Neutrino Mass Hierarchy and Mixing Parameters:
Long-baseline Measurements with IceCube
Laura Bodine Mass Hierarchy
Observables Matter Effects
Feasibility
University of Washington
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Neutrino Mass: Current status Most oscillation parameters: known
Reactor, Atmospheric & Solar expt 13 small, exact value unknown
Overall mass scale: limited Small allowed region Beta decay expt
Nature of neutrino: unknown Double-beta decay expt
Mass hierarchy: unknown Matter enhanced oscillations?
Implications for physics beyond the Standard Model as well as Cosmology
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Neutrino Mass Hierarchy
Sign of m221 known
from matter effects Charged current
Similar experiment may be possible for m2
32 Requires “large” 13
What if 13 = 0? Normal Inverted
solar ~ 810-5 eV2
solar ~ 810-5 eV2 atmospheric ~310-3 eV2
atmospheric ~310-3 eV2
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3 Flavor Neutrino Oscillations
Probability exists for neutrino to transition from state to Matrix elements are functions of mixing angles
The survival probability depends on 3 matrix elements, 3 mass gaps, the distance traveled and the neutrino energy
All terms contribute, even if 13 = 0
Interaction eigenstates Unitary matrix Mass
eigenstates
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Basic Experimental Setup
very long baseline detector
Look at muon neutrino probability to transition to electron neutrino or tau neutrino
The survival probability depends on the mass gaps, the distance traveled and the energy
Only sensitive to 13 via the matrix elements
source
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P Survival Probability
First “Solar” Minimum
Threshold for Čerenkov light in water
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Oscillation Maxima
Both look like straight lines…
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Linearity of Oscillation Maxima
Observable difference between normal and inverted hierarchies!
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Adding Matter Effects I Much smaller effect
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Adding Matter Effects II
Matter effects reduce sensitivity to hierarchy
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Requirements Ability to resolve the solar and atmospheric
mass gaps simultaneously Scan large a range of L/E
Ultra-narrowband neutrino beam Put energy selection on beam side A few percent energy spread Ability to scan energies in 100s MeV-GeV range
Efficient counting detector Use beam timing information to lower threshold
Huge detector very far from the source…
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Huge, Faraway Detector: IceCube at the South Pole
11600 km from Fermilab
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IC as a Low-Energy Counter 100 GeV std threshold, ~500 Hz dark noise rate
But we’re looking for neutrinos in 100s MeV- GeV range… Look for small amounts of light in time with beam
Typical spill times of s occurring every ~2 sec Expect 10-3 counts/spill background
May be able to use single count data for after the fact reconstruction Large trigger update may not be necessary Could run in parallel with other missions
Photon transport is the dominant open question Need to see small numbers of photons Deep Core may be the right venue
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Beam Prospects
Basic method employed in off-axis beams Improve energy spread by filtering pions in-flight Tune by movement of horn and filters
Can lower energy spread at expense of flux Recover event rate by use of large detector
This is a difficult task… But NuMI upgrade plans for 10% energy spread
when optimized for NOA which has limited sensitivity to low flux
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Other Mixing Parameters
Amplitude of oscillations depends on the mixing angles. Use peak heights to extract information
Frequency provide information on m2atm
Unknown sensitivity to CP 13-dependent, but we are planning to investigate
Could provide simultaneous measurements of several mixing parameters
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Summary
It is possible, at least in principle, to measure the hierarchy even if 13 = 0
Long baseline muon neutrino survival provides sensitivity to the mass hierarchy and other neutrino mixing parameters
New techniques would be necessary Ultra-narrowband neutrino beams from
monochromatic pion beams Alternative use of modern detector, like IceCube
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Acknowledgements
Work done in collaboration with Hamish Robertson
Supported by DOE Grant #DE-FG02-97ER41020
Thank you for listening!
University of Washington
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Matter Effects in More Detail PREM was used to calculate the average density MSW potential, with average density used in A Parameterize in terms of shifted m2
21 mass gap