Click to edit Master subtitle style 12/14/09 Search for Exotic Particles in the High Resolution Fly’s Eye (HiRes) Data Set S. Adam Blake 11

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12/14/09

Search for Exotic Particles in the High Resolution

Fly’s Eye (HiRes) Data SetS. Adam Blake

11

12/14/09

Note: While questions are encouraged, due to time

constraints I would prefer if questions were held to the

end.

22

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Outline

• Introduction to cosmic rays

• Overview of the HiRes experiment

• Motivation

• Method and data selection

• HiRes data set results

• Aperture and flux limit

• Conclusion 33

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Cosmic Rays

• Cosmic Rays are nucleons, radiation, or particles that strike the Earth from outside of our atmosphere

• 1912: First experimental evidence that cosmic rays came from outside our atmosphere provided by Victor F. Hess by balloon measurements

• 1938: Air showers discovered by Pierre Auger

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Particle Physics Originates with Cosmic Rays

55

• 1932 – Positron, discovered in cloud chamber• 1937 – Muon, discovered in cloud chamber• 1947 – Pion, discovered in photographic emulsions• 1947 – Σ, discovered in cloud chamber• 1947 – Kaon, discovered in cloud chamber• 1953 – Λ, discovered in cloud chamber • 1952 – Ξ, discovered in cloud chamber• 1964 – Ω- , discovered in cloud chamber

• A rich history of being used to discover new particles.

• Initially provided much higher energies than available from ground based accelerators.

A few discoveries:

Today, the HiRes data is orders of magnitude higher energy than found in accelerators.

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Cosmic Ray

Spectrum • Cosmic Rays

have been reported from ~109 eV to ~1020+ eV

• Need very large detectors at high energies

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High Resolution Fly’s Eye Detector (HiRes)

7

Each HiRes telescope consists of:

• Spherical mirror with 3.72m2 unobstructed collection area

• 16 x 16 array (hexagonally close-packed) of PMT pixels each viewing 1° cone of sky

Shower Interactions:• Inelastic collision between

primary and atmosphere produces hadronic core (Pions, K, protons, neutrons).

• Neutral Pions decay into photons.

• Photons pair produce• Electrons and Positrons

produce Bremsstrahlung radiation

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HiRes Stereo Detector

88

Fluorescence allows for much larger detectors. HiRes views an area of about 5000km^2.

Illustration of a Stereo event as seen by HiRes 1 and HiRes 2.

•Both sites consist of mirrors focusing fluorescence light on phototubes – called telescopes •Because there are two sites, you get “stereo” vision – i.e., you can determine things like shower geometry with relative ease.

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Florescence Technique

1010

• A ring of mirrors focuses UV light onto cameras

• Each camera has 256 phototubes

• Phototube signals are amplified and then used to reconstruct the shower

Event displays depicting an event seen by HiRes 1 and HiRes 2

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Analysis Topic:Search for Anomalous

Showers

1111

Why?

•Test current models•Check understanding of our own data•Quality control check for our reconstruction•Look for new physics HiRes has the largest stereo data set in the world at the extreme end of the energy spectrum. The energy of particles in question falls several orders of magnitude higher than the highest achieved by Earth based accelerators. This makes the data set an excellent place to look for more exotic physical phenomena.

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Acceleration:How Do Particles Get Their

Energy?

1212

Top Down•Anomalous physics or heavy particle decay

• Superstring decay• Strangelets• Relic Monopoles

• Fermi Acceleration

• AGN• Pulsars• Super Novae

Bottom Up

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Strangelets:Exotic Particles

1313

Massive Particles

•Conventional matter begins to become unstable around Iron (A~=50). This effectively limits the mass of conventional cosmic ray primaries.

•Conventional matter is made from up and down quarks.Possible Exotic Matter:

•Make matter up of equal parts strange, up, and down quarks.

•Simple models suggest that this type of “strange” matter could be stable into the A=1057 with significant fractions possible above the A=107 range.Ϯ

Ϯ - J. Phys. G: Nucl. Part. Phys. 31 (2005) S833–S839, Madsen

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Strangelets:Shower Speed < c

1414

A massive strangelet going through the atmosphere at a slow speed might undergo spallation. To a fluorescence detector, the result would look similar to a normal shower only at much lower speed.

