waves.
Propagation of a beam that began as ne.
Atmospheric neutrinos, long baseline accelerator
experiments
Reactor searches for q13
Solar neutrinos, reactor verification of the
solar neutrino oscillations.
10
Dependence on the zenith angle, i.e. on the path
length. Blue - no oscillations, red - with
oscillations. Fit sin22q 1, Dm2 2.5x10-3
eV2.
nm oscillate, presumably into nt, ne is not
affected.
This finding later confirmed by
accelerator experiments K2K and MINOS.
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Since only few MeV neutrinos are involved, test
of the neutrino disappearance
180 km (Kamland)
12
Confirmation of the solar neutrino
result, without matter effects and with
antineutrinos
13
Kamland convincingly shows that ne disappear and
that the spectrum is distorted in a way only
compatible with oscillations.
14
Oscillation of solar neutrinos
Effect of matter on neutrino propagation

• That is a preposterous idea the mean free path
  is too long l 1/Ns,
• N number density N0r 1024 cm-3, s cross
  section 10-43 cm2
• for low energy neutrinos , thus, l 1019 cm 10
  light years.
• The s is so small because it is GF2. But
  interaction energy with matter is GF and might
  affect the relative phase of states that are not
  energy eigenstates.

In matter the phase e-iEt, where E p m2/2p
should be replaced by E ltHeffgt, where ltHeffgt
represents the expectation value of the weak
interaction between the neutrinos and the
constituents of matter.
Thus in matter schematically Eeff E0 m2/2E0
21/2GFNe
This term is present only for ne and has a minus
sign for ne
15
All neutrinos interact equally through Z0
exchange (NC) with electrons and quarks
Electron neutrinos interact with electrons by Z0
and W- exchange
16
The matter oscillation length is therefore L0
2p/21/2GFNe 1.7x107 (meters)/Yer(g cm-3) Ye
Z/A (electron fraction) L0 is independent of
energy. For typical densities on Earth L0 Earth
diameter so matter effects are small.However, in
Sun or other astrophysical objects they are
decisive.
So, we can have two kinds of neutrino
oscillations, vacuum and matter. To see which of
them dominates, compare the two oscillation
lengths Losc/L0 23/2GFNe En/Dm2
0.22En(MeV)rYe(100g cm-3)7x10-5/Dm2(eV2
) If this ratio is gtgt 1 matter oscillations
dominate, if it is lt1, vacuum oscillations
dominate.
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• For constant density case there can be three
  distinct regimes
• Low density, L0 gtgt Losc matter has little
  effect on oscillations
• High density, L0 ltlt Losc ne -gt nH and
  oscillations are suppressed
• (since the amplitude sin22qm, where qm is
  the effective mixing
• angle in matter.
• Resonance, when 221/2EGFNe -gt Dm2cos2qv in
  that case the
• oscillations are enhanced since qm -gt p/4
  independently of qv.
• Note that the resonance condition
  depends on the sign of
• Dm2, and whether neutrinos or
  antineutrinos are involved.

The most interesting case is the case of
neutrinos propagating through an object of
varying density (e.g. the Sun) from the high
density regime to the low density regime.
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Edges of matter effects
Edges of nonadiabacity
19
Expected fluxes of solar neutrinos (Bahcall)
Components of the ne flux (no oscillations) and
ranges of the solar neutrino detection
experiments are indicated. Note the extreme log.
Scale.
20
Summary of results Ratio of the
observed/expected flux
Ga, Cl, SNOCC,SK are charged current measurement,
determine the flux of ne only
SNONC is the neutral current. Determines the flux
of all neutrinos
Note The Cl and SNOcc are below 0.3. Ratio
below 0.5 is impossible for two flavor vacuum
oscillations. This is a clear indication of
matter effects.
21
By combining the charged and neutral current
events, SNO was able to show convincingly that
the solar ne were transformed into another active
neutrino flavor.
(Fluxes F in units of 106 cm-2s-1) Shown are the
SNO results from the 391 day salt phase.
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• Summary of the positive evidence
• nm oscillate into nt with Dm2 2.4x10-3 eV2
  and nearly
• maximum mixing angle (near 450). The sign of Dm2
  remains
• unknown.
• ne oscillate into another active flavor with
• Dm2 8x10-5 eV2 and a large but not maximum
  mixing
• angle (q12 320). Because of the matter effects
  in the
• Sun, the sign of Dm2 is fixed (gt 0 by convention,
  ne
• are dominantly the lighter of the two).
• 3) But we do not know whether ne are affected by
• oscillations with Dm2 2.4x10-3 eV2 . If that
  effect
• exists, it is small.

