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PINGU and the Neutrino Mass
Hierarchy
Ken Clark, Penn State UniversityNeutrinos at the Forefront - Lyon, Oct 2012
Ken Clark - PSU Lyon, Oct 2012
Neutrino Oscillations
• Neutrino oscillations parametrized by
• mass squared differences Δm2ij
• mixing angles θij
• CP phase δCP
• Several questions remain
• What is the mass hierarchy (m3 > m1?)
2
Ken Clark - PSU Lyon, Oct 2012
Neutrino Mass Hierarchy
• Focus on the mass hierarchy in this talk
• We know Δm213 but not the sign
3
Ken Clark - PSU Lyon, Oct 2012
Experiments
• Several experiments targeting the mass hierarchy
• NOvA to start data collection soon
• R&D ongoing on Daya Bay II, LBNE, GLACIER, LENA, ORCA, PINGU
Ken Clark - PSU Lyon, Oct 2012
Theory - Atmospheric Neutrinos
• Why use atmospheric neutrinos?
• Not usually considered for use in precision parameter determination
• Broad range of baselines (~50 - 12500 km)
• Broad range of energies (~GeV - PeV)
5
Ken Clark - PSU Lyon, Oct 2012
Theory• Case for atmospheric neutrinos has been studied
previously (Phys. Rev. D 78, 093003 (2008) in particular although there are others)
• In essence this requires distinction between normal and inverted hierarchy in counts
• Hierarchy effects seen as neutrinos pass through matter
• ν oscillation probability is enhanced if hierarchy is normal
• ν̅ oscillation probability is enhanced if hierarchy is inverted
• and: ν, ν̅ have different cross sections
• Matter effects depend on size of θ13 which is now better defined
6
Ken Clark - PSU Lyon, Oct 2012
Starting Point Math
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
�
• Interested primarily the νμ survival probability
• Note in particular the dependence on Δm231
7
Ken Clark - PSU Lyon, Oct 2012
Starting Point Plots
Energy (GeV)5 10 15 20 25 30 35 40 45
Probability
0
0.2
0.4
0.6
0.8
1
)µν→µνP(
Normal Hierarchy
Inverted Hierarchy
• Clear differences emerge between the hierarchies
• This is at a fixed zenith angle, ~150 degrees
8
Ken Clark - PSU Lyon, Oct 2012
Preliminary Reference Earth Model (PREM)
• Current “best guess” as to the variation of density in the Earth
• Been around a long time, still retains the preliminary name
MantleInnerCore
OuterCore
Ken Clark - PSU Lyon, Oct 2012
Matter effects
• Previous probabilities were just for one path length
• upgoing neutrinos experience effect of traveling through the Earth (or a fraction of it)
10
Radius (km)0 1000 2000 3000 4000 5000 6000
)3D
ensi
ty (g
/cm
4
6
8
10
12
PREM Earth DensityPREM Earth Density
MantleInnerCore
OuterCore
Ken Clark - PSU Lyon, Oct 2012
Matter Effects - I°
• At angles >146°
• ν pass through mantle and core
• parametric enhancement of oscillations take place
11
146°
Mantle InnerCore
OuterCore
Ken Clark - PSU Lyon, Oct 2012
Matter Effects
Length (km)0 2000 4000 6000 8000 10000 12000
Eart
h D
ensi
ty (g
/cm
^3)
0
2
4
6
8
10
12
14Normal Hierarchy
Inverted Hierarchy
°) with Travel Through the Earth - 20 GeV, 179µν→µνP(
)µν
→µν
P(
00.10.20.30.40.50.60.70.80.91
Length (km)0 2000 4000 6000 8000 10000 12000
Eart
h D
ensi
ty (g
/cm
^3)
0
2
4
6
8
10
12
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
• These are almost directly upgoing
• Two different energies show magnitude of final effect
• This zenith dominated by parameteric resonance
12
Ken Clark - PSU Lyon, Oct 2012
Matter Effects - II
• At angles <146°
• ν pass through mantle only
• MSW enhances νμ to νe
13
Mantle InnerCore
OuterCore
Ken Clark - PSU Lyon, Oct 2012
