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