Post on 19-Jan-2018
description
Tests of Lorentz Invariance using Atmospheric Neutrinos and
AMANDA-IIJohn Kelley
for the IceCube CollaborationUniversity of Wisconsin, Madison
Workshop on Exotic Physics with Neutrino Telescopes
Uppsala, Sweden
September 21, 2006
Atmospheric Neutrinos as a New Physics Probe
• Mass-induced oscillations on solid ground — but subdominant effects at high energies?
• For E > 100 GeV and m < 1 eV, Lorentz > 1011
• Oscillations are a sensitive quantum-mechanical probe:small differences in energy large change in observable spectrum
Eidelman et al.: “It would be surprising if further surprises were not in store…”
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 pure states‡
* 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. Hawking, Commun. Math. Phys. 87 (1982), Ellis et al., Nucl. Phys. B241 (1984)
c - 1
c - 2
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 mixing VLI oscillations
* Glashow and Coleman, PRD 59 116008 (1999)
Conventional+VLI Oscillations
• For atmospheric , conventional oscillations turn off above ~50 GeV (L/E dependence)
• VLI oscillations turn on at high energy (n=1 above; L E dependence), depending on size of c/c, and distort the zenith angle / energy spectrum
González-García, Halzen, and Maltoni, hep-ph/0502223
Survival Probability
c/c = 10-27
AMANDA-II Data Sample
2000-2004 sky mapLivetime: 1001 days
4282 events (up-going)
No point sources or HE diffuse flux yet:clean atmospheric neutrino sample!Adding 2005 data: > 5000 events
Data Analysis
detectorMC
Zenith angle: angular resolution ~2ºBut energy reconstruction more difficult
Energy-correlated Observable
Nch (number of optical modules hit): stable observable, but acts more like an energy threshold
Other methods exist: dE/dx estimates, neural networks…
Observable Space (MC)
c/c = 10-25 No New Physics
Differences in both shape (near vertical) and normalization
VLI: AMANDA-II Sensitivity
Median Sensitivity c/c (sin(2) = 1)• 90%: 3.2 10-27
• 95%: 3.6 10-27
• 99%: 5.1 10-27
2000-05 livetimesimulated
• MACRO limit*: 2.5 10-26 (90%)
• Super-K + K2K limit†: 2.0 10-27 (90%)
*Battistoni et al., hep-ex/0503015†González-García & Maltoni, PRD 70 033010 (2004)
MC test analysis in 1-D observable (Nch) and parameter space (c/c)(Feldman-Cousins likelihood ratio method)
Summary and Outlook
• Preliminary sensitivity to VLI effects competitive with existing limits
• Expect improvements as analysis technique is refined
• Other new physics effects (e.g. quantum decoherence) are also being tested!
Extra Slides
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
dissipative term
QD Parameters
• Various proposals for how parameters depend on energy:
simplest preserves Lorentz invariance
recoiling D-branes!
Survival Probability ( model)
a = = 4 10-32 (E2 / 2)
Binned Likelihood Test
Poisson probability
Product over bins
Test Statistic: LLH
Testing the Parameter Space
Given a measurement, want to determine values of parameters {i} that are allowed / excluded
at some confidence level
c/c
sin(2)
allowed
excluded
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 (FC ordering principle)
• Once you have the data, compare Ldata to Lcrit at each point to determine exclusion region
• Primary advantage over 2 global scan technique: proper coverage
Feldman & Cousins, PRD 57 7 (1998)
1-D Examples
all normalized to datasin(2) = 1
Systematic Errors
• Atmospheric production uncertainties• Detector effects (OM sensitivity)• Ice Properties
Can be treated as nuisance parameters:minimize LLH with respect to them
Or, can simulate as fluctuations in MC experiments
Normalization is already included!(free parameter — could also constrain)
VLI: Sensitivity using Nch
Median Sensitivity c/c (sin(2) = 1)• 90%: 3.2 10-27
• 95%: 3.6 10-27
• 99%: 5.1 10-27
2000-05 livetimesimulated
allowed excluded
Decoherence Sensitivity(Using Nch, model)
Norm. constrained ±30%Normalization free
Decoherence Sensitivity
Median Sensitivitya, (GeV-1)
• 90%: 3.7 10-31
• 95%: 5.8 10-31
• 99%: 1.6 10-30ANTARES (3 yr sens, 90%)* : 10-44 GeV-1
* Morgan et al., astro-ph/0412618‡ Lisi, Marrone, and Montanino, PRL 85 6 (2000)
SuperK limit (90%)‡ : 0.9 10-27 GeV-1
Almost 4 orders of magnitude improvement!
(E2 energy dependence)