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GPU-based Online Tracking Algorithms & Application to D±→K∓π±π±

AndiH
February 03, 2015

GPU-based Online Tracking Algorithms & Application to D±→K∓π±π±

A seminar talk at RUB University

AndiH

February 03, 2015
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  1. Mitglied der Helmholtz-Gemeinschaft
    1
    RUB Seminar Talk
    3 February 2014, Andreas Herten
    GPU-based Online Tracking
    Algorithms &
    Application to D±→K∓π±π±

    View Slide

  2. Mitglied der Helmholtz-Gemeinschaft
    Outline
    • Online Tracking for PANDA
    • GPUs
    • Online Tracking Algorithms
    – Triplet Finder
    – Hough Transforms
    • D±→K∓π±π±
    – EvtGen
    – Hitcounting
    – Tracking Benchmark
    – Event Reconstruction
    2

    View Slide

  3. Mitglied der Helmholtz-Gemeinschaft
    PANDA &
    ONLINE TRACKING
    3

    View Slide

  4. Mitglied der Helmholtz-Gemeinschaft
    PANDA — The Experiment
    4
    13 m
    p
    p

    View Slide

  5. Mitglied der Helmholtz-Gemeinschaft
    PANDA — The Experiment
    4
    13 m
    p
    p
    Magnet
    STT
    MVD
    GEMs
    FTS

    View Slide

  6. Mitglied der Helmholtz-Gemeinschaft
    PANDA — Event Reconstruction
    • Continuous read out
    – Novel feature
    – Background & signal similar
    – No hardware trigger based on few sub-detectors,
    but online event reconstruction using full detector information
    5
    (Reject background events, save interesting events)
    Reduction
    Amount:
    Time:
    ~1/1000
    50 ns/evt
    Storage space for
    offline analysis
    3 PB/y
    Event:
    Raw data:
    2 × 107/s
    200 GB/s
    Rate Full version

    View Slide

  7. Mitglied der Helmholtz-Gemeinschaft
    PANDA — Read Out Scheme
    6

    View Slide

  8. Mitglied der Helmholtz-Gemeinschaft
    PANDA — Read Out Scheme
    6

    View Slide

  9. Mitglied der Helmholtz-Gemeinschaft
    PANDA — Read Out Scheme
    Requirements to
    Online Tracking
    • Fast
    • Sophisticated
    algorithms possible;
    reprogrammable
    • Parallelism beyond
    single devices
    • Speed ↔ precision
    6

    View Slide

  10. Mitglied der Helmholtz-Gemeinschaft
    PANDA — Read Out Scheme
    Requirements to
    Online Tracking
    • Fast
    • Sophisticated
    algorithms possible;
    reprogrammable
    • Parallelism beyond
    single devices
    • Speed ↔ precision
    6
    GPUs

    View Slide

  11. Mitglied der Helmholtz-Gemeinschaft
    GPUS
    7

    View Slide

  12. 8
    Mitglied der Helmholtz-Gemeinschaft
    CPU & GPU
    • Originally used for computer games
    • Programming available as
    General Purpose GPU, GPGPU
    StarCraft II

    View Slide

  13. 8
    Mitglied der Helmholtz-Gemeinschaft
    CPU & GPU
    CPU GPU
    • Originally used for computer games
    • Programming available as
    General Purpose GPU, GPGPU
    StarCraft II

    View Slide

  14. 8
    Mitglied der Helmholtz-Gemeinschaft
    CPU & GPU
    CPU GPU
    • Originally used for computer games
    • Programming available as
    General Purpose GPU, GPGPU
    StarCraft II

    View Slide

  15. Mitglied der Helmholtz-Gemeinschaft
    CPU & GPU
    9
    GPU
    CPU

    View Slide

  16. Mitglied der Helmholtz-Gemeinschaft
    CPU & GPU
    9
    GPU
    CPU
    a1
    → b1
    → c1
    a2
    → b2
    → c2
    a3
    → …
    parallel
    a1
    → b1
    → c1; a2
    → b2
    → c2; a3
    → …
    serial

