multiple muons at the far detector

Multiple Muons at the Far Detector

Andy BlakeCambridge University

Fermilab, December 2006

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.

Introduction (2)


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.

Multiple Muons at MINOS


• 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.

Multiple Muon Reconstruction


• 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.

Multiple Muon Reconstruction Method


(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

Example Event


Run 22992; Snarl 25336: a multi-muon event with 11 tracks.

(I) Group Strips


Group strips in each view (using a 4 plane, 20 strip clustering window)

(II) Hough Transform


• 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

(II) Hough Transform


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.

(III) 2D Muon Tracks


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

(III) 2D Muon Tracks


V tracks = 10

U tracks = 11

(IV) 3D Muon Tracks


• 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 ).

(IV) 3D Muon Tracks


Multiplicity = 11

(IV) 3D Muon Tracks


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

First Results


• 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.

(I) Multiplicities


MC

data

(I) Multiplicities


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)

(II) Random Error in Multiplicity


Scanning Exercises


• 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.

Scanning Exercises


High Multiplicity Event


Run 31217; Snarl 58670: high multiplicity event with ~20 tracks.



V tracks = 15

U tracks = 18



Multiplicity = 16

missedtracks

Summary


• 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!

multiple muons at the far detector

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