Neutrinos

1
Neutrinos
2
History (1900s - 1930s)

• Beta Decay Hints of Problems
• Pauli proposes new particle, Neutrino
• Initial experiments bound mass, lt500eV
• Bethe and Peierls anticipate extremely small
  cross-section

3
History (1940s 1950s)

• WWII, atomic bomb, and nuclear reactors
• Discovery of anti-neutrino in 1956 by Cowen and
  Reines, in cadmium-chloride water
• anti-? p -gtn e photons

4
History (Some Theory, 1950s)

• Theories proposed assuming neutrino mass is zero
• In 1957, B. Pontecorvo suggests Neutrino mass
  mixing based on Kaon mixing
• This concept of Neutrino oscillations largely
  buried until the end of the century

5
History (1950s)

• Solar Neutrino detector, Homestake
• ?solar 37Cl -gt 37Ar e-.
• 1500 meters below ground in gold mine, SD
• Saw a rate of 2.3 /- 0.3 SNU 8
• Expected rate was 7.9 /- 0.9 SNU 6
• SNU is a solar neutrino unit10-36 neutrino
  interactions per target particle per second

6
History (1960s 1970s)

• 1962, Muon Neutrino discovered (Brookhaven exp.)
• 1969, Gribov and Pontecorve wrote a paper
  claiming that neutrinos had mass
• MSW effect also developed in these decades
• Gallium exp. Proposed, ?e 71Ga -gte- 71Ge

7
History (1980s)

• Measurements of Z-boson lifetime at LEP, CERN
• 10-23 s 11
• Theory said that the fewer particles it can decay
  into, the longer the z-boson lifetime is that
  is, the fewer neutrino families there should be.
  
• Their data supported only 3 families11

8
History (1990s 2000s)

• Super-K saw flux of 2.35 /- 0.02(stat) /-
  0.08(sys) x106/cm2/sec 13
• Ratio of the data to the standard model
  expectation of the flux was 0.465 /- 0.005(stat)
  /- 0.016, -0.015(sys). 13
• Still missing flux

9
History (1990s 2000s)

• SNO saw value similar to Super-K in partial flux,
  which was also slightly sensitive to muon and tau
  neutrinos
• But it measured total flux 5.44 /- 0.99x106
  cm-2s-1 14
• This agreed with solar predictions
• A separate channel, with no sensitivity to
  electron neutrinos saw 1.75 /- 0.07(stat) /-
  0.12, -0.11(sys) /- 0.05(theor.) x106
  cm-2sec-1 14
• This was 3.3 sigma different from the channel
  comperable to the Super-K results, indicating a
  non-electron flavor active neutrino component in
  the solar flux 14

10
History (2000s)

• Finally, results from KamLAND offered evidence
  for non-solar oscillations
• It studied Neutrinos from nuclear reactors
• If 100 neutrinos were expected assuming neutrinos
  did not oscillate, it saw 61. 5
• However, if it were detecting from the sun, it
  would expect 35. 5
• This evidence squelched other theories on the
  matter and put neutrino oscillations to the front

11
The Standard Model

• Higgs particle gives mass to all fermions, except
  neutrinos. This makes the neutrino mass zero at
  the tree level.
• In perturbation theory, the only possible mass
  terms allowed by Lorentz invariance violate total
  lepton number by two units.
• Since the Standard Model Lagrangian necessitates
  exact lepton number symmetry after symmetry
  breaking, all perturbative effects give a zero
  value for the neutrino mass.

12
The Standard Model (cont.)

• The only known source for nonperturbative effects
  is the weak instanton effect.
• Since nonperturbative effects cannot violate B-L
  symmetry, they do not affect the neutrino mass.
• Thus, the neutrino mass vanishes to all orders of
  perturbation theory as well as non-perturbatively.
  

13
Neutrinos Have Mass!

• Experiments have shown that neutrinos oscillate
  between different flavor states.
• This can only occur if neutrinos have mass AND
  each neutrino flavor has a different mass.
• These masses are very small mi lt 1 eV.
• Neutrinos having mass immediately implies physics
  beyond the Standard Model.

14
Flavor and Mass Eigenstates

• a and i run from 1 to 3 denoting the electron
  (e), muon (µ), and tau (t) neutrinos.
• In the case of antineutrinos, the same equations
  hold, except the second Uai is conjugated instead
  of the first.
• Uai are the elements of the MNS matrix.

Neutrino with definite flavor
Neutrino with definite mass
15
The Maki-Nakagawa-Sataka Matrix

• s12 sin ?12 c12 cos ?12
• If the MNS matrix were the identity matrix, there
  would be no oscillation.
• a1 and a2 are non-zero if neutrinos are Majorana
  particles (more on that later.)
• d is non-zero if neutrinos violate CP symmetry.
• It is assumed that neutrinos do violate CP, but
  it has not yet been confirmed experimentally.