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Data Processing Cycle

HiRes reconstructionCorrect tube times based on stereo planesIterative line fit to filter bad tubes Bootstrap error estimationCuts

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HiRes Reconstruction

• HiRes reconstruction is used to determine shower geometry.

• Use stereo reconstruction.

• No timing information is used.

• No shower profile or particle energy.

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Shower Geometry

Also determined with shower axis are:

• - perpendicular vector between detector and shower axis

• Zenith and Azimuth angles

• Shower impact location

pRPPPPPPPPPPPPPP

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Shower Geometry

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• Each site has a plane fit through the tubes (shown for HiRes 2 on a MC event).

• Once plane fits are determined the intersection of those two planes defines the shower axis.



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Example Event

12/14/09 CALOR 2006Chicago 6/6/06

2020

Measured Shower Profile

Event by event:

Xmax in g/cm2 Total energy of the primary

particle Arrival direction

Statistically:

Composition p-air inelastic cross-section

Measured shower parameters.g/cm2 g/cm2

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Correcting Time and Finding Distance Along

Shower Axis

2121Show

er Axis

Uv

Rp

Mv

Tv

b

a

• b is the slant depth (or distance along shower axis measured from Rp)

• The time is calculated from the following formula:𝑡𝑐 = 𝑡𝑡 − 𝑎𝑐

Because this formula relies on the tube time given in data, the reconstruction cannot use timing information to improve plane fits or to find the shower axis.



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Iterative Line Fit

2222

• Once time and distance are known these can be represented by points.

• A standard weighted χ2 fit can be used to determine the slope for a line.

• Points are weighted by the number of reconstructed photoelectrons each tube receives.

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Bootstrap Error Estimation

Count “good” tubesCreate new empty showerRandomly select tubes for new showerRerun speed determination processRestore original shower

2323Application of the bootstrap statistical method to the tau-decay-mode problem Brad Efron, Physical Review D 39, 274-279.

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Data Selection

The purpose of this search is to look for a few exotic events in a very large data set. There are factors that can cause events in the data set to be reconstructed incorrectly.

Examples:

– Airplane triggers

– Full mirror triggers

– Difficult to fit geometries

These could give “false positives” in the search. This requires a set of data selection criteria (cuts) be established to minimize possible problems with the data set.

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Cuts

Several points considered while determining cuts:

• Want the largest possible data set while still minimizing any possible source of error.

• Cuts can add bias to results. Must be chosen carefully to avoid or minimize bias.

• Cuts should not be “tuned” to give desired results from data.

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Methodology for Selecting Cuts

• To avoid “tuning” cuts to real data, most cuts were determined entirely using Monte Carlo showers (generated at c and other speeds).

• A large number of possible cuts were studied. Only a few of these were chosen.

• Subtle but important considerations: Different cuts can reject the same event.

Some cuts are better at rejecting only problematic events than others.

This makes the order cuts are applied very important when setting actual values! It is not enough to consider each cut individually. Cut values are tested in order. One is applied, then others are adjusted to minimize data loss.

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“Small” list of some of the variables examined for cuts.

2727

The final iteration of cuts included about 65 different cuts. This table lists only those checked for order effects. For a legible version and more detailed explanations of individual cuts, see chapter VIII of my disertation.



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Example Cut:Opening Angle

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Example Cut:Normalized Difference

•This is the ratio of the difference in speeds to the combined error in the speeds calculated using the bootstrap method.

• The errors are correlated, so the covariant part of the correlation must be accounted for.

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All Cuts

•HR1 adjusted “good” tubes > 3

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HiRes Stereo Data Set

• Work included calibrated data taken from December of 1999 to November of 2005

• ~50,000 events had the correct information to do speed reconstruction

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Uncut DistributionsHiRes 1 HiRes 2

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Downward Speed of Light

UpwardSpeed of Light

NoiseZero Speed

Downward Speed of Light

NoiseZero Speed Upward

Speed of Light

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Events Removed By Cuts

3333* Errors calculated using bootstrap method



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Cut Distributions

HiRes 1 HiRes 2

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Cut Distributions

HiRes 1HiRes 2

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Processing Results

Processing resulted in 11 events that reported speeds differing from the speed of light by more than 3 RMS. These were each examined individually in a series of post processing calculations.

