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Neutrino Mass Hierarchy Determination with PINGU
Ken ClarkUniversity of Toronto
K Clark - NuFACT 2013
IceCube
AMANDA
DeepCore
scattering
DOM: Digital Optical Module
• First need to introduce IceCube
• Instrumented ~1km3 of ice with ~5000 DOMs
• 78 vertical strings, 60 DOMs per string
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IceCube Events
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IceCube
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)
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100 IceCube
PINGU Geometry - 26m String Spacing
125m
• 78 Strings
• 125m string spacing
• 17m DOM spacing
• Add 8 strings
• 75m string spacing
• 7m DOM spacing
• Add 20 strings
• 26m string spacing
• 5m DOM spacing10 TeV 1 EeV1 TeV100 GeV10 GeV1 GeV100 MeV
IceCube
10 MeV
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K Clark - NuFACT 2013
IceCube Results
• Designed to look for high energy (TeV - PeV) events
• Much success in recent studies at these energies
1.04 + 0.16 PeV 1.14 + 0.17 PeV
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IceCube
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PINGU Geometry - 26m String Spacing
• 78 Strings
• 125m string spacing
• 17m DOM spacing
• Add 8 strings
• 75m string spacing
• 7m DOM spacing
• Add 20 strings
• 26m string spacing
• 5m DOM spacing10 TeV 1 EeV1 TeV100 GeV10 GeV1 GeV100 MeV
IceCube
10 MeV
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125m
K Clark - NuFACT 2013
IceCube + DeepCore
• 78 Strings
• 125m string spacing
• 17m DOM spacing
• Add 8 strings
• 75m string spacing
• 7m DOM spacing
• Add 20 strings
• 26m string spacing
• 5m DOM spacing
X (m)-100 -50 0 50 100 150 200
Y (m
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-150
-100
-50
0
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100 IceCubeDeepCore
PINGU Geometry - 26m String Spacing
125m
10 TeV 1 EeV1 TeV100 GeV10 GeV1 GeV100 MeV
IceCube
10 MeV
DeepCore
7
75m
K Clark - NuFACT 2013
IceCube + DeepCore
• Addition of extra strings in closer proximity lowers the detection threshold energy
• Volumes shown are calculated at trigger level
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K Clark - NuFACT 2013
IceCube + DeepCore
• Addition of extra strings in closer proximity lowers the detection threshold energy
• This allows for sensitivity at the energy of an oscillation minimum
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K Clark - NuFACT 2013
DeepCore Results
• Approximately 1 year of data analyzed
• High rate in detector provides large event sample
• High energy sample constrains uncertainties in fit
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Phys. Rev. Lett. 111, 081801 (2013)
K Clark - NuFACT 2013
• Oscillation parameters extracted
• Very good agreement with world averages
• Possible improvement with more advanced reconstructions and event selection
DeepCore Results
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K Clark - NuFACT 2013
IceCube + DeepCore
• 78 Strings
• 125m string spacing
• 17m DOM spacing
• Add 8 strings
• 75m string spacing
• 7m DOM spacing
• Add 20 strings
• 26m string spacing
• 5m DOM spacing
X (m)-100 -50 0 50 100 150 200
Y (m
)
-150
-100
-50
0
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100 IceCubeDeepCore
PINGU Geometry - 26m String Spacing
125m
75m
10 TeV 1 EeV1 TeV100 GeV10 GeV1 GeV100 MeV
IceCube
10 MeV
DeepCore
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K Clark - NuFACT 2013
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)-150
-100
-50
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PINGU Geometry - 26m String Spacing
IceCube + DeepCore + PINGU• 78 Strings
• 125m string spacing
• 17m DOM spacing
• Add 8 strings
• 75m string spacing
• 7m DOM spacing
• Add >=20 strings
• 26m string spacing
• 5m DOM spacing
125m
75m
26m
10 TeV 1 EeV1 TeV100 GeV10 GeV1 GeV100 MeV
IceCube
10 MeV
DeepCorePINGU
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K Clark - NuFACT 2013
• 9.28 GeV Neutrino, 4.9 GeV muon, 4.5 GeV cascade
IceCube + DeepCore
Improvement with PINGU
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K Clark - NuFACT 2013
• 9.28 GeV Neutrino, 4.9 GeV muon, 4.5 GeV cascade
IceCube + DeepCore
Improvement with PINGU
IceCube + DeepCore + PINGU15
K Clark - NuFACT 2013
PINGU Physics• Many topics opened up by the lowering of
the energy threshold• muon neutrino disappearance• tau neutrino appearance• maximal θ23
• dark matter• neutrino mass hierarchy
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K Clark - NuFACT 2013
PINGU Physics• Many topics opened up by the lowering of
the energy threshold• muon neutrino disappearance• tau neutrino appearance• maximal θ23
• dark matter• neutrino mass hierarchy
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K Clark - NuFACT 2013
Neutrino Mass Hierarchy• Three flavour
oscillations mean disappearance/appearance of νμ are both important
P⌫µ!⌫µ = 1�
cos
2✓
m13sin
22✓23 ⇥ sin
2
1.27
✓�m
231 +A+ (�m
231)
m
2
◆L
E
�
�sin2✓m13sin22✓23 ⇥ sin2
1.27
✓�m2
31 +A� (�m231)
m
2
◆L
E
�
�sin4✓23sin22✓m13sin
2
1.27(�m2
31)m L
E
�
• Can be used to distinguish mass hieararchy
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K Clark - NuFACT 2013
1Length (km)
0 2000 4000 6000 8000 10000 12000
Eart
h D
ensi
ty (g
/cm
^3)
0
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14Normal Hierarchy
Inverted Hierarchy
°) with Travel Through the Earth - 10 GeV, 179µν→µνP(
)µν
→µν
P(
00.10.20.30.40.50.60.70.80.91
Why Atmospheric Neutrinos?