Matter Effects
Length (km)0 1000 2000 3000 4000 5000 6000 7000
Eart
h D
ensi
ty (g
/cm
^3)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
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
• Much less upgoing angles show MSW effects
• Note change in Earth density plot
14
Ken Clark - PSU Lyon, Oct 2012
Detection Method
• IceCube and DeepCore successfully detecting neutrinos for years
• IceCube: ~5160 PMTs in 1km3
• DeepCore: denser string and DOM spacing
• High efficiency PMTs
Ken Clark - PSU Lyon, Oct 2012
Detection Method
• IceCube and DeepCore successfully detecting neutrinos for years
• IceCube: ~5160 PMTs in 1km3
• DeepCore: denser string and DOM spacing
• High efficiency PMTs
Ken Clark - PSU Lyon, Oct 2012
DeepCore Energy Range
• Detection threshold lowered to ~10 GeV in DeepCore
• Effective volume at trigger level increased below 100 GeV
GeV)10
Energy (Logµν1.0 1.5 2.0 2.5 3.0
(meg
aton
)ef
fect
ive
Vic
eρ
0
50
100
150
200DeepCore TriggerDeepCore Online FilterIceCube Trigger w/o DC
Ken Clark - PSU Lyon, Oct 2012
Step up to PINGU
• Add another 20 strings
• Denser string and DOM spacing
• Energy threshold lowers again
X (m)-100 -50 0 50 100 150 200
Y (m
)
-150
-100
-50
0
50
100PINGU Geometry V6 (Dozier)
IceCube
DeepCore
PINGU (HQE)
PINGU Geometry V6 (Dozier)
Ken Clark - PSU Lyon, Oct 2012
Step up to PINGU
• Add another 20 strings
• Denser string and DOM spacing
• Energy threshold lowers again
Energy (GeV)10 20 30 40 50 60 70
(MTo
n)ef
fV
0
2
4
6
8
10
12
14
PINGU v6 Effective Volume, R < 150m
> 0 hits
> 10 hits
> 20 hits
> 50 hits
> 100 hits
PRELIMINARY
PRELIMINARY
Ken Clark - PSU Lyon, Oct 2012
2 Dimensional Plotting
(Degrees)zθ120 130 140 150 160 170 180
E (G
eV)
5
10
15
20
25
30
35
40
45
50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
) - Normal Hierarchyµν→µνP(
(Degrees)zθ120 130 140 150 160 170 180
E (G
eV)
5
10
15
20
25
30
35
40
45
50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
) - Inverted Hierarchyµν→µνP(
(Degrees)zθ120 130 140 150 160 170 180
E (G
eV)
5
10
15
20
25
30
35
40
45
50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
) - Normal Hierarchyµν→µνP(
(Degrees)zθ120 130 140 150 160 170 180
E (G
eV)
5
10
15
20
25
30
35
40
45
50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
) - Inverted Hierarchyµν→µνP(
• Now we need to extend this to two dimensions to show the probability vs energy and zenith angle
20
E ν (
GeV
)E ν
(G
eV)
θz (Degrees) θz (Degrees)
Ken Clark - PSU Lyon, Oct 2012
DistinguishabilityStot =
s
(⌃ij
(N IHij �NNH
ij )2
NNHij
Stot =
s
(⌃ij
(N IHij �NNH
ij )2
NNHij
Stot =
s
⌃ij
(N IHij �NNH
ij )2
NNHij
• Use method outlined in arXiv:1205.7071 (Akhmedov, Razzaque and Smirnov)
• Essentially bin everything up and subtract the two hierarchies, scaled by the number of events in the Normal hierarchy bin
21
Ken Clark - PSU Lyon, Oct 2012
Simulations• Simulations now carried out using IceCube
MC structure
• Currently studying different PINGU geometries with different spacings
X (m)-100 -50 0 50 100 150 200
Y (m
)
-150
-100
-50
0
50
100IceCube
DeepCore
PINGU (HQE)
PINGU Geometry V3
X (m)-100 -50 0 50 100 150 200
Y (m
)
-150
-100
-50
0
50
100PINGU Geometry V5 (Cappelletti)
IceCube
DeepCore
PINGU (HQE)
PINGU Geometry V5 (Cappelletti)
X (m)-100 -50 0 50 100 150 200
Y (m
)
-150
-100
-50
0
50
100PINGU Geometry V6 (Dozier)
IceCube
DeepCore
PINGU (HQE)
PINGU Geometry V6 (Dozier)
Ken Clark - PSU Lyon, Oct 2012
Simulations• Simulations now carried out using IceCube
