Speed Based Analysis of HiRes Data SetAdam Blake, June 9th 2008

Overview Results Quick Review Look at Some Data In Depth Look at One Anomalous

Event Conclusion

Results – June 1, 2008Stage in Process Total Remaining Events

All abnormal shower_speed events

57

Obviously bad removed* 12

Speed Difference† 11

Most Interesting 4

*By obviously bad, one of the following is true:• The plane did not fit right• The event is just noise• The event is on May 19th, 2004

† Will explain seperately

Most Interesting

HR1 Rp HR2 Rp Opening Angle

HR1 Track Length (rads)

HR2 Track Length(rads)

Shower Time HR1 Speed HR1 good

tubesHR2

SpeedHR2 good

tubes

25051.5 14780.8 0.383306 0.264101 0.505949 55633 -0.32382 26 -0.33022 65

27546.8 15869.9 0.228643 0.156995 0.399267 20499 -0.23128 6 -0.23655 43

12981.3 23750.3 0.268143 0.203096 0.323435 15843 -0.34481 12 -0.33297 26

4569.22 16567.1 0.174583 0.237581 0.304406 14347 -0.35073 32 -0.35708 37

Up to this point

Quick Review

Correcting Time and Finding Distance Along Shower Axis

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

Shower Axis

Uv

R p

Mv

T v

b

a

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

𝑏= 2𝐴𝐵+ 𝐵𝐶𝐶2 − 4𝐴𝐸,𝑎 = 𝐶𝑏− 𝐵2𝐴

Correcting Time and Finding Distance Along Shower Axis

Shower Axis

Uv

R p

Mv

T v

b

a

𝑏= 2𝐴𝐵+ 𝐵𝐶𝐶2 − 4𝐴𝐸,𝑎 = 𝐶𝑏− 𝐵2𝐴

• From this calculation, b is now 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.

Data Processing CycleHiRes Reconstruction

Correct tube times based on stereo planes

Iterative Line fit to filter bad tubes

Bootstrap error

estimation for Cut

Cuts

Statistics

Cuts

Data Processing Cuts My Cuts Both detectors must pass plane

fits Minimum PE per tube: 1.0 Minimum Tubes per event: 6 Minimum Average PE per tube

per event: 15.0 Maximum Track Length: Hr1 –

36.0°, Hr2 – 57.0° Minimum Track Length: Hr1 – 3°, Hr2 – 6° Cut if event crossing planes or

tube binning

10° > Opening Angle 170° < Opening Angle Bootstrap σ > .0012 m/ns Hr1 adjusted tubes < 3 Hr2 adjusted tubes < 6 Track Length < 8 degrees Tubes in 1 mirror > 170 Ψ > 120 Plog < 2.0 Rp < 4km from either site Speed difference to Error

difference ratio*

How Cuts Have Been Determined

Compare standard deviation calculated in standard way to percentage of data cut. Look for obvious breaks in the data.

At these points, calculate width and full width at half max of fits to binned data and look for appropriate statistical relations.

Comparison of percentage data cut and drop in standard deviation for Bootstrap estimated error of HiRes 2.

Ratio 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.

Resulting Distribution

Resulting histograms for HiRes 1 and HiRes 2

HiRes 1 HistogramDeveloped from set of 26000 Iron MC events thrown at the speed of light with energy 10E19, ~4500 of which made it through pass 4 and ~1800 made it through my cuts.

HiRes 2 HistogramDeveloped from set of 26000 Iron MC events thrown at the speed of light with energy 10E19, ~4500 of which made it through pass 4 and ~1800 made it through my cuts

Apertures

* Cuts are being reevaluated. This graph is done using current cuts but may change slightly. Proposed new cuts would increase apertures shown. Currently awaiting processing for other apertures.

Just a brief mention of what has been done with previous sets of “abnormal” events

Closer Look

Data Set Notes Starting with first processed data

runs in January, a good deal of effort has been put into looking at individual events to see why they have abnormal speeds.

Overall, the number of events that were not “well understood” has changed from several hundred to the 11 mentioned earlier.

Next slides: An example of what has been done.

July 27th, 2001Event Rp Hr1 Rp Hr2 Opening

AngleTrack Length Hr1

Track Length Hr1 m

Track Length Hr2

Track Length Hr2 m

Shower Time

Slope Hr1

Good Tubes Hr1

Slope Hr2

Good Tubes Hr2

3 14541.3 3292.82 0.49384 0.26358 4092.99 0.43654 1593.79 8150-

0.28885 31-

0.24917 72

Plane Fit Comparison

Mono Plane Fits Stereo Plane Fits

July 27th, 2001

When I try to fit this, I get a vertical plane for HiRes 2

This type of event is reason for current Rp cut. The shower goes right over the top of the detector so planes do not fit well. This throws speed off.