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Post Processing Checks

• Multiple different speed fits

• Examination of FADC traces

• Examination of linear fits

• Plane fit comparisons

• Stereo plane intersection review

• Plane rotation

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Most Anomal

ous Events

Explained

Through Plane

Rotation

Example event: April 6th, 2003

HiRes 1 Before: -0.231 m/ns


HiRes 1 After: -0.302 m/ns


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Indeterminate Shape

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All 11 flagged events were explained through one of the methods detailed in

my Dissertation

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Results

HiRes 1 HiRes 2

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Monte Carlo Integration:• Rejection Method

Start with a known area Throw events into that area Simulate detector Run reconstruction Calculate ratio of accepted to thrown Multiply by known aperture

• ~1.7M events generated at different speeds and energies.

Aperture

Measurement of the acceptance of the detector in relation to the area it views.

2 2max, ( , ) 2i i pA s E s E R

( , )( , )

( , )reconstructed i

ithrown i

N s Es E

N s E

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Apertures

Proton Iron

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Apertures

Proton Iron

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Flux Limit

• This is an upper limit calculation only

• Must be interpreted within the assumptions used in this study

Key Assumption: Particles react with the atmosphere in a manner that would allow detection by HiRes and have showers with a measurable speed difference

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Flux

Poisson statistics:

0 observed events (k=0), can calculate expected events (λ) for different probabilities (f(k; λ))

( ; )!

k

f kke

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Flux – Upper Limit

Proton Iron ,uli

NJ

t A s E

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Conclusion

• No candidate anomalous events found

• Apertures and upper limit to flux calculated

• Paper in process pending reviews by collaboration

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My Seven Beautiful Lines

Proton Iron ,uli

NJ

t A s E

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Monte Carlo Data Set

• ~50,000 events thrown at the speed of light (0.299 m/ns)

• Compared both “thrown” (or Monte Carlo generated) geometry and reconstructed geometry

• The same tools used to determine cuts were used on the actual data for analysis

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Speed Distributions: Thrown Geometry (MC)

HiRes 1 HiRes 2

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Speed Distributions: Reconstructed Geometry

(MC)HiRes 1HiRes 2

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Cut: Error

estimated via

bootstrap

method

Motivation: events that are difficult to fit are more likely to fit incorrectly

HiRes plots. Top plot shows a scatter plot of speed (slope_hr1) vs. error estimated via bootstrap method (sigma_hr1). Bottom plot shows a lego version of the same plot.

• As estimated error increases, the accuracy with which speed can be reconstructed decreases.

• Cut is shown with black line. Most events are before cut.

• Data is “all inclusive” – the structure that appears above the main portion of data in each case are events that did not reconstruct correctly.

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Cut: Error estimated via bootstrap method

HiRes 1HiRes 2

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Cut on Opening

AngleScatter plots showing speed vs. opening angle for HiRes 1 and HiRes 2.

• Motivation: For stereo observation, events that fall near the line connecting the two detectors are very difficult to reconstruct. The shower detector planes become parallel and the intersection poorly undefined.

• Lines show cut used

5555



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Cut on Opening Angle

HiRes 1HiRes 2

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Zenith and θ

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Zenith Angle

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θ

HiRes 1HiRes 2

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Normalized Difference Cut

• This is the ratio of the difference in speeds to the combined error in the speeds calculated using the bootstrap method.

• The errors are correlated, so the covariant part of the correlation must be accounted for.

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Normalized Difference Cut

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Rp cut

HiRes 1HiRes 2

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Combined Cuts

• Events that do not reconstruct correctly often fail more than one of the cuts.

• Start with cuts that remove events slowly but improve RMS of distribution quickly.

• After reviewing plots from above, opening angle removes data faster than estimated error.

• Estimated error was used as first cut, followed by opening angle, zenith, and θ

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Summary of explanations for 11 outliers

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Events Explained by Plane Rotation

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Poor initial Plane Fits

Event Removed by Eye Cut for poor plane fit. Rotated plane is shown for HiRes 2. This resulted in speeds of 0.291 m/ns for HiRes 1 and 0.300 m/ns for HiRes 2.

Event Removed by Eye Cut for poor plane fit. Event failed plane rotation due to location between detectors.