    View Slide

  17. Mitglied der Helmholtz-Gemeinschaft
    Challenges of GPU programming
    10
    =
    Leveraging GPU
    processing power
    Writing adequate
    algorithms adequately
    parallel • non-blocking • computing-intensive
    Getting data to GPU
    integration into DAQ • high-level data
    +

    View Slide

  18. Mitglied der Helmholtz-Gemeinschaft
    Challenges of GPU programming
    10
    =
    Leveraging GPU
    processing power
    Writing adequate
    algorithms adequately
    parallel • non-blocking • computing-intensive
    Getting data to GPU
    integration into DAQ • high-level data
    +

    View Slide

  19. Mitglied der Helmholtz-Gemeinschaft
    11
    ALGORITHMS #1
    Triplet Finder
    Hough Transform

    View Slide

  20. Mitglied der Helmholtz-Gemeinschaft
    12
    Triplet Finder
    • Algorithm specifically designed for the
    PANDA Straw Tube Tracker (STT)
    http://www.fz-juelich.de/ias/jsc/
    1.5 m
    • Ported to GPU
    – CUDA, Dynamic Parallelism, Thrust
    – Quality of tracks comparable to CPU
    Drift tubes: t0 needed
    for drift circles
    → r(tArrive-t0)
    1cm
    Resolution without t0: (0.1 cm)
    Resolution with t0: (0.015 cm)

    View Slide

  21. Mitglied der Helmholtz-Gemeinschaft
    13
    Triplet Finder
    • Idea: Use only subset of detector as seed
    – Don‘t use STT isochrones (drift times)
    • Features
    – Fast & robust algorithm, no t0 needed
    – Many tuning possibilities
    More

    View Slide

  22. Mitglied der Helmholtz-Gemeinschaft
    14
    Triplet Finder — Times
    K20X

    View Slide

  23. Mitglied der Helmholtz-Gemeinschaft
    14
    Triplet Finder — Times
    K20X

    View Slide

  24. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamps
    – Combine hits to sets (bunches) which occupy GPU best
    15

    View Slide

  25. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamps
    – Combine hits to sets (bunches) which occupy GPU best
    15
    Hit

    View Slide

  26. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamps
    – Combine hits to sets (bunches) which occupy GPU best
    15
    Hit Event

    View Slide

  27. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamps
    – Combine hits to sets (bunches) which occupy GPU best
    15
    Hit Event

    View Slide

  28. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamps
    – Combine hits to sets (bunches) which occupy GPU best
    15
    Hit Event
    Bunch

    View Slide

  29. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamps
    – Combine hits to sets (bunches) which occupy GPU best
    15
    Hit Event
    Bunch
    (N2) → (N)

    View Slide

  30. Mitglied der Helmholtz-Gemeinschaft
    16
    Triplet Finder — Bunching
    K20X
    Performance

    View Slide

  31. Mitglied der Helmholtz-Gemeinschaft
    17
    Triplet Finder — Kepler vs. Maxwell
    Performance for different GPUs
    K20X
    Maxwell
    Performance: 1.3 TFLOPSsingle
    Price: 130 €
    750 Ti
    Kepler
    Performance: 3.95 TFLOPSsingle
    Price: 3600 €

    View Slide

  32. Mitglied der Helmholtz-Gemeinschaft
    ALGORITHMS #2
    18
    Triplet Finder
    Hough Transform

    View Slide

  33. Mitglied der Helmholtz-Gemeinschaft
    Algorithm: Hough Transform
    • Basic Hough idea: Generate lots of independent track
    parameters; extract best-matching one.
    • Three Hough Transforms:
    – Line Hough Transform
    • Around point-like hits (MVD, STT-prefit)
    • Around isochronuous hits (STT)
    – Circle Hough Transform (MVD, STT, GEM, …)
    19
    x
    y
    x
    y
    Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Princip
    → Bin
    giv
    r
    α

    View Slide

  34. Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Variations
    20
    • Circle Hough with isochrones (xC, yC)ij = (xi + sij cos φj, yi + sij sin φj)
    2 sij = ρi
    2 - xi
    2 - yi
    2 / (xi cos φj + yi sin φj + ρi)