MC structure
• Currently studying different PINGU geometries with different spacings
X (m)-100 -50 0 50 100 150 200
Y (m
)
-150
-100
-50
0
50
100IceCube
DeepCore
PINGU (HQE)
PINGU Geometry V3
X (m)-100 -50 0 50 100 150 200
Y (m
)
-150
-100
-50
0
50
100PINGU Geometry V5 (Cappelletti)
IceCube
DeepCore
PINGU (HQE)
PINGU Geometry V5 (Cappelletti)
X (m)-100 -50 0 50 100 150 200
Y (m
)
-150
-100
-50
0
50
100PINGU Geometry V6 (Dozier)
IceCube
DeepCore
PINGU (HQE)
PINGU Geometry V6 (Dozier)
Ken Clark - PSU Lyon, Oct 2012
Distinguishability Plots
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)
4
6
8
10
12
14
16
18
20
-4
-2
0
2
4
6]1/2Distinguishability Metric [(IH-NH)/NH• Use our
simulations
• First use neutrino zenith angle and energy
• Shown without square root to illustrate pattern
24
PRELIMINARY
Ken Clark - PSU Lyon, Oct 2012
Distinguishability Plots
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)
4
6
8
10
12
14
16
18
20
-4
-2
0
2
4
6]1/2Distinguishability Metric [(IH-NH)/NH
• Matter effects due to MSW
25
PRELIMINARY
Ken Clark - PSU Lyon, Oct 2012
Distinguishability Plots
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)
4
6
8
10
12
14
16
18
20
-4
-2
0
2
4
6]1/2Distinguishability Metric [(IH-NH)/NH
• Primarily parametric oscillation effects in this region
26
PRELIMINARY
Ken Clark - PSU Lyon, Oct 2012
Distinguishability Plots
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)
4
6
8
10
12
14
16
18
20
-4
-2
0
2
4
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)
4
6
8
10
12
14
16
18
20
-4
-3
-2
-1
0
1
2
3
4
• Then use muon zenith angle and neutrino energy
• Shown without square root to illustrate pattern
27
PRELIMINARY
Ken Clark - PSU Lyon, Oct 2012
Reconstruction
• Previous plots showed perfect detector resolution
• This (probably) won’t be the case
• Need to account for the reconstruction effects
• Add a gaussian “smearing” to the angles and energies
Ken Clark - PSU MANTS, Oct 2012
Detector Resolution
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
6
8
10
12
14
16
18
20
-6
-4
-2
0
2
4
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
4
6
8
10
12
14
16
18
20
-1.5
-1
-0.5
0
0.5
1
1.5
]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
4
6
8
10
12
14
16
18
20
-1
-0.5
0
0.5
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)
2
4
6
8
10
12
14
16
18
20
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
]1/2Distinguishability Metric [(IH-NH)/NH
0 GeV, 0°
2 GeV, 11.25°
3 GeV, 15°
4 GeV, 22.5°
Ken Clark - PSU MANTS, Oct 2012
Detector Resolution
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
6
8
10
12
14
16
18
20
-6
-4
-2
0
2
4
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
4
6
8
10
12
14
16
18
20
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
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)
2
4
6
8
10
12
14
16
18
20
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
]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
4
6
8
10
12
14
16
18
20
-0.6
-0.4
-0.2
0
0.2
0.4
0.6]1/2Distinguishability Metric [(IH-NH)/NH
0 GeV, 0°
2 GeV, 11.25°
3 GeV, 15°
4 GeV, 22.5°
Ken Clark - PSU MANTS, Oct 2012
Comparisons
• Following model in publication, used three different resolution pairs
• (2GeV,11.25°),(3GeV,15°),(4GeV,22.5°)
31
2 GeV, 11.25 Deg 3 GeV,15 Deg 4 GeV,22.5 Deg
Tota
l Sig
ma
Valu
e
0
5
10
15
20
25
Akhmedov et al
Neutrino Angle 1 Year
Muon Angle 1 Year
Calculated Total Sigma - PINGU 1 Year
PRELIMINARY
Ken Clark - PSU Lyon, Oct 2012
Systematics
• Studied several effects
