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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

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Outline

• AMANDA detector

• Physics Goals of My Analysis

• Search strategies

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The AMANDA Detector

19 strings

677 Optical Modules

Full 19 string version(AMANDA-II) operationalstarting in 2000

200 meters diameter

500 meters in height

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Cherenkov Radiation

cosn

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

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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)

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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)

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mc2

(MeV)

ct Ecritical

(GeV)

π ± 140 7.8m 115

K± 494 3.7m 855

D± 1870 317µm 3.8*107

Ecritical=(mc2/ct)*h0

h0=6.4Km

Interaction VS Decay

Ref:hep-ph/0010306 v3 19 Jan 2001

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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

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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

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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/0209111 v1 10 Sep 2002

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Uncertainty in Prompt Muon Cross Sections

• The uncertainty spans three orders of magnitude. This is mainly because of the need to extrapolate accelerator 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/0209111 v1 10 Sep 2002

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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 production of accompanying π± and K± is negligible when required to estimate the flux at the surface of the earth. Ref: Doctoral thesis of

Prof.Varieschi

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Analysis Description

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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.

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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

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Zenith distribution

Cos(truezenith Angle)

• The true zenith distribution of signal is flat while the distribution of background is steep

BackgroundSignal

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•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

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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)

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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)

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Angular Resolution

• For muons greater than 650 in zenith the angular resolution is ~70 before the quality cuts and ~3.50 after quality cuts

Angular Resolution(Δθ)

BackgroundBackground(after Q.C)

SignalSignal

(after Q.C)

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Energy Spectra

log10(energy) GeVNumber 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

singlesmultiples

signal

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Data Agreement

• Data seems to be in reasonable agreement with the simulation after quality cuts and zenith cut.

Number of Hits

2001(data)B.GSignal

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•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

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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)/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.

Muon1Muon1

Muon2

Early Hit

Reconstructed track

A

B

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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)

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•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

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Limitations of Earlyhits method

timedelay(ns)

Data

B.G.

Signal

zoom

timedelay(ns)

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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)

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Time Delay Distribution by strings

timedelay(ns) timedelay(ns)

timedelay(ns)Strings1-4

Strings1-10 Strings 11-19

DataB.G. MCSignal

50m

100m

200m

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Dust

Dust

Clear Ice

Reconstructed track in dataTrue track

Geometrical Effect

Reconstructed track in simulation

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Earlyhits

Earlyhits(strings1-10) 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

SinglesMultiples

Signal

DataB.G.Signal

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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

SinglesMultipleSignal

DataB.Gsignal

Difference of Earlyhits between truncated fit and the cherenkov fit

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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 SignalSingles

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Data Agreement

• An overall reasonable agreement with the data has to ensured. The systematics really need to be grinded out.

Number of Hits

DataB.GSignal

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Agreement of Few other Observables

Cos(Reco Zenith)

smoothness

Track Length(m)

Chisquare

Data

B.G.

Signal

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●Apply all the cuts●nb=number of predicted background events

ns=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). no=number of observed events

upper limit = µ90(no, nb)

Calculate your flux limit.

90= * (µ90/ns)

Limit Setting

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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”( µ90

) = 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.

90nobs 0

90 nobs , n b

nbnobs

nobs !exp nb

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

Integral spectrum

Number Of Hits

Background

Signal

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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

90= * mrf Example of determining the mrf using this method.

Number Of Hits

Best MRF=0.39Signal there=25.20Background=11.2

Number Of Hits

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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 20.0

topology

0.39 300 25.6 11.8 63

MRF(RPQM)

Note: These MRF’S are computed using a 30% theoretical uncertainity on the background and 30% error on the systematics(detection efficiencies)

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Average Upper Limit on ZHV-D model

Integral Spectrum

BackgroundSignal

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.

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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=0.10Signal there=81.87Background=11.2

Number Of Hits

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AMANDA-II E-2

Constraining Charm Neutrino models by analysis of downgoing Muon Data

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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

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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

BackgroundSignal

Cut these

Track Length

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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

DataBGSignal

Cut these

Chisquare

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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

DataBG MCSG MC

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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

DataBGSignal

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Given a track hypothesis we can calculate the expected photonarrival times from an unscatteredCherenkov cone.

The time residual is the difference between the actual arrival time and the expected arrival time using a Cherenkov geometry

Cherenkov Geometry