Download - Multiple Muons at the Far Detector Andy Blake Cambridge University Fermilab, December 2006
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Multiple Muons at the Far Detector
Andy BlakeCambridge University
Fermilab, December 2006
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Introduction (1)
Andy Blake, Cambridge University Multiple Muon Talk, slide 2
“knee”
“ankle”
• One characteristic feature of the observed cosmic ray energy spectrum is the steepening that occurs at energies of ~107 GeV/nucleus.
– this feature is commonly known as the “knee”.
• Several explanations have been offered.
– e.g. variety of compact acceleration sources; propagation of cosmic rays through galaxy; physics of interactions at high energies.
– there are substantial differences among models in the predicted spectrum and composition of primary cosmic rays in the knee region.
• Measurements of multiple muons in underground detectors is one tool for indirectly studying the primary composition around the knee region.
– it has been shown that the muon multiplicity is sensitive to both the energy and mass number of the primary particles.
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Introduction (2)
Andy Blake, Cambridge University Multiple Muon Talk, slide 3
Soudan 2 multiple muon analysis [Kasahara et al. Phys. Rev. D55 (1997) 5282-94]
• Divide primary cosmic rays into five mass groups (H, He, CNO, Ne-S, Fe).
• Three trial composition models.
– “New Source P” exponential cut-off of the low energy component, switch-on of a new high energy component comprising protons.
– “Heavy” all mass groups follow same power law.
– “New Source Fe” exponential cut-off of the low energy component, switch-on of a new high energy component comprising Fe.
• Data provides best match to the low mass primary composition.
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Multiple Muons at MINOS
Andy Blake, Cambridge University Multiple Muon Talk, slide 4
• MINOS is well set up to study multiple muons.
– 700m depth of far detector corresponds to surface muon energies of ~1 TeV.
– 8m x 8m x 30m surface area should enclose the majority of multiple muons. (area is approximately double that of Soudan 2).
– 4cm x 6cm granularity should enable muon separation at the level of ~10-20 cm (the average separation of each muon pair is approximately ~1m).
– In addition, the magnetic field provides possibility of studying charge multiplicities.
• Requirements for MINOS multiple muon analysis.
– Multiple muon reconstruction.
- identification of multiplicities greater than ~10 muons. - measurement of detector acceptances, efficiencies etc…
– Multiple muon simulation.
- 3D simulation of atmospheric cascade. - 3D simulation of muon propagation through rock. - simulation of multiple muons in far detector.
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Multiple Muon Reconstruction
Andy Blake, Cambridge University Multiple Muon Talk, slide 5
• Multiple muon reconstruction is difficult!
– Detector geometry (detector has vertical scintillator planes, a coil hole, and two super-modules – steep tracks cross too few planes or are split!).
– De-multiplexing (multiple muons produce hits in multiple strips per plane).
• The standard track finder isn’t optimized for high multiplicities.
– developed for tracks with variety of curvatures and vertex showers.
– unable to resolve closely overlapping tracks.
• Instead, try using a Hough Transform method to reconstruct multiple muon tracks with the same gradient. – Very similar to the technique used in the de-muxer and online event display.
• Develop multiple muon reconstruction using Atmos Ntuples.
– Don’t have to keep running the offline reconstruction chain.
– Cross-talk has been tagged and removed from the event.
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Multiple Muon Reconstruction Method
Andy Blake, Cambridge University Multiple Muon Talk, slide 6
(I) Cluster together strips into groups.
(II) Apply Hough transform to groups. – project out gradient profile and find highest peak.
– project out intercept profile at highest gradient peak.
– use intercept peaks to obtain track trajectories.
(II) 2D track reconstruction. – assign strips to each track trajectory.
– merge associated trajectories.
(IV) 3D track reconstruction. – pair up overlapping 2D tracks in each view.
– add any unpaired but clearly defined tracks.
2D reconstruction
3D reconstruction
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Example Event
Andy Blake, Cambridge University Multiple Muon Talk, slide 7
Run 22992; Snarl 25336: a multi-muon event with 11 tracks.
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(I) Group Strips
Andy Blake, Cambridge University Multiple Muon Talk, slide 8
Group strips in each view (using a 4 plane, 20 strip clustering window)
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(II) Hough Transform
Andy Blake, Cambridge University Multiple Muon Talk, slide 9
• Take Hough Transform of each group of strips.
– Gradient bins: M=[-1,+1] (100 bins), 1/M=[-1,+1] (100 bins).
– Intercept bins: C=[-5m,+5m] (200 bins).
(N.B: C is defined relative to the centre of the group. Since only the peak gradient is needed initially, the absolute value of the intercept doesn’t matter. Clustering the strips into groups allows a narrower range of C to be used, and results in a cleaner Hough Transform).
• Project out gradient profile for each Hough Transform.
– The height of the gradient profile in the m’th bin is given by:
– The peak of this profile is chosen as the best fit muon direction.
c
2mc
groups
m hP
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(II) Hough Transform
Andy Blake, Cambridge University Multiple Muon Talk, slide 10
U view
1/m
V view
m
N.B: there is always a preferencefor horizontal and vertical tracks,
which has to be suppressed!
