1. Multiple Muons at the Far Detector Andy Blake Cambridge University Fermilab, December 2006

2. Introduction (1) Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 2 “knee” “ankle” One characteristic feature of the observed cosmic ray energy spectrum is the steepening that occurs at energies of ~10 7 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.

3. Introduction (2) Andy Blake, Cambridge UniversityMultiple 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.

4. Multiple Muons at MINOS Andy Blake, Cambridge UniversityMultiple 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.

5. Multiple Muon Reconstruction Andy Blake, Cambridge UniversityMultiple 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.

6. Multiple Muon Reconstruction Method Andy Blake, Cambridge UniversityMultiple 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

7. Example Event Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 7 Run 22992; Snarl 25336: a multi-muon event with 11 tracks.

8. (I) Group Strips Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 8 Group strips in each view (using a 4 plane, 20 strip clustering window)

9. (II) Hough Transform Andy Blake, Cambridge UniversityMultiple 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.

10. (II) Hough Transform Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 10 U view 1/m V view m N.B: there is always a preference for horizontal and vertical tracks, which has to be suppressed! Best fit gradient in the U view. Best fit gradient in the V view.

11. (III) 2D Muon Tracks Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 11 intercept peaks 4 strips C PcPc – 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T ZZ LL

12. (III) 2D Muon Tracks Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 12 V tracks = 10 U tracks = 11

13. (IV) 3D Muon Tracks Andy Blake, Cambridge UniversityMultiple 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 ).

14. (IV) 3D Muon Tracks Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 14 Multiplicity = 11

15. (IV) 3D Muon Tracks Andy Blake, Cambridge UniversityMultiple 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 in the multiplicity

16. First Results Andy Blake, Cambridge UniversityMultiple 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.

17. (I) Multiplicities Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 17 MC data

18. (I) Multiplicities Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 18 MultiplicityMark 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)

19. (II) Random Error in Multiplicity Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 19

20. (II) Random Error in Multiplicity Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 20

21. Scanning Exercises Andy Blake, Cambridge UniversityMultiple 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.

22. Scanning Exercises Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 22

23. High Multiplicity Event Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 23 Run 31217; Snarl 58670: high multiplicity event with ~20 tracks.

24. High Multiplicity Event Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 24 V tracks = 15 U tracks = 18

25. High Multiplicity Event Andy Blake, Cambridge UniversityMultiple Muon Talk, slide 25 Multiplicity = 16 missed tracks

26. Summary Andy Blake, Cambridge UniversityMultiple 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!