1. Searching for New Physics with Atmospheric Neutrinos and AMANDA-II
John Kelley Preliminary Exam
March 27, 2006

2. Questions to Answer Atmospheric neutrinos How do we detect them?
What are they? Where do they come from?
What physics can we learn from them?
How do we detect them?
How can we extract the physics from the data?

3. Atmospheric Neutrinos
Where do they come from? Cosmic rays!
Cosmic rays (p, He, etc.) interact in upper atmosphere, produce charged pions, kaons “What do you get when you slam junk into junk? You get pions!” — B. Balantekin
These decay and produce muons and neutrinos
Figure from Los Alamos Science 25 (1997)

4. Air Showers

5. Energy Spectra CR primary spectrum  Resulting  flux Knee
(uncertainties in primary flux, hadronic models)
Figure: Halzen, Bad Honnef (2004)
Figure: Gaisser, astro-ph/

6. Oscillations: Particle Physics with Atmospheric Neutrinos
Evidence (SuperK, SNO) that neutrinos oscillate flavors (hep-ex/ )
Mass and weak eigenstates not the same (mixing angle(s))
Implies weak states oscillate as they propagate (governed by energy differences)
Figures from Los Alamos Science 25 (1997)

7. Oscillation Probability

8. Three Families? Atmospheric    is essentially two-family
In theory: mixing is more complicated (3x3 matrix; 3 mixing angles and a CP-violation phase)
In practice: different energies and baselines (and small 13) mean approximate decoupling again into two families
Standard (non-inverted) hierarchy
Atmospheric    is essentially two-family

9. Atmospheric Baselines
Direction of neutrino (zenith angle) corresponds to different propagation baselines L
Happy coincidence of Earth size, m2, and atmospheric  energies
L ~ O(104 km)
L ~ O(102 km)

10. Experimental Results atmospheric Global oscillation fits
SuperK, hep-ex/
Global oscillation fits
(Maltoni et al., hep-ph/ )

11. Beyond the Standard Model
What is the structure of space-time on the smallest scales?
Are “fundamental” symmetries such as Lorentz invariance preserved at high energies?

12. Why Neutrinos? Neutrinos are already post-SM (massive)
For E > 100 GeV and m < 1 eV*, Lorentz  > 1011
Oscillations are a sensitive quantum-mechanical probe Eidelman et al.: “It would be surprising if further surprises were not in store…”
* From cosmological data, mi < 0.5 eV, Goobar et. al, astro-ph/

13. New Physics Effects
Violation of Lorentz invariance (VLI) in string theory or loop quantum gravity*
Violations of the equivalence principle (different gravitational coupling)†
Interaction of particles with space-time foam  quantum decoherence of flavor states‡
c - 1 
c - 2 
* see e.g. Carroll et al., PRL (2001), Colladay and Kostelecký, PRD (1998)
† see e.g. Gasperini, PRD (1989)
‡ see e.g. Anchordoqui et al., hep-ph/

14. Phenomenology Theory Pheno Experiment
Current status: theories are suggestive of modifications to SM, but cannot yet specify exact form / magnitude of effects
Amelino-Camelia on QG: “…a subject often derided as a safe haven for theorists wanting to speculate freely without any risk of being proven wrong by experimentalists.”
Theory / pheno / experimental feedback shaping future work!
(e.g., quasar halos and loop quantum gravity, gr-qc/ )

15. VLI Phenomenology Modification of dispersion relation*:
Different maximum attainable velocities ca (MAVs) for different particles: E ~ (c/c)E
For neutrinos: MAV eigenstates not necessarily flavor or mass eigenstates
* Glashow and Coleman, PRD (1999)

16. VLI Oscillations
Gonzalez-Garcia, Halzen, and Maltoni, hep-ph/
For atmospheric , conventional oscillations turn off above ~50 GeV (L/E dependence)
VLI oscillations turn on at high energy (L E dependence), depending on size of c/c, and distort the zenith angle / energy spectrum

17. Survival Probability
c/c = 10-27

18. Quantum Decoherence Phenomenology
Modify propagation through density matrix formalism:
Solve DEs for neutrino system, get oscillation probability*:
*for more details, please see Morgan et al., astro-ph/

19. preserves Lorentz invariance
QD Parameters
Various proposals for how parameters depend on energy:
preserves Lorentz invariance
simplest
recoiling D-branes!

