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London Collaboration Meeting
September 29, 2005
Search for a Diffuse Flux of Muon Neutrinos using
AMANDA-II Data from 2000 - 2003
Jessica HodgesUniversity of Wisconsin – Madison
Search for a Diffuse Flux of Neutrinos (TeV – PeV)
“Signal”
downgoing muons and neutrinos
E-3.7E-2
2000 – 2003 :
807 days of detector livetime
Monte Carlo simulation
Atmospheric Muons: muons created when cosmic rays hit the atmosphere, including simulation of simultaneous downgoing muons
Atmospheric Neutrinos: neutrinos created when cosmic rays hit the atmosphere. Have an E-3.7 energy spectrum.
Signal Neutrinos: extraterrestrial neutrinos with an E-2 energy spectrum
<1> Remove downgoing events with a zenith angle cut and by requiring high quality event observables.
<2> Separate atmospheric neutrinos from signal by an energy cut.
The zenith angle distribution of high quality events before an energy cut is applied.
The signal test flux is E2 = 10-6 GeV cm-2 s-1 sr-1.
After Event Quality Cuts
The likelihood ratio cut is zenith dependent. This allows events near the horizon to survive the quality cuts.
Track Length > 170 meters Ldirb[Pandel 32] > 170
Number of Direct Hits >13 Ndirc[Pandel 32] > 13
Smoothness < 0.250 abs(Smootallphit[Pandel 32]) < 0.250
Median resolution < 4.0 median_resolution(P08err1,P08err2)<4.0
Likelihood ratio vs zenith Jkchi[Bayesian 64] – Jkchi[Pandel 32] > -38.2*cos(Zenith[Pandel 32]/57.29)+27.506
Zenith > 100 Zenith[Pandel 32] >100
Number of channels >= 100 Nch >= 100
Additional cuts on the experimental data:
2000: 47 <= Gpsday <= 309
2001: 44 <= Gpsday <= 293
2002: 43 <= Gpsday <= 323
2003: 43 <= Gpsday <= 315
FINAL CUTS
*See my webpage for details of this function designed by T. Becka
Unblinding! Optimized Final Energy Cut: NChannel >= 100
Number of Atmospheric Neutrinos Predicted = 9.8
Signal (E2 flux = 10-6 ) Predicted = 60.8
Number of Data Events Observed = 6
Next steps:
1) Show that we understand the detector response for high energy (>100 channel) muon events.
2) Determine the systematic errors.
3) Set final sensitivity and limit (with and without errors) for different signal models.
To study the response of the detector to high energy muon events, I applied an inverted analysis to the minimum bias data and atmospheric muon Monte Carlo (dCorsika).
* Cuts on track length, number of direct hits, smoothness and median resolution remained the same.
* The likelihood ratio vs. zenith cut was inverted to select events with the highest probability of being downgoing after a new set of inverted fits was performed.
Do we understand high energy (Nch > 100) events?
Zenith distributions show agreement for events with high and low numbers of channels hit.
Cos(Zenith)
NChannel > 100
NChannel < 100
Data
Atms μ MC
Data
Atms μ MC
After applying an inverted analysis on the minimum bias files, the channel distribution shows agreement in shape.
DataAtms μ MC
Atms μ MC
Data
Number of Direct Hits (ndirc)
Number of Direct Hits (ndirc)
NChannel < 100
NChannel > 100
However, as reported in other analyses, the agreement between data and Monte Carlo for direct hit parameters is not so great.
Good agreement between the data and atmospheric muons at high quality levels
we understand how the detector responds to high energy muon events from any direction
Study systematic errors by considering other atmospheric neutrino flux models…
Thus far, all simulation done with Lipari model.
Use the NeutrinoFlux class written recently in Madison to test three other atmospheric neutrino models.
1 – Bartol (2004)
2 – Honda (2004)
3 - Fluka (2005)
The nusim normalization and number of events predicted in the final set (after the energy cut) will vary by model.
Comparing the flux models…
The data is generally below Lipari and Bartol and above Honda and Fluka.
Comparing the flux models…
Systematic errors and the normalization factor…
~11 atmospheric ν events survived to the final data set.
Normalization Used = 0.88 atmospheric ν prediction was 9.7
What if I had used a different neutrino model?
Lipari
Corrected normalization = 0.888 (not 0.88)
Corrected atmospheric ν prediction = 9.8 events (not 9.7)
My final cut level
Model Normalization
Lipari 0.888 +- 0.0122
Bartol 0.893 +- 0.0124
Honda 1.14 +- 0.0156
Fluka 1.08 +- 0.0149
The atmospheric neutrino model affects the nusim normalization.
Average Normalization over 4 Models = 1.00
Error in Normalization Factor = 0.14/1.00 = 14%
Nusim Normalization
Factor
MRF Nch Cut
(Nch>=x)
μ90 Integrated Background (Nch>=100)
after normalization
Integrated Signal
(Nch>=100) after
normalization
Lipari 0.888 0.110 100 6.70 9.8 60.8
Bartol 0.893 0.101 101 6.08 8.1 61.1
Honda 1.14 0.0763 98 6.15 7.3 78.0
Fluka 1.08 0.0701 101 5.09 5.1 73.9
Atmospheric ν prediction = Average from 4 Models = 7.6
Background range = 7.6 +- 2.5 = 7.6 +- 33%
Atmospheric Neutrinos vs E-2 Signal
Systematic Error on Background
Below 100 channels, all four models were normalized to the data. Finding the number of events predicted past 100 channels tests the shape of the different models.
average number of atmospheric neutrinos (Nch>=100) for the four models = 7.6 events
greatest that any model deviates from the average = 2.5 events
Nch>=100
NChannel100 680
Systematic Error on Signal Efficiency
This error takes into account uncertainty in the absolute normalization of the atmospheric neutrino flux.
