Searching for New Physics with Atmospheric Neutrinos and AMANDA-II

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

2. Questions to Answer • Atmospheric neutrinos • 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. Knee Energy Spectra CR primary spectrum  Resulting  flux (uncertainties in primary flux, hadronic models) Figure: Gaisser, astro-ph/0502380 Figure: Halzen, Bad Honnef (2004)

6. Oscillations: Particle Physics with Atmospheric Neutrinos • Evidence (SuperK, SNO) that neutrinos oscillate flavors(hep-ex/9807003) • 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? • In practice: different energies and baselines (and small 13) mean approximate decoupling again into two families • In theory: mixing is more complicated (3x3 matrix; 3 mixing angles and a CP-violation phase) 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 SuperK, hep-ex/0404034 Global oscillation fits (Maltoni et al., hep-ph/0405172)

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/0602155

13. New Physics Effects c - 1 • 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 - 2  * see e.g. Carroll et al., PRL 87 14 (2001), Colladay and Kostelecký, PRD 58 116002 (1998) † see e.g. Gasperini, PRD 39 3606 (1989) ‡ see e.g. Anchordoqui et al., hep-ph/0506168

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/0508121)

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 59 116008 (1999)

16. VLI Oscillations • For atmospheric , conventional oscillations turn off above ~50 GeV (L/E dependence) Gonzalez-Garcia, Halzen, and Maltoni, hep-ph/0502223 • 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/0412628

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

20. Survival Probability ( model) a =  = 4  10-32 (E2 / 2)

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. “Up-going” (from Northern sky) “Down-going” (from Southern sky) AMANDA-II AMANDA-II 19 strings 677 OMs Trigger rate: 80 Hz Data years: 2000- 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 reconst. 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 No New Physics c/c = 10-25

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 Lcritat which, say, 90% of the MC experiments have a lower L • Once you have the data, compare Ldatato Lcritat 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 2000-05 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  10-26 (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