    View Slide

  35. -300 -200 -100 0 100 200 300
    -300
    -200
    -100
    0
    100
    200
    300
    HoughHisto_1
    Entries 171941
    Mean x -3.39
    Mean y 14.01
    RMS x 101.6
    RMS y 123.5
    0
    2
    4
    6
    8
    10
    12
    14
    16
    18
    HoughHisto_1
    Entries 171941
    Mean x -3.39
    Mean y 14.01
    RMS x 101.6
    RMS y 123.5
    Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Variations
    21

    View Slide

  36. -300 -200 -100 0 100 200 300
    -300
    -200
    -100
    0
    100
    200
    300
    HoughHisto_1
    Entries 171941
    Mean x -3.39
    Mean y 14.01
    RMS x 101.6
    RMS y 123.5
    0
    2
    4
    6
    8
    10
    12
    14
    16
    18
    HoughHisto_1
    Entries 171941
    Mean x -3.39
    Mean y 14.01
    RMS x 101.6
    RMS y 123.5
    Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Variations
    21
    π+
    π-
    π-
    K-
    K+
    π+

    View Slide

  37. -300 -200 -100 0 100 200 300
    -300
    -200
    -100
    0
    100
    200
    300
    HoughHisto_1
    Entries 171941
    Mean x -3.39
    Mean y 14.01
    RMS x 101.6
    RMS y 123.5
    0
    2
    4
    6
    8
    10
    12
    14
    16
    18
    HoughHisto_1
    Entries 171941
    Mean x -3.39
    Mean y 14.01
    RMS x 101.6
    RMS y 123.5
    Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Variations
    22

    View Slide

  38. -300 -200 -100 0 100 200 300
    -300
    -200
    -100
    0
    100
    200
    300
    HoughHisto_1
    Entries 171941
    Mean x -3.39
    Mean y 14.01
    RMS x 101.6
    RMS y 123.5
    0
    2
    4
    6
    8
    10
    12
    14
    16
    18
    HoughHisto_1
    Entries 171941
    Mean x -3.39
    Mean y 14.01
    RMS x 101.6
    RMS y 123.5
    Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Variations
    22

    View Slide

  39. -300 -200 -100 0 100 200 300
    -300
    -200
    -100
    0
    100
    200
    300
    HoughHisto_1
    Entries 171941
    Mean x -3.39
    Mean y 14.01
    RMS x 101.6
    RMS y 123.5
    0
    2
    4
    6
    8
    10
    12
    14
    16
    18
    HoughHisto_1
    Entries 171941
    Mean x -3.39
    Mean y 14.01
    RMS x 101.6
    RMS y 123.5
    Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Variations
    22

    View Slide

  40. Mitglied der Helmholtz-Gemeinschaft
    Circle Hough — GPU Performance
    23
    i5 @ 3.3 GHz
    Variation of number of threads (and blocks): GPU vs. CPU
    GTX 580

    View Slide

  41. Mitglied der Helmholtz-Gemeinschaft
    Circle Hough — GPU Performance
    23
    i5 @ 3.3 GHz
    Variation of number of threads (and blocks): GPU vs. CPU
    GTX 580
    ~20 ×

    View Slide

  42. Mitglied der Helmholtz-Gemeinschaft
    Circle Hough — Challenges & Todo
    • CPU:
    – Benchmarking; cut parameters
    – Code cleanup
    • GPU:
    – Performance w/o PandaRoot
    – More parallelism (hit → set of hits)
    – Data transfer
    • Tracking: Data or computing intensive?
    • Different types of memories
    • Asynchronous transfer & processing
    24

    View Slide

  43. Mitglied der Helmholtz-Gemeinschaft
    GPUs — Summary
    • Triplet Finder: Performance-optimized
    – 14 µs / event
    • Circle Hough: PandaRoot-integrated
    • GPUs: Feasible for part of PANDA‘s online event
    reconstruction system
    – Also important: Data transfer to GPU
    25
    PndCircleHoughTask  *  chTracker  =  new  PndCircleHoughTask();
    chTracker-­‐>AddHitBranch("MVDHitsStrip");
    chTracker-­‐>AddHitBranch("STTHit");
    chTracker-­‐>SetUseGpu(true);

