1. Signal and Background MonteCarlo generation
Signal Montecarlo
Generic E-1 spectrum is generated at the surface of the Earth using a generator called mu0 and the events are propagated using standard AMANDA propagations codes.It generates muons on a plane at the surface of the earth according to a specified Zenith,Azimuth and Energy distribution.This is reweighed to the spectrum of charm(RPQM).
Background Montecarlo
The conventional muons produced from Pions and Kaon 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.

2. Observable Space
The observable space will be studied to design our cuts to improve
signal to background ratio and hence to improve our search for
charm muons .Possible separations of signal will be looked at by
distribution of various observables using the MC’s.
Defining Observable space
a)Zenith Angle
b)Energy
c)Topology(single muon and a bundle of muons)

3. Quality Parameters example1:The track length
Downgoing BG Muons
Downgoing SG Muons
Cut these
Cut These
Ldirb(2) VS Delang(2)
Ldirb(2) VS Delang(2)

4. 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)

5. Quality Parameters example2:chisquare(jkrchi(2))
Downgoing BG Muons
Downgoing SG Muons
Cut these
Cut these

6. 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

7. Quality Parameters example3:The smoothness
Downgoing BG Muons
Downgoing SG Muons
Cut these
Cut these
Abs(smootallphit(2))VS delang(2)
Abs(smootallphit(2))VS delang(2)

8. 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))

9. Quality Parameters example4:The ratio of chi-squares between Pandal and cascade fits
Downgoing BG muons
Downgoing SG muons
Cut these
Cut these
Jkrchi(8)-jkrchi(2)VS delang(2)
Jkrchi(8)-jkrchi(2)VS delang(2)

10. 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)

11. Quality Parameters Track length (ldirb(2))>120 Smoothness
(abs(smootallphit(2))<0.26
Chi Square
(jkrchi(2))<7.3
Ratio of Chi Square
(jkrchi(8)-jkrchi(2))>0.0

12. Angular Resolution BG
BG(after Q.C)
signal
SIGNAL
Singles(qc)
Singles
Multiple(qc)
Multiple
Delang(2)
Delang(2)vs truezenith
The quality cuts improve the angular resolution of tracks.It might be noted that angular resolution for single muons(conventional) is better than multiple muons and that the angular resolution of charm muons approximately goes like that of single conventional muons

13. ZENITH ANGLE
The spectrum of charm is flat because decay prevails over interaction,and thus at sealevel it goes like the primary cosmic ray spectrum whereas the spectrum of conventional muons is softer because of interaction.Further the spectra are also effected by the muon propagation through earth depending on the zenith angle. BG
signal
Cos(zenith(2))

14. ZENITH ANGLE
The problem with cutting at very large zenith angle is that the 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 but however there is a benefit because of better signal to background ratio by going to horizontal muons. Further the zenith cut serves as an energy cut at the surface too.
zenith(2)>65(cos(z)<0.45)
Cut these
Zenith(2)

15. Nhits VS Log10(energy) GeV
ENERGY SPECTRA
singles
multiples
signal
Log10(energy) GeV
Nhits VS 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 muons background and
there would be no way separate it at this stage.
In AMANDA we don’t reconstruct the energy of the muon directly.We look for a variable like the number of channels fired,the total number of
hits received in the channels fires etc as an obeservable for the true energy at AMANDA depth.As can be seen there is a correlation between the true energy and the number of hits received.

16. Data Agreement At this stage the data seems
B.G
At this stage the data seems
to be in reasonable agreement with the simulation
Signal
nhits

17. 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 P.E adc.
Idea2:Truncated cherenkov cone timing pattern fits the multiple muon hypothesis better than the ordinary cone.

18. Early Hit Illustration(Idea1)C D
Early Hit A
Noise hits usually occur with small adc and thus can be distinguished from hits that occur from multiple muon,which occur with larger adc(more than 3.5 P.E. or so). B
Muon1
snapshot
Reconstructed
track
Muon2

19. 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. C D B A
Muon1
Muon2
Muon3
Muon4
Muon5

20. Early Hits
If a hit is the first hit in an OM in the vicinity of the track(0-100m) and has a negative time residual(less than –15ns) and occurs with a large adc (> 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 3.5p.e. 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.

21. Limitations Of earlyhit method
Time delay(ns)
Data
B.G. MC
Signal
zoom
Timedelay(ns)

22. 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 is not so good?
clue
Angular Resolution and Misreconstructed muon
data
background

23. Time Delay Distribution by strings
data
B.G. MC
signal
Timedelay(ns)
Timedelay(ns)
Strings1-10
Strings 11-20
Timedelay(ns)
Strings1-4

24. Geometrical Effect
Real Track
Data
M.C
Dust
Clear Ice
Dust

25. Earlyhits As can be seen multiple muon events are more likely to have
singles
data
multiples
B.G.
signal
signal
Cut these
Earlyhits(strings1-10)
Earlyhits(strings1-10)
As can be seen multiple muon events are more likely to have
early hits as compared to single muon.
The data agrees with the M.C to a reasonable level.
The disagreement will be understood once we have a better
Simulation(Photonics) but it hs got to do with the angular
Resolution of tracks and ice properties

26. Truncated Cone Hypothesis
singles
data
multiple
B.G
signal
Cut these
signal
nearly(tr)-nearly(ch)
nearly(tr)-nearly(ch)
The correction between the two fits will be larger for multiple muon because
some of the early hits with cherenkov reconstruction will no longer be
early when the truncated cone hypothesis is used.
Data disagreement(to be understood) the same reasons discussed previously apply.

27. 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)

28. 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.
The average upper limit is
calculated for each restriction on the number of hits per event

29. 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=0.69
Signal There=11.8
Background There=8.0
Example of determining the
mrf using this method.

30. Data Agreement
An Overall reasonable agreement with the data has to ensured.The systematics really need to be grinded out .
nhits

31. MRF TABLE 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
0.69
300
11.8
8.0
41.0

32. CONCLUSIONS AND FUTURE WORK
The capability to constrain charm neutrino models by analyzing the 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 models of charm has to be studied in detail