searching for a diffuse flux of neutrinos with amanda-ii jessica hodges november 5, 2004 prelim exam

Searching for a Diffuse Flux of Neutrinos with AMANDA-II

Jessica Hodges

November 5, 2004Prelim Exam

Outline

● Why study neutrinos? ..... Cosmic ray and neutrino physics

● AMANDA-II detector .... Description of detector

● Analysis techniques .... How data is analyzed

● Diffuse neutrino analysis .... Work completed on the 2000 data set

● Future work .... Progress made on the 2000-2003 data set and what is to come

2

What are neutrinos?

● Neutral lepton that follows the rules of weak interactions

● Three flavors: electron (e), muon (), tau ()

● Have some mass, although not yet determined● Neutrinos can oscillate or change between flavors

or types● First experimentally proved to exist by Cowan

and Reines in the 1950s

3

Types of cosmic accelerators

● GRBs (Gamma Ray Bursts), supernova remnants, x-ray binaries, mini-quasars

● AGNs (Active Galactic Nuclei)

● Topological defects, primordial black holes, dark matter and other exotic phenomena

● ?

Crab Nebula (supernova remnant) 4

p + X +/- + Y +/- + ()

e+/- + e(

e) + ()

The above process also occurs with the decay of kaons (in place of pions).

p + + n + +

+ +

e+ + e+

p + p + o 2

The interacting proton splits its energy evenly between these two processes – one which creates neutrinos and one which creates gamma rays.

How are neutrinos created?

5

Cosmic rays hit the atmosphere and produce many particles, including muons and neutrinos which are detected by AMANDA

6Reference: University of Adelaide Astrophysics webpage

Cosmic Ray Spectrum

dN/dE ~ E-2.7 cosmic rays

dN/dE ~ E-3.7

atmospheric neutrinos created from the decay of cosmic rays

It is predicted that neutrinos created in cosmic accelerators will have...

dN/dE ~ E-2

Atmospheric neutrinos

7

How you get an E-2 spectrum ?

● Particles experience Fermi acceleration

E=kEo

N=P k No

dN/dE ~ E -1 and = ln P / ln After derivation, = -1

dN/dE ~ E-2 Eo = Initial energy

No = Number of particles with energy E

o

P = Probability of crossing shockk = Number of times that the shock is crossed

Reference frame....

of the shock

of the downstream material

of the upstream material

v2=(1/4)v

1v

1= |U|

(3/ 4) U

(3/ 4) U

The particle gains the same amount of energy every time it crosses the shock, regardless of which direction it is crossing.

8 Reference: Longair (1994)

Why study neutrinos instead of cosmic rays?

Neutrinos carry directional information. Cosmic rays have electric charge and are thus deflected by magnetic fields.

Neutrinos interact with matter via charged current scattering. This creates a lepton which triggers the detector.

l + N l _ + X l + N l + + X 9

Outline






10

AMANDA-II

AMANDA-II is a collection of 677 optical modules (“OMs”) buried in the ice at the South Pole

the 60 cm diameter holes were drilled with hot water and the OMs were lowered in before the ice refroze

19 strings each contain about 36 OMs

each OM contains a photomultiplier tube inside a pressure resistant glass sphere

all of the OMs on a string are connected to a main cable which transmits the information from the light pulses to the electronics at the surface

11

Amundsen-Scott South Pole Station

South PoleDome

Summer camp

AMANDA

road to work

1500 m

2000 m

[not to scale]

Where are we ?

12

What do OMs do?

The OMs contain the photomultiplier tubes which detect the Cherenkov light emitted by particles that pass through the ice.

Muon track Electron cascade

Particles emit Cherenkov light when they travel faster than the speed of light in that medium.

{~15 m

13

Which way is up?“Up-going”

(from Northern sky)“Down-going”(from Southern sky)

The PMT is pointing down (away from the South Pole surface)

Zenith angle = 0o Zenith angle = 180o

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“Down-going”(from Southern sky)

“Up-going”(from Northern sky)

Outline






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Background events

The goal is to detect extraterrestrial neutrinos. What background will be seen by the detector?