• Oscillation probability P(νμ→νμ) directly related to L/E• L measured using angle through the Earth
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K Clark - NuFACT 2013
1
1
2
2Length (km)
0 2000 4000 6000 8000 10000 12000
Eart
h D
ensi
ty (g
/cm
^3)
0
2
4
6
8
10
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14Normal Hierarchy
Inverted Hierarchy
°) with Travel Through the Earth - 10 GeV, 179µν→µνP(
)µν
→µν
P(
00.10.20.30.40.50.60.70.80.91
Length (km)0 1000 2000 3000 4000 5000 6000 7000
Eart
h D
ensi
ty (g
/cm
^3)
0
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1
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Normal Hierarchy
Inverted Hierarchy
°) with Travel Through the Earth - 6 GeV, 126µν→µνP(
)µν
→µν
P(
00.10.20.30.40.50.60.70.80.91
1
2
Why Atmospheric Neutrinos?
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K Clark - NuFACT 2013
PINGU Significance
i = cos(zenith)j = energy
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• Atmospheric neutrinos provide a large flux of incoming neutrinos at a range of incoming angles and energies
• Non-resonance MSW effects make up roughly 2/3 of PINGU’s sensitivity as (anti-)neutrinos travel through the mantle
• Parametric resonance occurs for neutrinos traveling through the core to make up the remaining 1/3
• Resonances are due to matter-induced oscillation phase changes
Core
K Clark - NuFACT 2013
Calculating Significance• Counts in one year are
binned depending on energy and zenith angle
• This includes both νμ and νμ
• There are differences in the number of counts per bin
• These differences create the patterns which give the distinguishability
N IHij �NNH
ijqNNH
ij
i = cos(zenith)j = energy
Cos(zenith angle)-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Ener
gy (G
eV)
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Counts in PINGU 1 Year - NH
Cos(zenith angle)-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Ener
gy (G
eV)
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1400Counts in PINGU 1 Year - IH
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Calculating Significance
N IHij �NNH
ijqNNH
ij
i = cos(zenith)j = energy
Cos(zenith angle)-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Ener
gy (G
eV)
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-6
-4
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6]1/2Distinguishability Metric [(IH-NH)/NH
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• As an illustration, a scaled subtraction between hierarchies can be done
• Not the way significance is calculated, but illustrative
• As an example of systematics, look at resolutions
Perfect detector resolution
K Clark - NuFACT 2013
Calculating Significance
N IHij �NNH
ijqNNH
ij
i = cos(zenith)j = energy
Cos(zenith angle)-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Ener
gy (G
eV)
2
4
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-6
-4
-2
0
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6]1/2Distinguishability Metric [(IH-NH)/NH
• As an illustration, a scaled subtraction between hierarchies can be done
• Not the way significance is calculated, but illustrative
• As an example of systematics, look at resolutions
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Zenith resolution: 10° Energy resolution 1 GeV
Cos(zenith angle)-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Ener
gy (G
eV)
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-0.8
-0.6
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1]1/2Distinguishability Metric [(IH-NH)/NH
K Clark - NuFACT 2013
Calculating Significance
N IHij �NNH
ijqNNH
ij
i = cos(zenith)j = energy
Cos(zenith angle)-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Ener
gy (G
eV)
2
4
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-6
-4
-2
0
2
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6]1/2Distinguishability Metric [(IH-NH)/NH
Cos(zenith angle)-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Ener
gy (G
eV)
2
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-0.8
-0.6
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1]1/2Distinguishability Metric [(IH-NH)/NH
Cos(zenith angle)-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Ener
gy (G
eV)
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]1/2Distinguishability Metric [(IH-NH)/NH
• As an illustration, a scaled subtraction between hierarchies can be done
• Not the way significance is calculated, but illustrative
• As an example of systematics, look at resolutions
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Zenith resolution: 12.5° Energy resolution 3 GeV
K Clark - NuFACT 2013
PINGU Systematics• Reconstructions are obviously a
significant factor in the hierarchy determination
• Currently using DeepCore algorithms
• New more computationally intensive algorithms may improve resolutions
• Also studying many other sytematics
• θ23, θ13 Δm2atm, δCP
• Atmospheric ν spectrum, efficiency errors, etc.