16
Propagation and Interference
The propagation of mass eigenstates is given by
the plane wave equation (c h 1)
In the ultra-relativistic case pi pi
mi Thus we can make the following approximation
for energy
Since mi is small, we can approximate (c)t L
(where L is the distance traveled,) we get
Thus, different flavors propagate at different
speeds. The lighter neutrinos travel faster than
the heavier ones and this difference in speeds
causes interference which, in turn, is seen as
neutrino oscillation.
The probability of an a neutrino being seen as a
ß neutrino at time t is given by
17
2x2 MNS Matrix

• Keeping track of all the mixing angles is
  cumbersome.
• Instead, well assume the neutrinos are only
  oscillating between two flavors.
• Thus the MNS matrix and probability equation
  become

18
Theory, in Graphs

• Flavor 1
• Mass 1
• Mass 2

19
Graphs - Initial State
Flavor 2, Mass 12
Flavor 1, Mass 12
20
Graphs After Time t
Flavor 1
Flavor 2
21
Graph - Oscillation
22
Observed Values

• All neutrinos are left-handed.
• sin2(2?13) lt .19 at 90 confidence level
• tan2(?12) .45 (-.007,.009)
• sin2(2?23) 1 (-.1,0)
• ?(m21)2 8.0 (-.04, .06) 10-5 eV2
• ?(m31)2 ?(m32)2 2.4 (-.05, .06) 10-3 eV2
• d is unknown

23
Majorana vs. Dirac Mass

• For electrically neutral particles, two mass
  terms are allowed by the theory
• ?TC-1? (Majorana)
• ?? (Dirac)
• The latter is invariant under a phase
  transformation eia.
• The first mass term dictates that neutrinos are
  their own antiparticles.
• If the Majorana mass term is not included, there
  must be an extra symmetry to ensure it is not
  generated in higher order terms.
• We dont know!! (See KATRIN, Double Beta decay,
  etc.)

_
24
Seesaw Mechanism

• Right handed Majorana neutrinos with large masses
  are added to the Standard Model.
• This causes the left handed neutrinos to be very
  light, since Mlight a 1/Mheavy
• The question now becomes, Why are the right
  handed neutrinos so heavy?

25
The Future

• Many theories are already on the table other than
  the ones mentioned above.
• Many experiments are currently in progress with
  many more being devised and built.

26
Neutrino Interactions

• Neutrinos interact only through the weak
  interaction.
• The mediators of this ineraction are the W and Z
  bosons.
• Interactions involving the W are called Charged
  Current and interactions involving the Z are
  called neutral current interactions.

27
Conservation Laws

• The neutrino carries electron, muon, or tau
  number of 1 depending on its generation.
• These numbers are conserved throughtout all weak
  interactions.
• This effectively limits the types of leptons
  which can be created through the weak
  interaction.

28
Interactions With Quarks

• The interactions of neutrinos with leptons are
  supressed in comparison to the interactions of
  nuetrinos with nuclei.
• The NC interactions effectively increase the
  energy of the nuclei allowing radiation of mesons
  and other particles.
• The CC interactions change the charge of quarks
• (u to d), and expel leptons such that total
  charge is conserved.

29
Example Diagrams

30
Neutrino Detector Design

• Neutrino interactions are rare, so in order to
  get reasonable statistics you need
• large detectors
• dense materials (high Z)
• long time intervals

31
MINOS

• The Main Injector
• Neutrino
• Oscillation Search
• A multipurpose long
• baseline neutrino
• oscillation experiment.

32
Design

• Near detector at Fermilab, far detector in
  Northern Minesota.
• Stacked planes of steel and solid scintillator.
  Near detector 1kT, Far detector 5.4kT.
• The use of 2 horns, which act as lenses focusing
  the charged particle beams which produce the
  nuetrinos. This design allows for much control
  of neutrino energy and composition.

33
Minos Results
34
NOvA

• NuMI Off-Axis ?e Appearance experiment.
• This is a future experiment (2010s) very similar
  to MINOS.
• Much more focused in purpose, ?µ to ?e
• measurement. Also measuring mass hierarchy,
  lepton cp violation as well as some astronomical
  phenomena.
• Uses the same neutrino source as MINOS.

35
NOvA Design

• The far detector is also in Northern Minesota,
  but is off-axis. This lowers beam intensity, but
  gives a much narrower neutrino energy
  distribution.
• The NOvA design is
• practically all active
• increasing resolution.
• The NOvA far
• detector is 25kT of
• low Z material, using
• a liquid, mineral oil,
• scintillator.

