1. Signal ,Background Simulation and Data
Signal Simulation
Generation of single muons with an assumed energy spectrum of prompt muons(RPQM) and isotropic in zenith and azimuth angle at the surface of the earth; and propagate them through Earth and a detector response to these muons is obtained.
Data
The conventional muons produced from Π and K decay will be a background to our detection of the charm muons. The program corsika 6.02 with the QGSJET model to simulate the hadron interactions and decay is used.
75 days life time worth data taken by the AMANDA detector during the year 2001 will be studied.

2. Strategies for separation of Signal from Background
The distributions of various observables were studied to design our cuts to improve signal to background ratio and hence to improve our search for prompt muons.
Defining Observables
Zenith Angle
Energy
Topology(single muon and a bundle of muons)

3. Cos(truezenith Angle)
Zenith distribution
Background
Signal
The true zenith distribution of signal is flat while the distribution of background is steep
Cos(truezenith Angle)

4. Ratios
The signal over background ratio tends to improve as we go towards the more horizontal region and hence we will likely increase our sensitivity by taking a cut on the Zenith angle.
True track
Reconstructed Track
b/s
Further more a cut on the Zenith angle acts like a natural cut on the energy at the surface (prompt muons have a harder energy spectra)
Cos(zenith)

5. Zenith Angle
Angular resolution of our detector is bad for very horizontal muons and a small error in angle translates to large amount of distance through earth.
Benefit: Better signal to background ratio and hence sensitivity.
Further the zenith cut serves as an natural cut on energy at surface.
reconstructed zenith>65
Cos(Z)<0.45
Cut these
Reconstructed Zenith angle

6. Angular Resolution(Δθ)
The angular reconstruction errors are large at this stage and the zenith angle distribution of background is much steeper than the signal
A small error in angular reconstruction for muons at large zenith angles traslates into several kilometers of propagation through Earth and incorrect energy losses
Angular Resolution(Δθ)

7. Quality Cuts Track Length(Tracklength>120)
Distance between direct hits projected on to the length of the track
Smoothness(|smoothness|<0.26)
Measure of how smoothly the hits are distributed along the track
Reduced Chi square(reduced chisquare<7.3)
Chisquare computed using time residuals and divided by total number of hits
Cascade to track likelihood Ratio
(likelihood of track greater than cascade )
Tracks that have a sphericity in the pattern of timing like cascades are hard to reconstruct(High energy muons with stochastic losses)

8. Angular Resolution(Δθ)
Background
Background
(after Q.C)
For muons greater than 65 degrees in zenith the angular resolution is ~7 degrees before the quality cuts and ~3.5 degrees after quality cuts.
Signal
Signal
(after Q.C)
Angular Resolution(Δθ)

9. Number of Hits Vs log10(energy) GeV
Energy Spectra
singles
multiples
signal
Number of Hits Vs log10(energy) GeV
log10(energy) GeV
The multiple muon background goes with the same slope as the charm so the signal will be masked out in the fluctuations of the multiple muon background
True muon energy correlates with energy released inside the detector and observed through parameters like number of optical module fired and number of hits

10. Data Agreement
2001(data)
B.G
Signal
Data seems to be in reasonable agreement with the simulation after quality cuts and zenith cut.
Number of Hits

11. A new method to separate single muons from multiple muons using the hit topology information
Idea1: Single Muons should have no early hits with greater than 3.5 photoelectron.
Idea2: Truncated cherenkov cone timing pattern fits the multiple muon hypothesis better than the ordinary cone.

12. Early Hit Illustration(Idea1)C D E
Think of this figure as one structure propagating in time relative to the tracks.
The hit at C is earlier by a time given by length(CE)/cice
Noise hits are random and can occur early as well and so the 3.5 photo electron cut is to ensure proximity to the track.
Early Hit
Muon1
snapshot
Reconstructed
track
Muon2

13. Truncated cone illustration(Idea 2)
Cone timing
pattern
In the limit that the muon distance becomes zero the timing pattern fits a truncated cherenkov structure.
Muon1
Muon2
Muon3
Muon4
Muon5

14. Early Hits
If a hit is the first hit in an OM in the vicinity of the track(0-50m) and has a negative time residual(less than –15ns) and occurs with a large amplitude (> 3.5p.e.) then it means that it is more likely to be a multiple muon event by the method described previously. I call the number of such hits per each event as “earlyhits”.
The 3.5 Photo Electron above is the expected adc in the vicinity of the track for hits produced by unscattered photons and thus is used as a benchmark for not cutting signal events which do have noise hits.

15. Limitations of Earlyhits method
zoom
Data
B.G.
Signal
timedelay(ns)
timedelay(ns)

16. Vertical Muons
The time delay distribution for vertical muons(<30degrees) fits well in the region on which early hits is defined but for horizontal muons we saw it is not so good?
Clue
Angular Resolution and misreconstructed muon
Data
Background
timedelay(ns)

17. Time Delay Distribution by strings
Data
B.G. MC
Signal
timedelay(ns)
timedelay(ns)
Strings1-10
Strings 11-19
timedelay(ns)
Strings1-4

18. Geometrical Effect Dust Clear Ice Dust Reconstructed track in data
True track
Dust
Reconstructed
track in simulation
Clear Ice
Dust

19. Earlyhits
Singles
Data
Multiples
B.G.
Signal
Signal
Cut these
Earlyhits(strings1-10)
Earlyhits(strings1-10)
Multiple muon events likely to have more early hits as compared to singles
The data agrees with the M.C to a reasonable level
The disagreement will be understood once we have a better simulation(Photonics).
Angular resolution of tracks and Ice properties.