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Events with Selection Applied - Energy
Events with Selection Applied - Zenith Angle
K Clark - NuFACT 2013
PINGU Hierarchy Analysis• For the final result, two different analysis
methods are being pursued• Both rely on the creation of “templates”
from simulated data
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Cos(zenith angle)-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
(Ene
rgy
(GeV
))10
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Inverted Hierarchy Template - Event Selection Applied
Cos(zenith angle)-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
(Ene
rgy
(GeV
))10
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Normal Hierarchy Template - Event Selection Applied
K Clark - NuFACT 2013
Analysis Method 1• Uses the “Asimov” method using the most likely dataset at
each value of the oscillation parameters
• Calculate the χ2 as a function of these parameters and minimize for Δm2>0 and Δm2<0
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Analysis Method 2
• Throw many pseudo-experiments varying the bin contents with statistical errors, allow oscillation parameters to be fit
• Generate likelihood ratios, determine significance from these
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lambdaInvExpInvCosHist_244_tot
Entries 1e+07Mean 15.84RMS 5.527
LLR-40 -20 0 20 40
1
10
210
310
410
510lambdaInvExpInvCosHist_244_tot
Entries 1e+07Mean 15.84RMS 5.527
= 2.44132MΔ(Observed Inv Exp Inv) / (Obs Inv Exp Norm)
lambdaNormExpInvCosHist_244_tot
Entries 1e+07Mean -13.57RMS 5.416
lambdaNormExpInvCosHist_244_tot
Entries 1e+07Mean -13.57RMS 5.416
lambdaNormExpInvCosHist_244_tot
Entries 1e+07Mean -13.57RMS 5.416
132MΔ
0.2100.2120.2140.2160.2180.2200.2220.2240.2260.2280.2300.2320.2340.2360.2380.2400.2420.2440.2460.2480.2500.2520.2540.2560.2580.2600.2620.2640.2660.2680
1000
2000
3000
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310× with Trial Sets Pulled at 0.24413
2MΔBest Likelihood value for
Template:IH Data:IH
Template:NH Data:NH
Template:NH Data:IH
Template:IH Data:NH
K Clark - NuFACT 2013
Supplemental Methods• Two relatively fast analysis methods used to
study effects of systematics & parameters
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K Clark - NuFACT 2013
Hierarchy Sensitivity
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• Calculated sensitivity shown under several assumptions• Event selection, efficiency and detector geometry varied
• Note that all systematics have not been included here
arXiv: 1306.5846
K Clark - NuFACT 2013
PINGU Current Activities• Clearly no data to show yet• Studies underway for detailed LoI• Example: choosing a detector geometry
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PINGU Geometry V6 (Dozier)
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PINGU Geometry V15 (Ellett)
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PINGU Geometry V14 (Domi)
K Clark - NuFACT 2013
PINGU Advantages• Relatively fast
• Deployment could begin in the 2016-2017 season, takes 2-3 years
• Relatively inexpensive• Start up costs on the order of $10M plus ~$1.25M
per string
• IceCube provides well understood veto • Well understood technology
• IceCube techniques have proven to be robust33
K Clark - NuFACT 2013
Conclusions
• IceCube and DeepCore have shown the viability of neutrino oscillation physics in the ice
• PINGU will extend the reach of these analyses to lower energies
• Detailed LoI and full proposal will be available soon
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K Clark - NuFACT 2013
The IceCube/PINGU Collaboration44 institutions - 4 continents - ~250 Physicists
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University of Toronto
K Clark - NuFACT 201336
K Clark - NuFACT 201337
Oscillograms
K Clark - NuFACT 2013
Monte Carlo Procedure• Neutrino interactions
modeled with GENIE• Results passed to
Geant4 to create light-generating particles
• Custom GPU software propagates light through detector
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K Clark - NuFACT 2013
PINGU Advantages• This is all known
technology
• Drilling, installation can be done “quickly”
• Low cost (relative to other experiments)
• “We know how to do this”
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