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