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Poor initial Plane FitsEvent

Removed by Eye Cut for poor plane fit. Rotated plane is shown for HiRes 2. This resulted in speeds of 0.284 m/ns for HiRes 1 and 0.293 m/ns for HiRes 2.

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• Final event was removed because of location. It had an opening angle that was borderline for the cut and failed plane rotation.

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Flux

6969

• A power law Eα with α~ -3

• Changes at “knee” & “ankle”

•

• Changes represent physics- could relate to changes in the source or propagation to us

• Expected cutoff at 6x1019 eV (GZK cutoff)

• HiRes designed for stereo measurement of cosmic rays with E > 3x1018 eV

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GZK Cutoff

7070

• GZK (Greisen – Zatsepin - Kuzmin) cutoff describes a predicted “end” to the cosmic ray spectrum due to interaction with the microwave background:𝑝+ 𝛾𝑐𝑚𝑏 →∆→𝑛(𝑝) + 𝜋+(𝜋0)

• This resonance should provide an effective cutoff to the cosmic ray spectrum at around 6x1019eV.

HiRes has observed the GZK cutoff

12/14/09

High Resolution Detector Location

7171

The HiRes site is located 60 miles fromSalt Lake City on the Dugway Proving Grounds.

The individual detectors are separated12.6 km at Five Mile Hill and Camel Back Mountain.

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Stereo Event

7272

Illustration of a Stereo event as seen by HiRes 1 and HiRes 2.

•The pattern of phototubes with a signal determines a shower detection plane. •The intersection of the two planes gives the axis of the shower.

Stereo events allow for geometry to be calculated without use of timing information.** The importance of this statement for this project will be covered later.

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Feasibility

7373

Time based reconstruction assumes the speed of light.

Of the 4 types of detectors commonly used at this energy, only stereo fluorescence does not use timing information to determine the geometry.

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Other Exotics:Tachyons

7474

It is also possible to observe showers that move faster than the speed of light. One such shower was reported in 1973 by Phillip Crough and Roger Cray.* This result has never been reproduced.

* Nature 248, 28 - 30 (01 March 1974); doi:10.1038/248028a0

When the Tachyon reacts, an observer would not see the particle itself but a form of double shock waves moving “backwards” from when the particle interacted. To a cosmic ray detector, this would appear as a shower moving faster than the speed of light.



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Overlaid Distributions

HiRes 1HiRes 2

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Resulting Distribution: HiRes 1 (MC)

Before CutsAfter Cuts

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Resulting Distribution: HiRes 2 (MC)

Before CutsAfter Cuts

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In Depth Event

• The decision to focus on this event first resulted from:

– Good track in both mirrors

– Both Hr1 and Hr2 speeds match very closely

– Reconstructed Energy was available for this event from HiRes 2 Mono

– Speed was > 7 sigma from speed of light

• Other events received similar treatment.

• This event has no HiRes 1 mono.

• The various models used to try and explain this event have resulted in explanations for each of the 11 events.

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April 6th, 2003

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Various Speed Fits

• -0.40994

• Shower_speed is speed fit by my program

• sab_plane_fit is speed fit after refitting the plane using a plane fitter 1 wrote

• Shower_speed/Origin is speed fit by Origin based on points from shower_speed

• Hires_Soft/Mathematica is the HiRes plane fit used with Mathematica to correct tube times then fit in Origin

• Hires_Soft/Mathematica no weight is the HiRes plane fit used with mathematica to correct tube times then fit in Mathematica with no additional weighting

• No Correction, No weight is a fit performed straight on HiRes raw data with no corrections.

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FADC traces

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Line Fits

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Plane Fit Comparisons

• -0.4442• Comparison for

plane vectors done by various fitting

• Rutgers and HiRes planes use relative timing to aide in plane fitting.

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Event Profile – Stereo Planes

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Plane RotationTwo

separate plane rotations were performed on both the HiRes 1 and HiRes 2 plane. The first was a rotation around the azimuth angle. The second was a rotation of the plane around a weighted “centroid” of the event.

These rotations were performed with the result of a generalized rotation matrix. To perform this rotation efficiently, a method using homogeneous coordinates frequently used computer graphics was applied.

