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.

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)

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)

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)

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

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

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)

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))

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)

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)

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

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

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))

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)

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.

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

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.

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

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

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.

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

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

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

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

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

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.

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)

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

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.

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

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

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