This event is the event I have spent the most time on to this point. Other possible candidates will receive similar treatment.

In Depth Event

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 is > 7 sigma from speed of light

Other events will receive similar treatment to this event. This event has no HiRes 1 mono. It only has 6 good

HiRes 1 tubes. That is enough to pass my cuts and stereo cuts but not mono.

The various models used to try and explain this event have resulted in explanations for almost every other abnormal event – however they have not resulted in an explanation for this event.

April 6th, 2003Event Rp Hr1 Rp Hr2 Opening

AngleTrack Length Hr1

Track Length Hr1 m

Track Length Hr2

Track Length Hr2 m

Shower Time

Slope Hr1

Good Tubes Hr1

Slope Hr2

Good Tubes Hr2

7 27546.8 15869.9 0.22864 0.15683 5115.78 0.39692 9708.08 20499-

0.23368 6-

0.23613 43

Event Profile – Stereo Planes

Various Speed Fits

Speeds: m/nsshower_speed -0.23617sab_plane_fit -0.24294shower_speed/Origin -0.23717Hires_soft/Mathematica -0.24119Hires_Soft/Mathematica No weight -0.266082No Correction, No weight -0.40994

Shower_speed is speed fit by my program

sab_plane_fit is speed fit after refitting the plane using a plane fitter I 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.

Plane Fit Comparisons

Plane Vectors Hr1_X Hr1_y Hr1_zReconstructed 0.6919 -0.5204 -0.5004

My fit 0.691894 -0.520425 -0.500441

       

  Hr2_x Hr2_y Hr2_zReconstructed 0.827 -0.3457 -0.44323

My fit 0.830386 -0.346267 -0.43651

Rutgers 0.8266 -0.3456 -0.4442

Comparison for plane vectors done by various fitting

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

Parameter Comparison

Comparison Table Mine Reconstruction

Impact X -16927 -16995

Impact Y -22497.5 -22594.5

rp HR1 27234.5 27548.1

rp HR2 15612 15894.7

phi -64.6372 -61.73

theta 33.1445 32.48

psi HR1 103.05 103.01

psi HR2 109.818 109.77

Comparison for various parameters.

Mine refers to parameters calculated using my planes and Mathematica

Reconstruction are values pulled from reconstruction.

FADC traces

FADC traces

Looking at this another wayCan I reproduce this effect in Monte Carlo events?

Event Rp Hr1 Rp Hr2 Opening Angle

Track Length Hr1

Track Length Hr1 m

Track Length Hr2

Track Length Hr2 m

Shower Time

Slope Hr1

Good Tubes Hr1

Slope Hr2

Good Tubes Hr2

1 26446.8 14435.5 0.19735 0.23796 0.5155 30109 -0.2289 11 -0.24523 32 1 26446.8

What happened with this event?

The Reconstructed plane fits do not match the pre-reconstruction plane fits.

Fit x y zMC HiRes 2

0.7758 -0.4252 0.4662

MC HiRes 1

0.6401 -0.5513 .5351

Rec HiRes 2

0.7769 -0.4284 0.4615

Rec HiRes 1

0.6542 -0.5812 0.4835

Mine HiRes 2

0.7761 -0.4270 0.4639

Mine HiRes 1

0.6542 -0.5812 0.4640

Plane Comparison

HiRes 1 planes HiRes 2 planes

Plane Comparison

Actual Planes Reconstructed Planes

Shifting the Planes – Work in Progress

Theta consists of a rotation about the z axis.

Psi is a rotation about the axis perpendicular to both shower normal and shower core.

This is a non-weighted fit to HiRes 2 points

0 0.5 1 1.5 psi0 -0.27351 -0.27944 -0.2802 -0.27566

0.5 -0.27799 -0.28512 -0.28764 -0.285581 -0.28157 -0.28945 -0.2933 -0.29331

1.5 -0.28431 -0.2925 -0.29719 -0.298732 -0.28631 -0.29439 -0.29948 -0.30198

2.5 -0.28768 -0.29536 -0.30043 -0.303393 -0.28858 -0.29562 -0.30041 -0.30342

theta

Current State Still have a finite number of events

that reconstruct with unusual speeds.

Currently looking at rotating planes to see what would need to be done for planes to fit

Also currently in the process of reevaluating cuts based on some slight changes to procedure

Calculating Apertures with new cuts