1. Atmospheric Neutrino AnomalyBy
Tasneem Mohsinally

2. History
Neutrino 
- predicted by Pauli (1930’s) to explain Standard Model
energy conservation in beta decay
- neutral, spin 1/2
- 3 flavours: e  
- weak force (short range)
W, Z
Weak force is short range acting only through the very massive W and Z particles. The range of a force is inversely proportional to the mass of the particle carrying the force (uncertainty principle) (~em and gravity have infinet ranges and force carriers have 0 mass)

3. Solar Neutrino Puzzle - < 20MeV
- 400 billion per second per square inch
Raymond Davis Homestake Experiment (1970’s)
- chlorine based detector
- ~5000 ft underground
- each neutrino interaction resulted in argon atom production.
Confirmed sun produces neutrinos
Only one third the number of neutrinos
predicted by theory were detected
Where were the rest?
Motivation for mass. 100,000 gallons of dry-cleaning fluid Underground to protect from contamination by cosmic rays. Large target because probability of capture was 10 quadrillion times smaller than fro an neutron in a neuclear reactor. Solved by neutrino theory exmplanation by SNO experiment in 2002.

4. Atmospheric Neutrino Anomaly
Cosmic Rays hitting the earth’s atmosphere
Spray of secondary particles decay resulting in neutrinos
Expected  : e = 2 : 1
IMB experiment (1985)
Kamiokande II
Soudan
observed  to e interactions was closer to one
 coming from the far side of the earth were depleted by about one
half compared to those coming from the atmosphere overhead.
alternative explanations could not convincingly fit the results found
Secondary particles- mainly pions and kaons, from well known nutrino production there should be twice as many m neutrinos versus e neutrinos from the atmosphere.
The effect is large and depends only uopon ratios of measured quantities.
Alternative explanantions – problems with neutrino flux calculations, neutrino interaction rates, problems unique to water detectors…..

5. Neutrino Oscillations
Neutrinos do not propagate as a single wave but as a pre-packaged combination of two mass eigenstates
- neutrino is composed of two different masses!
- different periodicities
in one phase the pair may act as a muon neutrino and when shifted 90
degrees may make a tau neutrino
Quantum mechanical effect. Particle wave duality- when particles behave as waves they exhibit a frequency proportional to their energy. interaction frequency is related to the difference in the two original frequencies. Oscillations due to Mismatch between flavour and mass eigenstates. The mass eigens attes travelling at difernt frequencies oscillate in and out of phase .

6. Neutrino Oscillations
Mixing relationship between flavour and mass eigenstates:
Allowing the mass states to propogate at different frequencies

7. Neutrino Oscillations
Probability for a muon neutrino changing into a tau neutrino:
Mixing probability α mass difference squared
If neutrinos have different (non-zero) masses and if they mix so that each neutrino represents a mixture of two or more different masses, Neutrino
oscillations will occur.

8. Super Kamiokande (1996)
Proton decay, solar neutrinos, atmospheric neutrinos
Estimated 2:1 flux ratio of muon to electron neutrinos
Detector
ft. underground
- 50,000 tonne tank of ultra-pure water
- ~12,000 photomultiplier tubes
benefit: of large detector allows to catch higher energy muon neutrinos and at much increased numbers. Charged particles are absorbed by the ground.

9. - strikes a quark in an oxygen nucleus, snatches a charge becoming
Neutrino Interaction
- strikes a quark in an oxygen nucleus, snatches a charge becoming
either muon or electron
- energetically charged elementary particle emits Cherenkov radiation
Cherenkov radiation:
direction of outgoing particle correlated to direction of neutrino
high energies ~ 15°
Amount of light radiated is a measure of neutrino energy
Particles move close to speed of light in vacuum , exceeding speed of light in water, - results in the optical equivalent of a sonic boom – emitting cherenkov radiation – flash emitted 42degrees halfangle cone trailing the particle – directional burts of light.

10. High Acquisition rate ~ 100 triggers per second
Partial analysis of events is done as they arrive and then sent to a laboratory outside the mine via fiber optics where fully contained events are identified by a pattern recognition algorithms and filtered into different analysis streams for immediate processing.
Single ring events ~ 5.5 per day
~ 98% accuracy
By measureing number of events of each type as a function of energy and direction we can find neutrino oscillations affect the results. Neutrino oscillations can affect the number of neutrinos detected as a function of distance travelled . The distance travelled is determined by the arrival angle with respect to the vertical zenith.