36
Background

• Primary source of background is p0s created in NC
  interactions.
• Decays of p0s appear identical to electrons, due
  to electron-positron creation from high energy
  photons, except for the gap between creation and
  decay, and split showers.
• You need a fine-grained detector to make this
  distinction.

37
Liquid Argon Calorimeters

• Liquid Argon Detectors for use with high energy
  neutrino experiments are planned for the next
  generation of neutrino experiments.
• Liquid argon detectors work through detection of
  ionization through electric potentials, rather
  than optical signals.
• Detectors of this type are expected to be about
  5x more sensitive.

38
Sources

• Most History information not explicitly citied
  from 1 and 11.
• 1 Bilenky, S. M., The History of Neutrino
  Oscillations Phys.Scripta T121 (2005) 17-22,
  http//arxiv.org/PS_cache/hep-ph/pdf/0410/0410090.
  pdf
• 2 Bahcall, John N., The Evolution of Neutrino
  Astronomy Publ.Astron.Soc.Pac. 112 (2000)
  429-433, http//www.sns.ias.edu/jnb/Papers/Popula
  r/Millennium/paper.pdf
• 3 Bahcall, John N., Astrophysical Neutrinos
  20th Century and Beyond Nucl.Phys.Proc.Suppl. 91
  (2001) 9-17 Int.J.Mod.Phys. A16 (2000)
  4955-4968, http//xxx.lanl.gov/PS_cache/hep-ph/pdf
  /0009/0009044.pdf
• 5 Wark, David. Now You See Them, Now You
  Dont Nature 421, 485-486 (30 January 2003),
  http//www.nature.com/nature/journal/v421/n6922/fu
  ll/421485a.html
• 6 Bahcall, John N., Solar Neutrinos, in
  Encyclopedia of Physics, 3rd edition, Vol. 2,
  eds. G. Trigg and R. Lerner (Wiley-VCH, Weinheim
  2005), p. 2242. http//arxiv.org/PS_cache/physics
  /pdf/0411/0411190.pdf
• 8 Bahcall, John N., Solar Neutrinos
  McGraw-Hill Encyclopedia of Science and
  Technology, 9th edition, 16 (2002),
  http//www.sns.ias.edu/jnb/

39
Sources (cont)

• 11 Verkindt, Didier, Neutrino History, 26
  June 1999, http//wwwlapp.in2p3.fr/neutrinos/anhis
  tory.html
• 12 Zralek, M., From kaons to neutrinos
  quantum mechanics of particle oscillations, Acta
  Phys.Polon. B29 (1998) 3925-3956,
  http//arxiv.org/PS_cache/hep-ph/pdf/9810/9810543.
  pdf
• 13 Koshio, Y., The recent results of solar
  neutrino measurements in Super-Kamiokande
  http//arxiv.org/PS_cache/hep-ex/pdf/0306/0306002.
  pdf
• 14 SNO Collaboration, Measurement of the rate
  of nu_e d --gt p p e- interactions produced
  by 8B solar neutrinos at the Sudbury Neutrino
  Observatory Phys.Rev.Lett. 87 (2001) 071301,
  http//arxiv.org/PS_cache/nucl-ex/pdf/0106/0106015
  .pdf
• 15 Motta, Leonardo, Atom, http//scienceworld.
  wolfram.com/physics/Atom.html. 1996
• 16 Wirsing, Bernd. Did "Dark Matter" Create
  the First Stars?. Press release for P.L.
  Biermann A. Kusenko, Relic keV sterile
  neutrinos and reionization, Physical Review
  Letters, 10 March 2006. http//www.mpg.de/english
  /illustrationsDocumentation/documentation/pressRel
  eases/2006/pressRelease200603142/index.html
• 17 Whitehouse, David. Science finds particle
  perfection, BBC News Online, 20 July, 2000,
  http//news.bbc.co.uk/1/hi/sci/tech/843163.stm

40
Sources (cont)

• 18 MINOS Collaboration, http//www-numi.fnal.gov
  /PublicInfo/mintdr_3.pdf
• 19 MINOS Collaboration, March 2006,
  http//www-numi.fnal.gov/talks/blessed/minos_1.gif
  
• 20 NOvA Collaboration, March 21, 2005,
  http//www-nova.fnal.gov/NOvA_Proposal/NOvA_P929_M
  arch21_2005.pdf
• 21 Feldman, Gary, April 18, 2006,
  http//www-nova.fnal.gov/NOvA_reports_page/NOVA-P5
  -Apr06.pdf
• 22 Griffiths, David, Introduction to Elementary
  Particles, John Wiley Sons, Inc., Germany, 1987