1. London Collaboration Meeting September 29, 2005 Search for a Diffuse Flux of Muon Neutrinos using AMANDA-II Data from 2000 - 2003 Jessica Hodges University of Wisconsin – Madison

2. Search for a Diffuse Flux of Neutrinos (TeV – PeV)    “Signal” downgoing muons and neutrinos E -3.7 E -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 Remove downgoing events with a zenith angle cut and by requiring high quality event observables. Separate atmospheric neutrinos from signal by an energy cut.

3. The zenith angle distribution of high quality events before an energy cut is applied. The signal test flux is E 2  = 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.

4. 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

5. Unblinding! Optimized Final Energy Cut: NChannel >= 100 Number of Atmospheric Neutrinos Predicted = 9.8 Signal (E 2 flux = 10 -6 ) Predicted = 60.8 Number of Data Events Observed = 6

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.

7. 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?

8. 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

9. After applying an inverted analysis on the minimum bias files, the channel distribution shows agreement in shape.

10. Data Atms μ MC Data 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.

11. 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

12. 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.

13. Comparing the flux models… The data is generally below Lipari and Bartol and above Honda and Fluka.

14. Comparing the flux models…

15. 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

16. ModelNormalization Lipari0.888 +- 0.0122 Bartol0.893 +- 0.0124 Honda1.14 +- 0.0156 Fluka1.08 +- 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%

17. Nusim Normalization Factor MRF Nch Cut (Nch>=x) μ 90 Integrated Background (Nch>=100) after normalization Integrated Signal (Nch>=100) after normalization Lipari0.8880.1101006.709.860.8 Bartol0.8930.1011016.088.161.1 Honda1.140.0763986.157.378.0 Fluka1.080.07011015.095.173.9 Atmospheric ν prediction = Average from 4 Models = 7.6 Background range = 7.6 +- 2.5 = 7.6 +- 33% Atmospheric Neutrinos vs E -2 Signal

18. 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 NChannel 100680

19. 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 100680NChannel This 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%.

20. BackgroundEfficiencyProbability of this Scenario 5.10.9181/12 5.11.081/12 5.11.241/12 7.30.9691/12 7.31.141/12 7.31.311/12 8.10.7591/12 8.10.8931/12 8.11.031/12 9.80.7551/12 9.80.8881/12 9.81.021/12 Fluka Honda Bartol Lipari - 15 % +15 % How the Systematic Error Code Works The 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.

21. Systematic errors widen the confidence belt. 0 0 No Errors Applied X = number of events measured μ = true but unknown signal

22. Systematic errors widen the confidence belt. 4m μ = true but unknown signal Correlated Systematic Errors Applied X = number of events measured

23. Event Upper Limit with Systematic Errors = 4.52  ν μ (E) < ( μ / n signal )  test E -2  ν μ (E) < (4.52 / 68.45) 10 -6 E -2 GeV cm -2 s -1 sr -1  ν μ (E) < 6.6 *10 -8 E -2 GeV cm -2 s -1 sr -1 Limit on Diffuse Flux of ν μ with systematic errors

25. Nusim Normalization Factor MRF Nch Cut (Nch>=x) μ 90 Integrated Background (Nch>=cut) after normalization Integrated Signal (Nch>=cut) after normalization LipariNone0.4807112.9246.226.9 BartolNone0.4577112.3041.326.9 HondaNone0.3997110.7530.526.9 FlukaNone0.374768.7619.023.4 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!

26. Nusim Normalization Factor MRF Nch Cut (Nch>=x) μ 90 Integrated Background (Nch>=cut) after normalization Integrated Signal (Nch>=cut) after normalization LipariNone0.1171324.483.138.3 BartolNone0.1071443.551.433.2 HondaNone0.0961343.611.537.4 FlukaNone0.0851343.200.9037.4 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!

27. More Prompt ν Models Nusim normalization MRF Nch cut (Nch >= x) μ 90 Integrated Background Integrated Signal Naumov RQPM 0.893 (Bartol) 2.697111.736.94.3 Martin GBW 0.893 (Bartol) 30.25519.6114.00.65 Background = Conventional Neutrinos (Bartol) Signal = Prompt Neutrinos to be continued with more models and with all four conventional atmospheric fluxes ….. Preliminary

28. 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 ν μ with systematic errors: *Other prompt neutrino models are under investigation. I will send out an unblinding proposal.  ν μ (E) < E -2 6.6 *10 -8 GeV cm -2 s -1 sr -1

31. True Energy of the Monte Carlo before and after the Energy Cut

32. Without Errors ( GeV cm -2 s -1 sr -1 ) With Errors (E -2 GeV cm -2 s -1 sr -1 ) Sensitivity μ 90 / n s 8.87 x 10 -8 9.90 x 10 -8 Limit μ 90 / n s 5.90 x 10 -8 6.6 x 10 -8 Values for E -2 Diffuse Muon Flux

33. 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 Data Likelihood Ratio (down to up) NChannel < 100 NChannel > 100

34. As reported in other analyses, there is poor agreement between data and Monte Carlo for direct hit parameters. Data Atms μ MC Data Track Length (ldirb) NChannel < 100 NChannel > 100

35. Systematic errors widen the confidence belt. 30

36. Table from 1997 Diffuse Paper