11. a deficit in muon neutrinos - significant up/down asymmetry
Super K data indicated atmospheric neutrino anomaly due specifically to
a deficit in muon neutrinos
- significant up/down asymmetry
Neutrino flux should be equal for equal angles with the zenith
Observations showed depletion of muon neutrinos travelling in from far side of the earth versus those coming in from the atmosphere overhead
The second piece of evidence for neutrino oscillations is that we measure a significant up-down asymmetry of high energy muon neutrino events. Above a few GeV, atmospheric neutrinos can be traced back to primary cosmic rays of energy greater than 10 GeV. Above this energy, the primary cosmic rays are not deflected very much by the earth's magnetic field. Cosmic rays arrive at the earth almost isotropically, having been randomized by interstellar magnetic fields. This results in the prediction that the flux of atmospheric neutrinos should be equal for equal angles with the zenith and nadir. Another way of saying this is that the cosine(zenith) distribution should be symmetric. Bit is unlikely that energy and momentum are vanishing from the universse

12. For low energies however an asymmetry is expected which can be traced to the effect where the earth’s magnetic field deflects incoming cosmic rays. – east- west phenomenon.
This graph is a preliminary result based on the current full data-set; details of the analysis of high energy events based on the first 414 days of data were published in Phys. Lett. B436(1998)p.33
(hep-ex/ ).

13. Oscillate with Tau neutrinos Economic Pi-zero events
This deficit as a function of energy and arrival angle indicates that muon neutrinos oscillate to some other flavour
Probability of oscillation is related to the distance travelled by the neutrino from its point of production to detection
Oscillate with Tau neutrinos
Economic
Pi-zero events
Muon neutrinos change from one flavour to another as they travel close to the speed of light. Tau for economic reasons. Tau versus sterile neutrino due to detection of neutral pions production produced via a weak neutral Zo interaction (signal 1 in 40). These pi-zeros decay almost immediately to two gamma rays which leave distinctive double ring pattern ojn the detector wall. Sterile neutrinos do not even partake in the weak force . The 3 flavour neutrinos make the same rate of neutral events. If muon neutrinos are oscillating to taus there will be no change in the total rate of neutral events however if muons are oscilating to a sterile neutrino there will be an up/down assymetry and decreased rate since sterile neutrinos will NOT make pi-zero events. Initial look favours taus.
MiniBoone results and tends to refute the existence of the sterile neutrino. The news enables theoretical physicists to close an ugly chapter in the search for neutrino mass, because sterile neutrinos have no place in the standard model of particle physics. It would also have interfered with the growth of galaxies, changing the distribution of matter in the universe in a way that we do not observe, i.e., cosmologically, there should not be a sterile neutrino

14. Implications Standard model Revise current model Unified theory
Contribution to mass in the universe
~ 50 billion neutrinos per electron
Big Crunch / Cool Expansion
Majorana neutrino
Travel slower than c
Predicts a reversal in chirality
Violations of lepton number
Current model the neutrino mass is zero. The mixing is also very peculiar, hope to make progress towards a unififed theory which explains the generations, and predicts partcile masses. Fact that mass is nonzero is very important in the mathematics of the theory.
On a lowere limit ~0.07ev per neutrino they would still amount to a significant fraction of the baryonic mass in the universe. If we go up to ~1ev they could be the dominant mass in the universe. # Neutrinos could constitute anything from 0.1 to 7 per cent of the mass of the universe (the dark matter)
Anti neutrinos are righthanded., neutrinos are left handed. Neutrinos interact with the higgs boson to change handedness. The standard model does not account for this. Experiment to check for majorana mass is through double beta decay . Can only occur if a anti neutrino can change into a neutrino

15. References Neutrino Oscillation; http://hep.bu.edu/~superk/osc.html
Neutrino oscillation; (2007, November 22). In Wikipedia, The Free Encyclopedia.
Retrieved 03:40, December 2, 2007, from
Discovery of Neutrino Mass and Oscillations;
Solar Energy Generation Theory tested at Brookhaven National Laboratory;
Atmospheric Neutrinos;
Super Kamiokande;
Neutrino Mass;