1 Raghunath Ganugapati(Newt) Preliminary Exam 08/27/04 Strategies for the search for prompt muons in the downgoing atmospheric muon flux with the AMANDA Detector

2 Outline AMANDA detector Physics Goals of My Analysis Search strategies

3 The AMANDA Detector 19 strings 677 Optical Modules Full 19 string version (AMANDA-II) operational starting in meters diameter 500 meters in height

4 Cherenkov Radiation cos  n   v/c, n= refraction index  We detect Cherenkov light obtained from the neutrino ice interaction as the muon travels faster than the speed of light in ice  

5 Different Potential Event Origins Extra Terrestrial Neutrinos (E -2 spectrum) Backgrounds Atmospheric Muons (E -3.7 spectrum) Atmosphere Neutrinos and muons from conventional mode of decay (π ±, K ± ) (E -3.7 spectrum) Possible Atmospheric neutrino from charm (E -2.7 spectrum)

6 Origin of Atmospheric Components The number of particles starts to increase rapidly as the shower moves downwards in the atmosphere on their way and in each interaction the particles loose energy. The number of particles reaching the earth depends on the energy and type of the incident cosmic ray and the ground altitude (sea level)

7 mc 2 (MeV) ctE critical (GeV) π ± m115 K±K± m855 D±D± µm3.8*10 7 E critical =(mc 2 /ct)*h 0 h 0 =6.4Km Interaction VS Decay Ref:hep-ph/ v3 19 Jan 2001

8 Prompt Muons Charmed particles decay before interacting hence muons from decays of charm are called prompt muon The flux of prompt muons differs qualitatively from ordinary muons (conventional π ±, K ± decay) in two ways The Energy spectrum is flatter (E -2.7 ) VS E -3.7 for conventional muons due to interaction The angular distribution is isotropic

9 Neutrino Fluxes The ZHV-D model of prompt neutrinos could not be constrained by looking at the neutrino data for one single year. We shall see towards the end if we could constrain this model of charm production from the stand point of looking at muon data. Can we do better with downgoing Muons? AMANDA-II E -2 

10 Neutrino Vs Muon Fluxes The prompt muonic neutrino fluxes and the prompt muon flux are essentially the same at sea level. This result is independent of the charm production model and hence a constraint on a prompt muon is equivalent to a constraint on prompt neutrinos Ref:GGV,hep-ph/ v1 10 Sep 2002

11 Uncertainty in Prompt Muon Cross Sections The uncertainty spans three orders of magnitude. This is mainly because of the need to extrapolateaccelerator data to very high energies and not much is known about p-p interactions. Note that the crossing between conventional to prompt muon fluxes happens between 40TeV and 3 PeV. Ref: GGV,hep-ph/ v1 10 Sep 2002

12 Charm Mechanism Vs π ±, K ± Mechanism The interaction of a high energy cosmic ray with air nuclei produces a D ± which takes up most of the energy and momentum of the primary. Showering effect and the productionof accompanying π ± and K ± is negligible when required to estimate the flux at the surface of the earth. Ref: Doctoral thesis of Prof.Varieschi

13 Analysis Description

14 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. The conventional muons produced from and 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. Signal,Background Simulation and Data Background Data 75 days life time worth data taken by the AMANDA detector during the year 2001 will be studied.

15 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. Zenith Angle Energy Topology(single muon and a bundle of muons) Defining Observables Strategies for separation of Signal from Background

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

17 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 Ratios Further more a cut on the Zenith angle acts like a natural cut on the energy at the surface due to larger distance of propagation through the Earth b/s Cos(zenith) True track Reconstructed Track Cut these out

18 Angular Resolution 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 the angular reconstruction for muons at large zenith angles translates to several kilometers propagation through Earth and incorrect energy losses Angular Resolution(Δθ)

19 Quality Cuts Track Length(>120m) Distance between direct hits projected on to the length of the track Smoothness(<0.26) Measure of how smoothly the hits are distributed along the track Reduced Chi square(<7.3) Chisquare computed using time residuals and divided by total number of hits Cascade to track likelihood Ratio(<1) Tracks that have a sphericity in the pattern of timing like cascades are hard to reconstruct(High energy muons with stochastic losses)

