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

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?

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)

Air Showers

Energy Spectra CR primary spectrum  Resulting  flux Knee (uncertainties in primary flux, hadronic models) Figure: Halzen, Bad Honnef (2004) Figure: Gaisser, astro-ph/0502380

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)

Oscillation Probability

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

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)

Experimental Results atmospheric Global oscillation fits SuperK, hep-ex/0404034 Global oscillation fits (Maltoni et al., hep-ph/0405172)

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?

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

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 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

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)

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)

VLI Oscillations Gonzalez-Garcia, Halzen, and Maltoni, hep-ph/0502223 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

Survival Probability c/c = 10-27

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

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

Survival Probability ( model)

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 

Čerenkov Cone

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

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

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

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

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)

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

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

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

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…

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

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

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)

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)

1-D Examples (all normalized to data)

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%)

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

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!

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