2 2 2

2 2 2 2 2 2 2 2 2

1 1 1

2 2 2

2 2 2 2 2

0 0

2 2 2 2

coscos 1 coscos sin sin 1 coscos sin sin

coscos1 coscos sin sin 1 c

( ) (

os cos sin si

)

n

xz xz z z xz z xz

u v w uv wl uw vl

u v w u v w u v w

v u wuv wl u

RT T R R

w ul

u v w u v w u v

R

w

R R T

2 2 2 2

2 2 2

2 2 2 2

2 2 2

2 2 2 2 2

2 2 2 2 2 2 2 2 2

( coscos ( )

coscos

coscos1 coscos sin sin 1 coscos sin sin

0 0 0

a v w u bv cw u bv cw a v w bw cv lsin

u v w

b u w v au cw v au cw b u w cu aw lsin

u v w

w u v c u vuw vl vw ul

u v w u v w u v w

2 2

2 2 2

coscos

1

w au bv w au bv c u v av bu lsin

u v w

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Rotation steps for plane defined by n by -45 degrees about the x axis. Plot a represents the plane before any transformations are applied. Plots b, and c, and d represent a translation and subsequent rotations moving the vector to the desired axis. Plot e is the actual rotation by angle theta. Plots f and g undo the movement to the axis, and Plot h undoes the translation.

Plane Rotation

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Third Outline Level


Fifth Outline Level

Sixth Outline Level




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Before and

After for April 6th, 2009 event





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Anatomy of a Shower

• Incoming particle hits upper atmosphere and “interacts” creating some combination of pions and nucleons.• Pions further interact and/or decay into an electromagnetic component and a muonic component.• Nucleons from the original interaction interact further down in the atmosphere, also creating possible combinations of pions and nucleons.• Process continues until shower hits the ground or energy of primary particle is entirely deposited in the atmosphere• 90-95% of shower energy goes into the EM component of the shower.

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Correcting Tube Times

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HiRes 1 and HiRes 2 operate on different electronics. The recorded time is dependant on those electronics and must be corrected for travel time between shower and detector.HiRes 1: Sample and Hold

HiRes 2: FADC

Plot of signal vs. time binSignal is recorded in 100 time bins. This signal can be fit and the peak used as the time for the tube firing.

Single pulse. Time is recorded as start of the pulse.

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Correcting Time and Finding Distance Along

Shower Axis

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Basic Problem:

• Find the closest point of approach for two lines in 3D space.

Shower Axis

Uv

Rp

Mv

Tv

b

a

𝑟Ԧ= 𝑚𝑣ሬሬሬሬሬԦ+ 𝑎∙𝑡𝑣ሬሬሬԦ 𝑠Ԧ= 𝑟𝑝ሬሬሬԦ+ 𝑏∙𝑢𝑣ሬሬሬሬԦ 𝑅2 = ȁ�𝑟Ԧ− 𝑠Ԧȁ�2

𝑏= 2𝐴𝐵+ 𝐵𝐶𝐶2 − 4𝐴𝐸,𝑎 = 𝐶𝑏− 𝐵2𝐴

𝐴= 𝑡𝑣ሬሬሬԦ∙𝑡𝑣ሬሬሬԦ,𝐵= 2൫𝑚𝑣ሬሬሬሬሬԦ∙𝑡𝑣ሬሬሬԦ− 𝑟𝑝ሬሬሬԦ∙𝑡𝑣ሬሬሬԦ൯,𝐶= 2൫𝑡𝑣ሬሬሬԦ∙𝑢𝑣ሬሬሬሬԦ൯,𝐷= 2൫𝑟𝑝ሬሬሬԦ∙𝑢𝑣ሬሬሬሬԦ− 𝑚𝑣ሬሬሬሬሬԦ∙𝑢𝑣ሬሬሬሬԦ൯,𝐸= 𝑢𝑣ሬሬሬሬԦ∙𝑢𝑣ሬሬሬሬԦ

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Iterative Fit

Speed Fit Compare Each point to MeanRemove tubes greater than 5 RMS from MeanRMS and Mean of distance from fit

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max2 2 2

0 0 0 0

, ( , , , ) ( , ) sinpR

i i iA s E dAd s E s E d rdr d d

Documents

Click to edit Master subtitle style 12/14/09 Search for Exotic Particles in the High Resolution Fly’s Eye (HiRes) Data Set S. Adam Blake 11