1. Systematic energy shift +/-5%, +/-10%
2. Systematic angle broadening +/-5%, +/-10%
3. PREM quantities incorrect
• Core radii +/-5%, +/-10%
• Core densities +/-5%, +/-10%
32
Ken Clark - PSU MANTS, Oct 2012
Systematics - Illustrated
33
IH(T ) NH(T )
�2(IH(T ) : NH(T ))
Ken Clark - PSU Lyon, Oct 2012
Systematics - Illustrated
34
IH(T ) NH(T )
NH(S)
�2(IH(T ) : NH(S))
��2 = �2(IH(T ) : NH(S))� �2(NH(T ) : NH(S))
��
2> 0 ! ProperID
��
2< 0 ! WrongID
�2(NH(T ) : NH(S))
Ken Clark - PSU Lyon, Oct 2012
Energy Shift
• Systematic shift in energy has little effect
Run Length (years)1 1.5 2 2.5 3 3.5 4 4.5 5
2 χ Δ
20
25
30
35
40
° - Detector Resolution 2 GeV, 11.252χ Δ
No Systematic Shift
Energy Shift +5%
Energy Shift +10%
35
PRELIMINARY
Ken Clark - PSU Lyon, Oct 2012
Angle Broadening
• Not a systematic shift in zenith
• Misunderstanding of the detector resolution
Run Length (years)1 1.5 2 2.5 3 3.5 4 4.5 5
2 χ Δ
20
25
30
35
40
° - Detector Resolution 2 GeV, 11.252χ Δ
No Systematic Shift
Angle Broadening +5%
Angle Broadening +10%
36
PRELIMINARY
Ken Clark - PSU Lyon, Oct 2012
Next Steps
• Next objective is to include detector resolution effects properly using reconstructions
• Need to perform detailed analysis of systematics
• Start with quantification of best geometry
37
Ken Clark - PSU Lyon, Oct 2012
Timescale
March 2011
Early 2012
Begin simulation studies for 18-20 string
detector with threshold ~1GeV. Targeted Physics: neutrino
hierarchy, WIMPs, SN
Submit PINGU Proposal
Complete 1st DeepCore analyses.
Spring 2012
Winter 2016/17
Begin deploying PINGU
Winter 2017/18
Finish deploying PINGU including
R&D strings.Start data-taking early
2018
1st PINGU workshop -
NIKHEF
2nd PINGU workshop - Penn State
Jan 2012
Fall 2012
3rd PINGU workshop -
Erlangen
May 2012
Submit Letter
of Interest to NSF
Finish Detailed PINGU studies
Summer 2013
Fall 2013
Ken Clark - PSU Lyon, Oct 2012
Conclusion
• Determination of the neutrino mass hierarchy with atmospheric neutrinos appears feasible
• PINGU allows for this determination quickly in a cost effective implementation
Ken Clark - PSU Lyon, Oct 2012
Ken Clark - PSU Lyon, Oct 2012
Comparison
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)
4
6
8
10
12
14
16
18
20
-4
-2
0
2
4
6]1/2Distinguishability Metric [(IH-NH)/NH
Things seem to compare reasonably well
41
Ken Clark - PSU Lyon, Oct 2012
Detector Resolution Plots
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
6
8
10
12
14
16
18
20
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
]1/2Distinguishability Metric [(IH-NH)/NH
• Shown with detector resolution 2 GeV, 11.25°
42
Ken Clark - PSU Lyon, Oct 2012
Reality(-ish)
Zenith Angle (degrees)120 130 140 150 160 170 180
Ener
gy (G
eV)
5
10
15
20
25
30
35
40
45
50
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
) - Inverted Hierarchy (NuMu+NuMuBar)µν→µνP(
Zenith Angle (degrees)120 130 140 150 160 170 180
Ener
gy (G
eV)
5
10
15
20
25
30
35
40
45
50
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
) - Normal Hierarchy (NuMu+NuMuBar)µν→µνP(
• For νμ-like events we really get a mixture of νμ and νμ
43
Ken Clark - PSU Lyon, Oct 2012
Systematics• Can also add systematics on the simulated
data:
1. Apply detector resolution to both hierarchies (IH and NH)
2. Copy both hierarchies
3. Apply systematic shift to one copy for each
4. For each copy, calculate the significance of the opposite unshifted hierarchy and the same unshifted hierarchy
5. Subtract the same from the opposite value
44