click to edit master subtitle style 12/14/09 search for exotic particles in the high resolution...
Post on 28-Dec-2015
215 Views
Preview:
TRANSCRIPT
Click to edit Master subtitle style
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
12/14/09
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
12/14/09
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
44
12/14/09
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.
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
12/14/09
Cosmic Ray
Spectrum • Cosmic Rays
have been reported from ~109 eV to ~1020+ eV
• Need very large detectors at high energies
66
12/14/09
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
12/14/09
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.
12/14/09 99
12/14/09
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
12/14/09
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.
12/14/09
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
12/14/09
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
12/14/09
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.
12/14/09
Data Processing Cycle
HiRes reconstructionCorrect tube times based on stereo planesIterative line fit to filter bad tubes Bootstrap error estimationCuts
1515
12/14/09
HiRes Reconstruction
• HiRes reconstruction is used to determine shower geometry.
• Use stereo reconstruction.
• No timing information is used.
• No shower profile or particle energy.
1616
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
12/14/09
Shower Geometry
Also determined with shower axis are:
• - perpendicular vector between detector and shower axis
• Zenith and Azimuth angles
• Shower impact location
pRPPPPPPPPPPPPPP
1717
12/14/09
Shower Geometry
1818
• 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.
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
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
12/14/09
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.
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
12/14/09
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.
12/14/09
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.
12/14/09
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.
2424
12/14/09
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.
2525
12/14/09
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.
2626
12/14/09
“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.
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
• Ninth Outline LevelClick to edit Master text styles
– Second level
• Third level
– Fourth level
» Fifth level
12/14/09
Example Cut:Opening Angle
2828
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
• Ninth Outline LevelClick to edit Master text styles
– Second level
• Third level
– Fourth level
» Fifth level
12/14/09
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.
12/14/09
All Cuts
•HR1 adjusted “good” tubes > 3
3030
12/14/09
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
3131
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Uncut DistributionsHiRes 1 HiRes 2
3232
Downward Speed of Light
UpwardSpeed of Light
NoiseZero Speed
Downward Speed of Light
NoiseZero Speed Upward
Speed of Light
12/14/09
Events Removed By Cuts
3333* Errors calculated using bootstrap method
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Cut Distributions
HiRes 1 HiRes 2
3434
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Cut Distributions
HiRes 1HiRes 2
3535
12/14/09
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.
3636
12/14/09
Post Processing Checks
• Multiple different speed fits
• Examination of FADC traces
• Examination of linear fits
• Plane fit comparisons
• Stereo plane intersection review
• Plane rotation
3737
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
12/14/09
Most Anomal
ous Events
Explained
Through Plane
Rotation
Example event: April 6th, 2003
HiRes 1 Before: -0.231 m/ns
HiRes 2 Before: -0.237 m/ns
HiRes 1 After: -0.302 m/ns
HiRes 2 After: -0.296 m/ns
3838
12/14/09
Indeterminate Shape
3939
12/14/09
All 11 flagged events were explained through one of the methods detailed in
my Dissertation
4040
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Results
HiRes 1 HiRes 2
4141
12/14/09
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
4242
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Apertures
Proton Iron
4343
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Apertures
Proton Iron
4444
12/14/09
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
4545
12/14/09
Flux
Poisson statistics:
0 observed events (k=0), can calculate expected events (λ) for different probabilities (f(k; λ))
( ; )!
k
f kke
4646
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Flux – Upper Limit
Proton Iron ,uli
NJ
t A s E
4747
12/14/09
Conclusion
• No candidate anomalous events found
• Apertures and upper limit to flux calculated
• Paper in process pending reviews by collaboration
4848
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
My Seven Beautiful Lines
Proton Iron ,uli
NJ
t A s E
4949
12/14/09
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
5050
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
• Ninth Outline LevelClick to edit Master text styles
– Second level
• Third level
– Fourth level
» Fifth level
12/14/09
Speed Distributions: Thrown Geometry (MC)
HiRes 1 HiRes 2
5151
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Speed Distributions: Reconstructed Geometry
(MC)HiRes 1HiRes 2
5252
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
12/14/09
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.
5353
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Cut: Error estimated via bootstrap method
HiRes 1HiRes 2
5454
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
12/14/09
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
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Cut on Opening Angle
HiRes 1HiRes 2
5656
12/14/09
Zenith and θ
5757
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Zenith Angle
HiRes 1HiRes 2
5858
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
θ
HiRes 1HiRes 2
5959
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
12/14/09
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.
6060
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Normalized Difference Cut
HiRes 1HiRes 2
6161
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Rp cut
HiRes 1HiRes 2
6262
12/14/09
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
6363
12/14/09
Summary of explanations for 11 outliers
6464
12/14/09
Events Explained by Plane Rotation
6565
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
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.
6666
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
12/14/09
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.
6767
12/14/09
• Final event was removed because of location. It had an opening angle that was borderline for the cut and failed plane rotation.
6868
12/14/09
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
12/14/09
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.
12/14/09
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.
12/14/09
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.
12/14/09
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.
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Overlaid Distributions
HiRes 1HiRes 2
7575
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Resulting Distribution: HiRes 1 (MC)
Before CutsAfter Cuts
7676
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
Resulting Distribution: HiRes 2 (MC)
Before CutsAfter Cuts
7777
12/14/09
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.
7878
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level
12/14/09
April 6th, 2003
7979
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
• Ninth Outline LevelClick to edit Master text styles
– Second level
• Third level
– Fourth level
» Fifth level
12/14/09
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.
8080
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
• Ninth Outline LevelClick to edit Master text styles
– Second level
• Third level
– Fourth level
» Fifth level
12/14/09
FADC traces
8181
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
• Ninth Outline LevelClick to edit Master text styles
– Second level
• Third level
– Fourth level
» Fifth level
12/14/09
Line Fits
8282
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
• Ninth Outline LevelClick to edit Master text styles
– Second level
• Third level
– Fourth level
» Fifth level
12/14/09
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.
8383
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
• Ninth Outline LevelClick to edit Master text styles
– Second level
• Third level
– Fourth level
» Fifth level
12/14/09
Event Profile – Stereo Planes
8484
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
12/14/09
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
8585
12/14/09
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
8686
Click to edit the outline text format
Second Outline Level
Third Outline Level
Fourth Outline Level
Fifth Outline Level
Sixth Outline Level
Seventh Outline Level
Eighth Outline Level
Ninth Outline LevelClick to edit Master text styles
12/14/09
Before and
After for April 6th, 2009 event
HiRes 1 Before: -0.231 m/ns
HiRes 2 Before: -0.237 m/ns
HiRes 1 After: -0.302 m/ns
HiRes 2 After: -0.296 m/ns
8787
12/14/09
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.
8888
12/14/09
Correcting Tube Times
8989
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.
12/14/09
Correcting Time and Finding Distance Along
Shower Axis
9090
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
12/14/09
Iterative Fit
Speed Fit Compare Each point to MeanRemove tubes greater than 5 RMS from MeanRMS and Mean of distance from fit
9191
12/14/09 9292
max2 2 2
0 0 0 0
, ( , , , ) ( , ) sinpR
i i iA s E dAd s E s E d rdr d d
top related