1) muons or muon bundles created when cosmic rays interact with the atmosphere

Downgoing muons need at least 2 MeV / cm * 1500 m = 300 GeV to make it through the ice to the detector. Muons created on the other side of the Earth lose all of their energy before making it to the detector.

2) neutrinos created when cosmic rays interact with the atmosphere

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“Signal”

Rate of Events

The trigger rate for AMANDA-II is about 80 Hz. These are predominately downgoing cosmic ray muons.

In 2000, the detector was triggered every time at least 24 OMs were hit within a 2.5 s interval. Once the detector is triggered, all hits from a 32 s interval are read out.

There is a chance that two particles went through the detector at the same time.

This leads to another type of background that we simulate in the detector – coincident muons.

17

Coincident Muons

Coincident muons refer to the situation where two or more muons or muon bundles from different cosmic ray showers interact with the ice and hit the detector within the same trigger window.

How two downgoing muons can be reconstructed as an upgoing eventblue hits occur just prior to the purple hits, but all within a 32 s window of the trigger 18Orange = reconstructed track

Viewing the Events

Data event from the cascade analysis

Energy ~175 TeV

Energy ~10 TeV

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Muon Neutrino event

Outline






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21

Diffuse Muon Neutrino Fluxes

Test Spectrum

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1) Nellen et al: pp interactions in the core of AGNs2) Stecker & Salamon: p- interactions in the core of AGNs3) Mannheim et al: p- interactions in extragalactic photoproduction sources4) Mannheim: p- interactions in blazar jets5) Rachen & Biermann: p- interactions in radio galaxies6) Mannheim: pp interactions in host galaxies of blazar jets7) Waman & Bahcall: gamma-ray bursts8) Sigl et al and Birkel & Sarkar: topological defects

Reference: Learned and Mannheim

General premise of the Diffuse Analysis

1) Remove the muon background. Make cuts on the data based on the fact that a lot of the data looks like downgoing muon background or coincident muons.

2) The remaining data is assumed to be a combination of atmospheric neutrinos or signal neutrinos. Separate the atmospheric and signal Monte Carlo with an energy cut optimized with the Model Rejection Potential.

3) Apply all of the cuts to the data to get the final number of events.

4) Compute a limit based on the number of observed events, number of predicted background events, and number of predicted signal events.

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Initial zenith cut

1) First, an 80o zenith angle cut was applied to the data set to quickly eliminate downgoing muons2) Many misreconstructed downgoing muons survived this zenith cut3) Four cuts were then chosen as good ways to separate these misreconstructed downgoing muons from neutrinos that have traveled all the way through the Earth

Number of Events Surviving this Cut (197 / 2 = 98.5 days)Downgoing Muon MC Coincident Muon MC Atmospheric Neutrino MC Signal MC Data

44550 2655 1955 323 245857

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South Pole

Events cut out

80o

The Four Quality Cuts

These four cuts were moved from very “loose” levels (passing most events) to very “tight” levels (letting very few events through)

The cut level established for the analysis was the level at which all of the misreconstructed downgoing muon background Monte Carlo had just been entirely removed by the cuts

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Num

ber

of e

vent

s

Parameter X

Each red line is a possible cut level Cut Parameters chosen:track lengthnumber of direct hitslikelihood ratio (up to down)smoothness of hits along the track

Cut Parameters

By recording hit time and amplitude, many parameters can be constructed which allow you study the data. Some of the most useful parameters are:

number of optical modules hit: usually referred to as nchannel or nch

smoothness: how smooth the hits are along the track

track length: length of the reconstructed particle path

number of direct hits: number of hits that are very close to an optical module

zenith angle: angle of the reconstructed track

jkchi: -log(likelihood L)