20. Survival Probability ( model)

21. How Do We Detect ?
Need an interaction — small cross-section necessitates a big target!
Then detect the interaction products (say, using their radiation)
Čerenkov
effect 

22. Čerenkov Cone

23. Location, Location, Location
Where on Earth could we have a huge natural target of a transparent medium?!

24. Obligatory South Pole Photo
~3 km ice!
photo by J. Braun

25. AMANDA-II AMANDA-II 19 strings 677 OMs Trigger rate: 80 Hz
Data years: 2000-
“Up-going”
(from Northern sky)
“Down-going”
(from Southern sky)
Optical Module
PMT noise: ~1 kHz

26. Muon Neutrino Events
Can reconstruct muon direction to 2-3º (timing / light propagation in ice)
Quality cuts:
smoothness of hits along track
likelihood of up vs. down
resolution of track fit …
Allows rejection of large muon background

27. Data Sample 2000-2003 sky map Livetime: 807 days
3329 events (up-going)
<5% fake events
No point sources found:
pure atmospheric sample!
Adding 2004, 2005 data:
> 5000 events (before cut optimization)

28. Analysis Or, how to extract the physics from the data?
detector MC
…only in a perfect world!

29. Closer to Reality Zenith angle reconstruction — still looks good
The problem is knowing the neutrino energy!

30. Muon Energy Loss -dE/dx ≈ a + b log(E)
Stochastic losses produce mini-showers along track
Light output is a reasonable
handle on energy
Figure by T. Montaruli

31. Number of OMs hit
Nch (number of OMs hit): stable observable, but acts more like an energy threshold
Other methods exist: dE/dx estimates, neural networks…

32. Observables
c/c = 10-25
No New Physics

33. Binned Likelihood Test
Poisson probability
Product over bins
Test Statistic: LLH

34. Testing the Parameter Space
excluded
Given a measurement, want to determine values of parameters {i} that are allowed / excluded at some confidence level
c/c
allowed
sin(2)

35. Feldman-Cousins Recipe
For each point in parameter space {i}, sample many times from parent Monte Carlo distribution (MC “experiments”)
For each MC experiment, calculate likelihood ratio: L = LLH at parent {i} - minimum LLH at some {i,best}
For each point {i}, find Lcrit at which, say, 90% of the MC experiments have a lower L
Once you have the data, compare Ldata to Lcrit at each point to determine exclusion region
Feldman & Cousins, PRD 57 7 (1998)

36. 1-D Examples
(all normalized to data)

37. Finding the Sensitivity: Zenith Angle
simulated
Sensitivity to c/c
• 90%: 2.1  10-26
• 95%: 2.5  10-26
• 99%: 2.9  10-26
allowed
excluded
MACRO limit:
2.5  (90%)

38. Sensitivity using Nch 2000-05 simulated Sensitivity to c/c
• 90%: 2.5  10-27
• 95%: 3.0  10-27
• 99%: 3.9  10-27

39. Systematic Errors Atmospheric production uncertainties
Detector effects (OM sensitivity)
Ice Properties
Can be treated as nuisance parameters:
minimize LLH with respect to them
Normalization is already included!

40. To Do List 2004-05 data and Monte Carlo processing
Optimize quality cuts
Extend analysis capabilities
better energy estimator?
full systematic error treatment
multiple dimensions
optimize binning
Analyze data (discover Lorentz violations)
Write thesis
Vacation in Papua New Guinea