1. Response of AMANDA-II to Cosmic Ray Muons and study of Systematics
Newt,Paolo and Teresa

2. Outline
Motivation : Study of Cosmic Ray muons as a test beam to check the experiment systematics and enhance understanding of our detector response
Muon Angular and Vertical Depth intensity and differences between data and montecarlo
Methodology and Assumptions
Angular Reconstruction
Some notes on Convoluted Pandel Likelihood

3. Motivation
We have huge statistics of down going muon data and this could be used to get a better understanding of AMANDA-II performance and could enhance our filtering ,Event Reconstruction and Systematics.
Compare a measurement of the intensity of down going muon flux as a function of the zenith angle and demonstrate good agreement within systematics
Possibly a flat component of Charm induced muons could be detected(If we have angular resolution under control) at large Zenith angles

4. Methodology
Cosmic Ray muons are simulated using Corsika 6.03 and QGSJET01 hadronic interaction model and detector response obtained using trigger conditions and events are reconstructed.
Now from the experimental data if we want to make a Physics measurement of the muon Intensity we will have to account for Triggering & reconstruction efficiencies.
Triggering efficiency accounted by looking at actual events generated from the mmc files
Assumed that the ratio of events for which the detector triggers (reconstructed events) to the true events generated remains the same in the data and the simulation to get the Physical measurement of the flux from experimental data

5. Methodology
Now we have a finite angular resolution so what we reconstruct is not the true angle, but however if we adjust the bin size in such a way as to minimize the overlapping than the correlations between the bins of the zenith angle could be ignored and each bin could be treated independently
Prior to doing this we could also use some basic quality cuts to improve reconstruction
Track Length,Chi Square,Difference of Odd and Even hits from a time ordered hit sample.

6. Correlation: Misreco Angle VS Zenith Angle
Cos(Reco Zenith) Convoluted Pandel
Cos(Reco Zenith) Patched Pandel

7. Correlation: Misreco Angle VS Number of Channel(Energy Observable)
Quality cuts
Track Length>120m
Chi Square<7.3
ABS(zenith(odd)-zenith(even)<3
Nch>40
Misreco Angle
Number Of Channel Fired

8. Zenith Angle Resolution Plots
After quality cut
Before quality cut
Patched
Convoluted

9. Zenith Angle Resolution Plots
counts
Before quality cut
After quality cut
Recozenith-Truezenith

10. Cos (zenith) Cos (zenith) -1.537 (4.14 -1.28 (4.12) -1.07 (4.17)
Convoluted
(before qc)
21.2
(5.55)
19.1
(6.5)
15.5
(7.0)
11.4
(6.96)
8.04
(6.34)
5.6
(5.5)
3.86
(4.76)
2.6
(4.13)
1.55
(3.69)
0.55
(3.26)
(afterqc)
14.3
(7.12)
8.01
(5.09)
5.27
(4.14)
3.22
(3.34)
2.36
(2.93)
1.77
(2.71)
1.435
(2.57)
1.18
(2.46)
0.97
(2.34)
0.69
(2.13))
Cos
(zenith)
Convoluted
(before qc)
-1.537
(4.14
-1.28
(4.12)
-1.07
(4.17)
-0.802
(4.05)
-0.66
(3.91)
-0.5
(3.7)
-0.33
(3.68)
-0.11
(3.6)
0.13
(3.5)
0.733
(3.35)
(afterqc)
-0.82
(2.39)
-0.51
(2.37)
-0.52
(2.34)
-0.50
(2.16)
-0.30
(2.09)
(1.86)
-0.242
(1.83)
-0.19
(1.80)
-0.1
0.143
(2.0)

11. Results-Angular Distribution

12. Results-MC-Data disagreement
The data/MC becomes larger close to horizon

13. Interbin Correlations-Overlap
Cos(zenithReco)-Cos(Truezenith)

14. Redefining Bin-Sizes 11 bin(with rms value as half bin size) 0.0-0.15
Cos(zenithReco)-Cos(Truezenith)

15. Convoluted Vs Patched Pandel Negative Time Delay Distributions
The Convoluted Pandel
Convoluting Gaussian PMT noise smearing with Pandel function using Confluent Hyper geometric functions (George and Mathieu)
Much better Angular resolution and description of time delay distributions
High energy
Muon
With nhits>200
Time delay (ns) (16-fold ppandel)
“1-fold iterated Convoluted Pandel has approximately same angular resolution Of a 16-fold ppandel”
-Mathieu Ribordy
(AMANDA collaboration meeting,Mons)

16. Convoluted Vs Patched Pandel Data Agreement
B.G
Signal
Cut out
To speeden up
Proceessing
time
Number Of Hits
Number Of Hits