20. Truncated Cone Hypothesis
Singles
Data
Multiple
B.G
Signal
Cut these
signal
Difference of Earlyhits between
truncated fit and the cherenkov fit
Difference of Earlyhits between
truncated fit and the cherenkov fit
Early hits characterize not so good reconstruction and likelihood function has a large penality on them.
Truncated cone is better fit hypothesis for multiple muon compared with ordinary cherenkov cone.
Differences between the early hits are larger for multiple muon
Data disagreement(to be understood) the same reasons discussed previously apply.

21. Pass Rates plot After Topology Cuts
Multiples
As can be seen we reject a lot of high energy multiple muons background and this comes at the cost of reduction in signal but still we reject more background compared with signal
Signal
Singles
Number Of Hits

22. nb=number of predicted background events
Limit Setting
Apply all the cuts
nb=number of predicted background events
ns=number of predicted background events f((ø,P)
predicted flux
Probability of an event
given detector response
Make your observation and find the limit on the number of signal events (Feldman&Cousins,1999) no=number of observed events
upper limit = µ90(no, nb)
Calculate your flux limit.
ø90=ø * (µ90/ns)

23. Average Upper Limit Integral spectrum
Since we cannot know the actual upper limit until we look at the data, simulations can be used to calculate the average upper limit.
“Average upper limit” (90) = the sum of expected upper limits, weighted by their Poisson probability of occurance.
Background
Signal
Number Of Hits
The average upper limit is calculated for each restriction on the number of hits per event

24. Model Rejection Potential
The “model rejection factor” is defined as
mrf= µ90/ns
over an ensemble of experiments the optimal selection criteria minimize the “model rejection factor”.
The sensitivity is then given by
ø90=ø * mrf
Best MRF=0.39
Signal there=25.20
Background=11.2
Number Of Hits
Number Of Hits
Example of determining the
mrf using this method.

25. MRF(RPQM) MRF Cut (Nhits) Signal B.G Data ZENITH 5.1 (last B.G) 510
2.03
19.8
20.0
Q.C
2.79
420
1.48
1.54
topology
0.39
300
25.6
11.8 63

26. Average Upper Limit on ZHV-D model
Integral Spectrum
Background
Since we cannot know the actual upper limit until we look at the data, simulations can be used to calculate the average upper limit.
Signal
Average Upper limit
Number Of Hits

27. MRF ON ZHV-D Model
The model rejection factor on the ZHV-D model is 0.1 which means that it could be constrained by an order of magnitude with just 75 days of statistics!!!!
Best MRF=0.10
Signal there=81.87
Background=11.2
Number Of Hits

28. Data Agreement
Data
B.G
Signal
An overall reasonable agreement with the data has to ensured. The systematics really need to be grinded out.
Number of Hits

29. Agreement of Few other Observables
Data
B.G.
Signal
Cos(Reco Zenith)
Track Length
smoothness
Chisquare

30. Constraining Charm Neutrino models by analysis of downgoing Muon Data
AMANDA-II E-2 nm

31. Conclusions And Future Work
The capability to constrain charm neutrino models by analyzing the downgoing muon data looks promising.
The systematics and error calculations need to be done in detail.
The issue of Angular resolution has to be studied in detail for a range of ice properties and a more accurate simulation(Photonics) has to be looked into.
The capability to constrain various other models of charm has to be studied in detail

32. DATA DESCRIPTION FOR EXAMPLE 1
SPARE Transparency
DATA DESCRIPTION FOR EXAMPLE 1
Track length is correlated with quality of the event.As seen from the previous plot events with short track length have poor quality.As can be seen the MC doesn’t describe the data too for these events.
The cut is
Ldirb(2)>120
Cut these
Data
Background
Signal
Ldirb(2)

33. DATA DESCRIPTION FOR EXAMPLE 2
SPARE TRANS
DATA DESCRIPTION FOR EXAMPLE 2
The chi square is a measure of how well the track fits the timing hypothesis and is a measure of the quality of the event.Large Chi square per hit means that is a poor quality event.
The cut is
jkrchi(2)<7.3
Cut these
Data BG
Signal

34. DATA DESCRIPTION FOR EXAMPLE 3
SPARE TRANS
DATA DESCRIPTION FOR EXAMPLE 3
Smoothness is a measure of how regular the photon density is distributed along the track and so a well reconstructed muon track is more likely to have a higher smoothness.
The cut is
abs(smootallphit(2))<0.26
Cut these
Data
BG MC
SG MC
Abs(smootallphit(2))

35. DATA DESCRIPTION FOR EXAMPLE 4
SPARE TRANS
DATA DESCRIPTION FOR EXAMPLE 4
This ratio represents if an event is more track like or cascade like. And is a measure of sphericity of timing.Good quality tracks look more track like.
The cut is
Jkrchi(8)-Jkrchi(2)>0.0
Data BG
Signal
Cut these
Jkrchi(8)-jkrchi(2)