Use the normalization as the efficiency value.
Nch>=100
100 680NChannelThis is equivalent to the error in the number of signal (E-2) events predicted after the final energy cut.
average normalization factor for the four models = 1.00
greatest that any model deviates from the average = 0.14
However, simply claiming an efficiency error based on the four models is not enough. There is still an overall uncertainty in the neutrino flux of 10 -15%.
Background Efficiency Probability of this Scenario
5.1 0.918 1/12
5.1 1.08 1/12
5.1 1.24 1/12
7.3 0.969 1/12
7.3 1.14 1/12
7.3 1.31 1/12
8.1 0.759 1/12
8.1 0.893 1/12
8.1 1.03 1/12
9.8 0.755 1/12
9.8 0.888 1/12
9.8 1.02 1/12
Fluka
Honda
Bartol
Lipari
- 15 %
+15 %
How the Systematic Error Code WorksThe code recalculates the pdf for each value of the unknown μ and constructs a “smeared”, wider confidence belt based on the 12 equally likely inputs.
Systematic errors widen the confidence belt.
0 0
No Errors Applied
X = number of events measured
μ =
tru
e bu
t un
know
n s
ign
al
Systematic errors widen the confidence belt.
4m
μ =
tru
e bu
t un
know
n s
ign
al
Correlated Systematic Errors Applied
X = number of events measured
Event Upper Limit with Systematic Errors = 4.52
νμ(E) < ( μ / nsignal) test E-2
νμ(E) < (4.52 / 68.45) 10-6 E-2 GeV cm-2s-1sr-1
νμ(E) < 6.6 *10-8 E-2 GeV cm-2s-1sr-1
Limit on Diffuse Flux of νμ with systematic errors
Nusim Normalization
Factor
MRF Nch Cut
(Nch>=x)
μ90 Integrated Background (Nch>=cut)
after normalization
Integrated Signal
(Nch>=cut) after
normalization
Lipari None 0.480 71 12.92 46.2 26.9
Bartol None 0.457 71 12.30 41.3 26.9
Honda None 0.399 71 10.75 30.5 26.9
Fluka None 0.374 76 8.76 19.0 23.4
Atmospheric ν prediction = Average from 4 Models = 34.3
Background range = 34.3 +- 15.3 = 34.3 +- 45%
Atmospheric Neutrinos vs Charm D Signal
* These numbers are coming soon!
Nusim Normalization
Factor
MRF Nch Cut
(Nch>=x)
μ90 Integrated Background (Nch>=cut)
after normalization
Integrated Signal
(Nch>=cut) after
normalization
Lipari None 0.117 132 4.48 3.1 38.3
Bartol None 0.107 144 3.55 1.4 33.2
Honda None 0.096 134 3.61 1.5 37.4
Fluka None 0.085 134 3.20 0.90 37.4
Atmospheric ν prediction = Average from 4 Models = 1.7
Background range = 1.7 +- 1.4 = 1.7 +- 82%
Atmospheric Neutrinos vs SDSS Prompt Signal
* These numbers are coming soon!
More Prompt ν Models
Nusim normalization
MRF Nch cut (Nch >= x)
μ90 Integrated Background
Integrated Signal
Naumov RQPM
0.893 (Bartol) 2.69 71 11.7 36.9 4.3
Martin GBW
0.893 (Bartol) 30.2 55 19.6 114.0 0.65
Background = Conventional Neutrinos (Bartol)
Signal = Prompt Neutrinos
to be continued with more models and with all four conventional atmospheric fluxes …..
Preliminary
Summary
* After unblinding the data (Nch>=100), 6 events were seen.
* We understand how the detector responds to high energy (Nch >= 100) events because we see good agreement between the high quality muon tracks in the downgoing muon data and dCorsika minimum bias files.
* Four conventional atmospheric neutrino models were compared. Systematic errors were settled from this study.
* Limit on a diffuse flux of E-2 νμ with systematic errors:
*Other prompt neutrino models are under investigation. I will send out an unblinding proposal.
νμ(E) < E-2 6.6 *10-8 GeV cm-2s-1sr-1
True Energy of the Monte Carlo
before and after the Energy Cut
Without Errors( GeV cm-2 s-1 sr-1)
With Errors (E-2 GeV cm-2 s-1 sr-1)
Sensitivity
μ90 / ns
8.87 x 10-8 9.90 x 10-8
Limit
μ90 / ns
5.90 x 10-8 6.6 x 10-8
Values for E-2 Diffuse Muon Flux
After applying an inverted analysis on the minimum bias files, the likelihood ratio (down to up) distribution shows agreement in shape.
Data
Atms μ MC
Atms μ MC
Data
Likelihood Ratio (down to up)
Likelihood Ratio (down to up)
NChannel < 100
NChannel > 100
As reported in other analyses, there is poor agreement between data and Monte Carlo for direct hit parameters.
DataAtms μ MC
Atms μ MC
Data
Track Length (ldirb)
Track Length (ldirb)
NChannel < 100
NChannel > 100
Systematic errors widen the confidence belt.
30 30
Table from 1997 Diffuse Paper