[jkchi(down)-jkchi(up) = likelihood ratio = log (L up

/ L down

)]25

Viewing the Events

Data event from the cascade analysis

Energy ~175 TeV

Energy ~10 TeV

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Muon Neutrino event

Cuts Applied:track lengthsmoothnessnumber of directs hitsNot Applied:likelihood ratio

Cut Keep

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Atms MCSignal MC

A portion of the remaining data events (circled in yellow) are simulated only by coincident muons (not by atmospheric or signal neutrinos).

cuts applied in these plots:track length

likelihood ratio of going up to downsmoothness of hits along the track

number of direct hits along the track

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Conclusion Drawn:Must find a coincidentmuon cut and reoptimize the cuts

MC

MuonMC

Signal MC

A large fraction of the signal Monte Carlo is also removed by this cut, but further investigation showed that this did not have a large effect on the limit setting ability of the analysis.

Consider a coincident muon cut on the reduced upgoing likelihood

cutkeep

keepkeep

keep cut

cut cut

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Coincident muon MC

Signal MCMC

Cuts Applied:likelihood ratiotrack lengthnumber of directs hitssmoothnessNot Applied:reduced upgoing likelihood

Keep

Cut

Reduced upgoing likelihood30

Atms MCSignal MCCoincident muon MC

Atmospheric neutrino MCSignal MC

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We know that atmospheric neutrinos and signal neutrinos have different energy spectrum. Thus it makes sense to look for a parameter that scales like the energy and use it to make an “energy” cut.

log10

[True Energy in GeV]

of the Monte Carlo

Number of Optical Modules hit32

True Energy ~ 103.6 GeVTrue Energy ~ 105 GeV

Key Point: Events with higher energy reconstruct with higher numbers of optical modules hit.

Number of Optical Modules Hit

Distribution of “ number of OMs hit ” before the energy cut is applied

The slope of the atmospheric neutrino Monte Carlo drops off before the signal Monte Carlo.

Need to find a cut to best separate the atmospheric and signal Monte Carlo.

= number of OMs hit33

Note that the data and atmospheric neutrino MC agree reasonably well

Atms MCSignal MCAtms MCSignal MC

# data events = 154# atmospheric events = 180.5# signal events = 39.9

The Model Rejection Potential is a way of quantifying the limit setting potential of an experiment.

If NO signal is observed, THEN an upper limit can be set for the highest possible flux that the events could have had.

(E, ) 90% confidence interval

= (E, )theoretical

The value of 90

is determined by Feldman – Cousins statistics.

This value CAN NOT be defined until the cuts have been set and a number of data events in the final sample has been determined. To optimize the cuts that determine the final sample, work with the average upper limit,

90, instead.

Model Rejection Potential

90(n

obs,n

b)

ns

Observed events

Predicted backgroundevents

Predicted signalevents

34Reference: Feldman-Cousins (1998) and Hill and Rawlins (2002)

How to calculate the Average Upper Limit

To optimize the cuts without looking at the data, use the average upper limit

90

Assume that there is no signal ns = 0

Find the expected number of background events, nb

Find the upper limit for each possible value of observed events

Add up all of the upper limits and weight them by their Poisson probability

By looking only at Monte Carlo files, you can define the Model Rejection Factor = MRF =

90 / n

signal . The best limit for the analysis can be set when

the MRF is at a minimum.

average upper limit, 90

35Reference: Hill and Rawlins (2002)

Model rejection factor plot

Model Rejection Factor

90

ns

Choose Nch (number of OMs registering hits) cut where the Model Rejection Factor is a minimum

= number of OMs hit

36

Final Energy Cut on the Number of OMs Hit (Nch) Parameter

According to the Model Rejection Potential, the energy cut should be placed at nch > 80.

cut keep

First, count... 1) number of data events2) number of signal MC events3) number of background MC events Then, set a limit using the Feldman-Cousins method.

