1. 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

2. 12/14/09 Note: While questions are encouraged, due to time constraints I would prefer if questions were held to the end. 22

3. 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

4. 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

5. 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.

6. 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

7. 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

8. 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.

9. 12/14/0999

10. 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

11. 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. 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

13. 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

14. 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.

15. 12/14/09 Data Processing Cycle HiRes reconstructionCorrect tube times based on stereo planesIterative line fit to filter bad tubesBootstrap error estimationCuts 1515

16. 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

17. 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 1717

18. 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.

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20. 12/14/09CALOR 2006 Chicago 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

21. 12/14/09 Correcting Time and Finding Distance Along Shower Axis 2121 Shower 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: 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.

22. 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.

23. 12/14/09 Bootstrap Error Estimation Count “good” tubesCreate new empty showerRandomly select tubes for new showerRerun speed determination processRestore original shower 2323 Application of the bootstrap statistical method to the tau-decay-mode problem Brad Efron, Physical Review D 39, 274-279.

24. 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

25. 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

26. 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

27. 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.

28. 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

29. 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.

30. 12/14/09 All Cuts HR1 adjusted “good” tubes > 3 3030

31. 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

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33. 12/14/09 Events Removed By Cuts 3333 * Errors calculated using bootstrap method

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35. 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

36. 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

37. 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

38. 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 Anomalo us Events Explaine d 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

39. 12/14/09 Indeterminate Shape 3939

40. 12/14/09 All 11 flagged events were explained through one of the methods detailed in my Dissertation 4040

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42. 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. 4242

43. 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 ProtonIron 4343

44. 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 ProtonIron 4444

45. 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

46. 12/14/09 Flux Poisson statistics: 0 observed events (k=0), can calculate expected events (λ) for different probabilities (f(k; λ))‏ 4646

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48. 12/14/09 Conclusion No candidate anomalous events found Apertures and upper limit to flux calculated Paper in process pending reviews by collaboration 4848

49. 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 ProtonIron 4949

50. 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

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53. 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 estimate d 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 reconstruct ed 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

54. 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

55. 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 Angle Scatter 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

56. 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

57. 12/14/09 Zenith and θ 5757

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60. 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

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63. 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

64. 12/14/09 Summary of explanations for 11 outliers 6464

65. 12/14/09 Events Explained by Plane Rotation 6565

66. 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

67. 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 Fits Event 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

68. 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

69. 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

70. 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:microwave background This resonance should provide an effective cutoff to the cosmic ray spectrum at around 6x1019eV. HiRes has observed the GZK cutoff

71. 12/14/09 High Resolution Detector Location 7171 The HiRes site is located 60 miles from Salt Lake City on the Dugway Proving Grounds. The individual detectors are separated 12.6 km at Five Mile Hill and Camel Back Mountain.

72. 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.

73. 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.

74. 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.

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77. 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

78. 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

79. 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

80. 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

81. 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

82. 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

83. 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

84. 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

85. 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 Rotation Two 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 generalize d rotation matrix. To perform this rotation efficiently, a method using homogene ous coordinate s frequently used computer graphics was applied. 8585

86. 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

87. 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

88. 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

89. 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 bin Signal 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.

90. 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 TvTv b a

91. 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

92. 12/14/099292