20 Angular Resolution For muons greater than 65 0 in zenith the angular resolution is ~7 0 before the quality cuts and ~3.5 0 after quality cuts Angular Resolution(Δθ) Background (after Q.C) Signal (after Q.C)

21 Energy Spectra log10(energy) GeV Number of Hits Vs log10(energy) GeV The multiple muon background goes with the same slope as the signal so the signal will be masked 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 singles multiples signal

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

23 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. A new method to separate single muons from multiple muons using the hit topology information

24 Early Hit Illustration(Idea1) snapshot Think of the cherenkov structure as propagating in time relative to the tracks. The hit at B is earlier by a time given by length(AB)/c ice 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. Muon1 Muon2 Early Hit Reconstructed track A B

25 Muon1 Muon4 Muon2 Truncated Cone timing pattern Muon3 Muon5 In the limit that the distance between two adjacent muons becomes zero the timing pattern fits a truncated cherenkov structure Truncated cone illustration(Idea 2)

26 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. Early Hits

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

28 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 Data Background timedelay(ns)

29 Time Delay Distribution by strings timedelay(ns) Strings1-4 Strings1-10Strings Data B.G. MC Signal 50m 100m 200m

30 Dust Clear Ice Reconstructed track in data True track Geometrical Effect Reconstructed track in simulation

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

32 Difference of Earlyhits between truncated fit and the cherenkov fit Truncated Cone Hypothesis 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. Data disagreement(to be understood) the same reasons discussed previously apply. Cut these Singles Multiple Signal Data B.G signal Difference of Earlyhits between truncated fit and the cherenkov fit

33 Pass Rates plot After Topology Cuts 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. The cuts were picked with eye so there is a possibility of doing better!!! Number Of Hits Multiples Signal Singles

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

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

36 ● Apply all the cuts ● n b =number of predicted background events n s =number of predicted signal events f(( ,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). n o =number of observed events upper limit = µ 90 (n o, n b ) Calculate your flux limit.  90 =  * (µ 90 /n s ) Limit Setting

37 Average Upper Limit 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”( µ 90 ) = the sum of expected upper limits, weighted by their Poisson probability of occurance and is done under the assumption of zero signal. This is the same as sensitivity. The average upper limit is calculated for each restriction on the number of hits per event Integral spectrum Number Of Hits Background Signal

38 Model Rejection Potential The “model rejection factor” is defined as mrf= µ 90 /n s over an ensemble of experiments the optimal selection criteria minimize the “model rejection factor”. The sensitivity is then given by  90 =  * mrf Example of determining the mrf using this method. Number Of Hits Best MRF=0.39 Signal there=25.20 Background=11.2 Number Of Hits

39 MRFCut (Nhits) SignalB.GData ZENITH5.1 (last B.G) Q.C topology MRF(RPQM) Note: These MRF’S are computed using a 30% theoretical uncertainity on the background and 30% error on the systematics(detection efficiencies)

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

41 MRF ON ZHV-D Model The model rejection factor on the ZHV-D model assuming a 30% systematic error(detection efficiency) and a 30% theoretical uncertainty on the theoretical background is 0.1(preliminary); this 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

42 AMANDA-II E -2  Constraining Charm Neutrino models by analysis of downgoing Muon Data

43 Conclusions And Future Work The capability to constrain prompt neutrino models by analyzing the downgoing muon data looks promising The systematic 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 prompt muon model has to be studied in detail

44 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 Track Length>120 Data Background Signal Cut these Track Length

45 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 Reduced Chisquare<7.3 Data BG Signal Cut these Chisquare

46 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 Smoothness<0.26 smoothness Cut these Data BG MC SG MC

47 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 Ratio>0.0 Diff of Chi squares Cut these Data BG Signal

48 Given a track hypothesis we can calculate the expected photon arrival times from an unscattered Cherenkov cone. The time residual is the difference between the actual arrival time and the expected arrival time using a Cherenkov geometry Cherenkov Geometry