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What about the corresponding mixing angle ????
We have argued that the determination of the ?e
component of atmospheric neutrino flux does not
give very useful information on the angle ???.
The most natural way of determining that angle is
to look for the ?e disappearance (or appearance)
at distances corresponding to ?m2atmos.
Two such experiments with reactor antineutrinos,
CHOOZ and Palo Verde were done in late nineties
when it was unclear whether the atmospheric
neutrinos involve ??????????or ???????e. The
characteristic distance is km, and no effect
was seen. Hence these result constrain ????from
above to rather small value.
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Constraints on ??? from the Chooz and Palo Verde
reactor experiments. The region to the right of
the curves is excluded. Note that the
maximum sin2?13 value depends on the so far
poorly determined ?m312 value.
??????-3eV2
Global fits give sin2?13 0.9-0.92.3x10-2 at 95
CL, consistent with vanishing ????
25
Present status of our knowledge of oscillation
parameters or
what do we know?
7.90.4-0.4x 10-5 eV2 (2007)
2.38-0.160.2x10-3 eV2 (2007)
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The Mixing Matrix, decomposition into three
simple rotations .
27
The spectrum, showing its approximate flavor
content (note that the absolute mass value
remains undetermined)
Inverted
Normal
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Fly in the ointment
Decay at rest (DAR)
There were no (essentially) ne in the neutrino
beam, baseline 30m
Excess events
signal backgrounds
Oscillation probability
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For LSND L(m)/E(MeV) 1 so the simple
oscillation picture requires that Dm2 1 eV2,
clearly not compatible with the 3 neutrino
picture with solar and atmospheric Dm2. Hence at
least one sterile neutrino is required.
To test this hypothesis the MiniBoone
experiment at Fermilab used similar L/E but E
500-1500 MeV (See Phys.Rev.Lett.98,231801)
30
MiniBoone data above the previously chosen
threshold of 475 MeV are compatible with
background. LSND oscillation signal not observed.
300
600
900
1200 MeV
31
Pseudo discoveries (or claims that cannot be
substantiated, at least so far) attract lots of
attention 30 eV neutrino of Lubimov see V.
Lubimov et al., Phys. Lett. B94, 266(1980) 285
citations 17 keV neutrino see J.J.Simpson,
Phys.Rev.Lett.54,1891(1985) 272 citations Time
variation of the solar neutrino flux (this is
not real measure since the evidence was not
published separately, I use a theory paper
instead) M.B.Voloshin et al, Sov.J.Nucl.Phys.44,44
(1986) 145 citations LSND oscillation
evidence see C. Athanassopoulos et al.,
Phys.Rev.Lett.77,3082(1996) 492
citations Evidence for the 0nbb decay (this
has not been shown that it is incorrect, but it
is controversial) see H.V.Klapdor-Kleingrothaus
et alo., Mod.Phys.Lett.A16,2409(2001) 268
citations
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Experimental goals for near future

1. Determine the mixing angle q13
2. Resolve the mass hierarchy (sign of Dm2atm)
3. Determine the Dirac CP phase d
4. Determine how close is q23 to 450
5. Determine the absolute mass scale

In order to solve the problems 1.-4. it is
necessary to go beyond the 2 flavor picture and
observe subdominant oscillations, suppressed
by one of the small parameters, sin22q13 or
Dm2sol/Dm2atm. The mass hierarchy can be resolved
by matter effects. The CP violation is
proportional to the product (Jarlskog
invariant) sin22q13 sin22q12 sin22q23sin2Dm221L/En
sin2Dm231L/En sin2Dm232L/Ensind
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MINOS experiment
Running since 3/2005. Results so far Dm223
2.380.20-0.16 x 10-3 eV2, sin22q23 gt 0.87
(68CL), and (v-c)/c (5.1 2.9)
x 10-5.
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at Gran Sasso
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Determining q13 with reactor neutrinos
ne survival probability with two oscillation
lengths
36
Projected sensitivity of the Daya-Bay experiment (
ultimately to sin22q13 0.01)
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Double Chooz experiment projected sensitivity
sin22q13 0.03.
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in a nm beam
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NOnA experiment at Ash River, 810 km from FermiLab
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Parameter degeneracy There are several solutions
with different Q13, sign of hierarchy, CP phase d
giving the same P(nm -gt ne)
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Reactor measurements of q13 will complement the
long baseline exp.
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DUSEL Deep Underground Science and Engineering
Laboratory The Homestake (South Dakota) site now
chosen
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The appearance of wrong sign muon represents
golden measurement
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guaranteed pure ne or ne beams
The accelerated ions could be 6He (T1/2 0.8s, Q
3.5MeV, b-, g 150) and 18Ne (T1/2 1.7s,Q
4.4 MeV, b, g 60) with 1018 decays/year