37

Atms MCSignal MC

= number of OMs hit

Diffuse 2000 Results...10 data events in 197-day sample (“1 year”)

with normalization, expected number of events for 197 days:

atmospheric 's = 9.4 events

signal 's = 25.0 events

The Feldman-Cousins signal event upper limit for 10 observed events on a background of 9.4 events is

90%

= 7.5

Thus, the neutrino flux limit is:

E290%

= E2 * * 90%

/ nsignal

= 10-6 * 7.5 / 25

E2 limit = 3 * 10-7 GeV / cm2 *s *sr

38

Initially used a test spectrum of E2 = 10 - 6 GeV/ cm2 * s * sr

{

Reference: Feldman-Cousins (1998) and Hill and Rawlins (2002)

104.0 GeV = 10 TeV 106.25 GeV = 1.8 PeV

log10

(true energy)

True Energy Spectrum of the Monte Carlo

39

40

AMANDA-II Limit 1yr (this work)

Test Spectrum

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Outline






41

Diffuse 2000-2003 Status

• My collaborators at DESY-Zeuthen in Germany processed the data and neutrino simulation files for the 4-year data set

• I am generating downgoing muon Monte Carlo and coincident muon Monte Carlo for each of these years

• I am replicating their processing chain by using the Datahandler software that they provided for me

42

I will look at 100 % of the data set AFTER all of the cuts have been developed on the Monte Carlo and I am approved for unblinding.

Diffuse 2000-2003 Status

4-year Monte Carlo sample

The neutrino files are prepared and normalized, as are a limited number of coincident muon files. Downgoing muon files are in processing and coincident muon generation continues.

This is the nch plot before any of the quality cuts have been applied

43


= number of OMs hit

Preliminary look at cuts

4-year Monte Carlo sample

cuts made on:likelihood ratio (up to down)

track lengthnumber of direct hits

smoothnessreduced upgoing likelihood

* The cuts applied correspond to the cut levels for the 2000 analysis. The cuts for the 4-year analysis are not yet optimized.

Nch plot with preliminary quality cuts applied

44


= number of OMs hit

Optimizing the nch cut with the Model Rejection Potential

IF THE CUTS stay exactly the same as they were for the single year (2000) analysis, then

1) the best nch cut will be at 124

(it was 80 for the single year analysis)

2) Model Rejection Factor = 0.0848

expected upper limit = 0.0848 * 10-6

= 8.5 * 10-8

for 807 days

(“four years”)

45

Optimizing the nch cut with the Model Rejection Potential

Cuts will be determined after coincident muons are ready.

It is expected that any coincident muons that survive the quality cuts will be removed by the much tighter final energy (nch) cut.

Note the nch cut is expected to move from nch = 80 for the single year analysis to nch = 124 for the 4-year analysis.

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IceCube 3yrs

AMANDA-II Limit: 1yr

Test Spectrum

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Predicted AMANDA-II Limit: 4 yr




References

Cooley-Sekula, Jodi, dissertation, 2003.Desiati, Paolo, presentation for ECRS Firenze, 2004.Feldman, Gary and Robert Cousins, Unified approach to the classical statistical analysis of small signals, 1998.Halzen, Francis, Summer School proceedings, 2004. Hill, Gary, Experimental and Theoretical Aspects of High Energy Neutrino Astrophysics, September 1996.Hill, Gary and Katherine Rawlins, Unbiased cut selection for optimal upper limits in neutrino detectors: the

model rejection potential technique, 2002.Hill, Gary, Matthias Leuthold, Jodi Cooley for the AMANDA collaboration, Search for Diffuse Fluxes of

Extraterrestrial Muon-Neutrinos with the AMANDA Detectors.Kowalski, Marek, dissertation.Longair, Malcolm, High Energy Astrophysics, 1994.Woschnagg, Kurt, presentation for Neutrino 2004.Plot from http://www.physics.adelaide.edu.au/astrophysics/cr_new.html

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http://www.physics.adelaide.edu.au/astrophysics/cr_new.html

searching for a diffuse flux of neutrinos with amanda-ii jessica hodges november 5, 2004 prelim exam

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atmospheric neutrinos

cosmic raysdnde

diffuse flux of neutrinos

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data setfuture work

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