Best fit gradient in the U view.
Best fit gradient in the V view.
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(III) 2D Muon Tracks
Andy Blake, Cambridge University Multiple Muon Talk, slide 11
intercept peaks
4 strips
C
Pc
– For each group of strips in each view, project out the intercept profile along the best fit gradient.
– Each intercept peak containing >4 strips defines a muon trajectory in (m,c) space.
– For each muon track, collect up any strips located within 10 cm from the track, and then cluster any other associated strips within a 2 plane, 2 strip window.
– Merge together tracks that are separated by L, Z, T < 10cm or contain common strips.
• Identifying muon tracks
• Merging muon tracks
T
Z
L
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(III) 2D Muon Tracks
Andy Blake, Cambridge University Multiple Muon Talk, slide 12
V tracks = 10
U tracks = 11
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(IV) 3D Muon Tracks
Andy Blake, Cambridge University Multiple Muon Talk, slide 13
• Compare U and V views and pair up overlapping 2D tracks, giving preference to the pairs that overlap the most.
• Add any un-paired tracks that are clearly defined:
– track planes > 10 (track crosses sufficient planes).
– L > 50 cm (track is sufficiently isolated).
• Multiplicity is given by: max ( U tracks, V tracks ).
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(IV) 3D Muon Tracks
Andy Blake, Cambridge University Multiple Muon Talk, slide 14
Multiplicity = 11
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(IV) 3D Muon Tracks
Andy Blake, Cambridge University Multiple Muon Talk, slide 15
These are probably the same track, which gives
an over-count in the muon multiplicity.
This is probably two Tracks, which gives
an under-count inthe multiplicity
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First Results
Andy Blake, Cambridge University Multiple Muon Talk, slide 16
• Far detector cosmic muon data.
– January-August 2005.
– Trigger Word != Spill Trigger.
– Live Time ~ 200 days.
• Far detector cosmic muon MC.
– runs 651-800 (Cambridge MC).
– N.B: these are single muons!
– Live Time ~ 200 days.
• Measurements made on data and MC.
– track multiplicities in each view.
– overall muon multiplicity.
– scanning high multiplicity events.
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(I) Multiplicities
Andy Blake, Cambridge University Multiple Muon Talk, slide 17
MC
data
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(I) Multiplicities
Andy Blake, Cambridge University Multiple Muon Talk, slide 18
Multiplicity Mark Thomson(N = 42,500)
Data(N=7,575,000)
MC(N=6,950,000)
1 0.96118(85) 0.96025(6) 0.99943(1)
2 0.03015(84) 0.03090(6) 0.00057(1)
3 0.00531(35) 0.00559(3) 0.00000(0)
4 0.00202(22) 0.00178(2) -
5 0.00061(12) 0.00072(1) -
6 0.00040(10) 0.00035(1) -
7 0.00028(8) 0.000182(5) -
8 0.00002(2) 0.000101(4) -
9 0.00002(2) 0.000054(1) -
10 - 0.000030(2) -
11 - 0.000017(2) -
12 - 0.000010(1) -
(N.B: statistical error in last decimal place shown in brackets)
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(II) Random Error in Multiplicity
Andy Blake, Cambridge University Multiple Muon Talk, slide 19
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(II) Random Error in Multiplicity
Andy Blake, Cambridge University Multiple Muon Talk, slide 20
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Scanning Exercises
Andy Blake, Cambridge University Multiple Muon Talk, slide 21
• Hand-scanned 200 events with multiplicities >5 muons.
• General conclusions from scanning exercise. – Reconstruction is reliable to ±2 up to multiplicities of ~10 muons.
– High multiplicities are under-estimated by my algorithm.
– This needs careful optimization!
• Reasons for under-counting and over-counting muons:
Reasons for multiplicity to be over-counted:
– Split tracks (“S-shaped” tracks, tracks through coil hole etc…).
– Large showers on a track give a peak in Hough Transform.
– “Shadow” of hits parallel to track (cross-talk, de-muxing etc…).
Reasons for multiplicity to be under-counted:
– Tracks don’t cross enough planes.
– Tracks are too close together and are merged.
– Tracks lost when pairing 2D tracks to form 3D tracks.
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Scanning Exercises
Andy Blake, Cambridge University Multiple Muon Talk, slide 22
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High Multiplicity Event
Andy Blake, Cambridge University Multiple Muon Talk, slide 23
Run 31217; Snarl 58670: high multiplicity event with ~20 tracks.
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High Multiplicity Event
Andy Blake, Cambridge University Multiple Muon Talk, slide 24
V tracks = 15
U tracks = 18
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High Multiplicity Event
Andy Blake, Cambridge University Multiple Muon Talk, slide 25
Multiplicity = 16
missedtracks
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Summary
Andy Blake, Cambridge University Multiple Muon Talk, slide 26
• Multiple muon reconstruction algorithm in development.
– currently works okay up to multiplicities of ~10 muons.
• Future Work:
– Continue to develop multiple muon reconstruction.
– Optimize algorithm for higher multiplicities.
– Integrate code into offline framework.
• Need a multiple muon simulation for this analysis.
– Developing such a simulation is a non-trivial piece of work!