Selected topic in neutrino physics Petr Vogel, Caltech

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Selected topic in neutrino physics Petr Vogel,
Caltech

• Overview of oscillation phenomenology
• KamLAND, a culmination of half century of reactor
  neutrino studies
• Neutrinoless double beta decay from rates
• to Majorana masses
• Mechanism of lepton number violation
• An example of model building

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New era of neutrino physics

• Atmospheric neutrino oscillations
• (in particular zenith angle dependence of the
  muon neutrino flux, confirmed by K2K)
• 2. Solar neutrino deficit
• (in particular the difference in neutrino fluxes
  deduced from the charged and neutral current
  reaction rates)
• 3. KamLAND
• (reactor ne disappearance, oscillations seen with
  the terrestrial sources)
• 4. LSND oscillation observations
• (unconfirmed, but soon to be checked if correct
  all bets are off)

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Consequences
This is a first clear manifestation of physics
beyond the Standard model.

• At least some neutrinos are massive.
• Lower limits are 50 and 10 meV,
• upper limit 2 eV from tritium b decay, or
  alternatively,
• Smn lt 1 eV from cosmology and astrophysics.
• Mixing exists.
• Two mixing angles are large, one is small)
• But we do not know the absolute mass scale
• We do not know the behavior under charge
  conjugation
• We know nothing about CP symmetry of leptons

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(entries evaluated for Ue3 0.1, near the middle
of allowed range)
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Neutrino mass and oscillationsAn overview

• In the standard electroweak model neutrinos are
  massless and the lepton flavors are exactly
  conserved. Formally this is a consequence of the
  absence of the right-handed weak singlet
  components. Neutrino masses do not arise even
  through loop effects.
• Charged lepton and neutrino fields form doublets
  in SU(2)L

From the width of Z it follows that Nn 2.984 -
0.008. BBN is compatible with 3 flavors and
disfavors 4.
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• Neutrino mass is generated by a phenomenological
  mass
• term, connecting the left and righthanded fields

The mass is analogous to the mass term of charged
leptons, it might violate flavor, but conserves
the lepton number. The Majorana mass might exist
if there are no additive conserved charges. It
violates the total lepton number. For N
lefthanded neutrinos ni and n sterile nj
Mn has N n Majorana eigenstates nkc nk.
For N lefthanded neutrinos there are N masses,
N(N-1)/2 mixing angles, (N-1)(N-2)/2 CP phases,
and (N-1) Majorana phases.
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• NxN unitary mixing matrix has 2N2 real
  parameters.
• N is used for normalization, N(N-1) for
  orthogonality,
• N is absorbed by charged lepton phases.
• Thus N2 is left. N phases can be eliminated by
• choosing the phases of the charged lepton fields.
• There are N(N-1) parameters left.
• (N-1)(N-2)/2 CP phases (N-1) Majorana phases
• N(N-1)/2 phases altogether
• N(N-1)/2 angles
• Altogether N(N-1) mixing parameters N-1 mass
• differences 1 mass scale

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Basic formulae for vacuum oscillations
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Parametrization of the 3x3 mixing (MNS or PMNS)
matrix
Majorana phases ai do not affect flavor
oscillations
Since q13 is small, q12 qsolar, and q23 qatm
(or En in MeV and Losc in m)
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The magnitude of CP or T violation in flavor
oscillations is
sind
where Dij (mi2 mj2)L/4E. Thus the size of the
effect is the same in all channels. CP violation
is possible only when all three angles and all
three mass differences are nonvanishing.
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Oscillations in matter

• When neutrinos propagate in matter, additional
  phase appears,
• due to effective neutrino-matter interaction with
  electrons
• (only for electron neutrinos and antineutrinos)

And with nucleons for all active neutrinos
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The additional phase is then
And the corresponding oscillation length is
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The equations of motion can be rewritten either
in the vacuum mass eigenstate basis,
Or in the flavor eigenstate basis
In either case the matter eigenstates depend on
L0, Losc, and on the vacuum mixing angle q
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There is a resonance, i.e. maximum mixing,
if Losc/Locos2q 1.
In practical units the ratio Losc/Lo is
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We can thus consider several special cases
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Why is the survival probability increasing again
for large En? At resonance the two eigenvalues
are essentially degenerate, and there is a
probability Px for jumping from one eigenstate to
another.
Since cos2qm(rmax) -1, and at high energies Px
1, ltP(ne -gt ne)gt -gt cos2q.
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• Thus solar neutrinos (from 8B decay observed in
  SK and
• SNO) actually do not oscillate. They are
• born as the heavier eigenstate n2, and propagate
  like
• that all the way to a detector.
• The fact that the oscillation parameters derived
  from
• the solar n and reactor ne agree is a sign of not
  only
• CPT invariance but test the whole concept of
  vacuum
• and matter oscillations.

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Atmospheric neutrinos. Best fit Dm322
2x10-3eV2, sin22q23 gt 0.94
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Allowed regions of parameter space (2003)
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Present status of our knowledge of oscillation
parameters
8.2-0.50.6x10-5(2004)
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LSND fly in the ointment

• L 30 m, En 20-50 MeV, decay at rest
  spectrum
• Oscillations nm -gt ne, 87.9 - 22.4 - 6.0
  events,
• oscillation probability 0.264 - 0.067 - 0.45
• Most of the parameter range excluded by reactor
• and KARMEN experiments, but a sliver with
• 0.2 lt Dm2 lt 10 eV2 remains.
• Requires existence of sterile neutrinos !!!
• At present tested by Mini-BOONE at Fermilab, wait
• and see(until 2005 at least)

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Reminder, direct neutrino mass mesurement

• 1) Time of flight not sensitive enough
• 2) Two body decays, e.g. p -gt m nm, not
  sensitive enough
• 3) Three body decay (b decay of 3H)

This is essentially model independent, based on
kinematics only. Incoherent sum, mn (S Uei2
mi2)1/2 is determined. Present limit 2.5 2.8
eV, planned sensitivity 0.3eV (KATRIN).
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Cosmological constraints

• The presently observed distribution of matter
  (through
• high resolution galaxy surveys) and CMB are both
  affected
• by the presence of massive neutrinos in the early
  Universe.
• Combined analysis is sensitive to Smi.