    View Slide

  44. Mitglied der Helmholtz-Gemeinschaft
    D± → K∓ π± π±
    26
    Description & EvtGen
    Detector Response
    Tracking Performance
    Event Reconstruction

    View Slide

  45. Mitglied der Helmholtz-Gemeinschaft
    D± → K∓ π± π±
    27
    Description & EvtGen
    Detector Response
    Tracking Performance
    Event Reconstruction

    View Slide

  46. 4 Proceedings of the DPF-2009 Conference, Detroi
    Mass (MeV)
    3000
    3500
    4000
    4500
    Charmonium Spectrum

    ?
    K
    c
    J/\
    K'
    c
    \'
    \(4040)
    \(4415)
    \(4160)
    h
    c
    F
    c0
    F
    c1
    F
    c2
    F'
    c2
    \''
    13S
    1
    23S
    1
    13D
    1
    11S
    0
    21S
    0
    31S
    0
    41S
    0
    11P
    1
    21P
    1
    13P
    1
    23P
    1
    23P
    0
    13P
    0
    13P
    2
    23P
    2
    13F
    2
    11D
    2
    13D
    2
    13D
    3
    23D
    3
    23D
    2
    21D
    2
    33S
    1
    23D
    1
    43S
    1
    33D
    1
    DD
    DD*
    53S
    1
    Y(4260)
    Z(3940)
    Y(4660)
    Y(4350)
    Y(4008)
    Z+(4430)
    Z
    1
    (4050)
    X(3872)
    X(3940)
    Y(3940)
    Z
    2
    (4250)
    X(4160)
    Y(4140)
    D
    s
    D
    s
    D*D*
    D
    s
    D*
    s
    D*
    s
    D*
    s
    DD
    1
    D
    s
    D
    s1
    , D*
    s
    D
    s0
    D*D
    2
    D*
    s
    D
    s2
    Y(4630)
    Figure 5: The Charmonium spectrum. The solid lines
    are quark mode predictions [21] the shaded lines are the
    observed conventional charmonium states [22], the hori-
    zontal dashed lines represent various D(∗)
    s
    ¯
    D(∗)
    s
    thresholds,
    and the (red) dots are the newly discovered charmonium-
    like states placed in the column with the most probable
    spin assignment. The states in the last column do not fit
    elsewhere and appear to be truly exotic.
    Figure 6
    in B →
    mass di
    the B+
    backgro
    total un
    4143.0
    3.7 Me
    JP C =
    argue t
    in B →
    re 1.
    (Left) Invariant mass of the 3⇡ system for 0.1 GeV/c2 < t0 < 1.0 GeV2/c2 (histogram), and intensity of the background wave
    a flat distribution in three-body phase space (red triangles), obtained from a partial wave analysis in 40 MeV/c2 bins of the 3⇡ mas
    escaled to the binning of the histogram (from [1]). (Right) Intensities of major waves (a) 1++0+⇢⇡ S, (b) 2 +0+ f2⇡ S, (c) 2++1+⇢⇡,
    as the intensity of the exotic wave (d) 1 +⇢⇡ P, as determined in the fit in mass bins (data points with error bars). The lines represen
    sult of the mass-dependent fit (from [1]).
    .
    Ds
    Ds
    *
    D
    Ds(2317)
    (2317)
    Ds(2460)
    (2460)
    Ds(2710)
    (2710)
    Ds (2860)
    (2860)
    J
    Ds(3040)
    (3040)
    Observed
    Ds1
    Ds2
    Mass (MeV/c )
    3000
    3500
    4000
    4500
    ?
    c
    J/
    '
    c
    '
    (4040)
    (4415)
    (4160)
    h
    c
    c0
    c1
    c2
    '
    c2
    ''
    13S
    1
    23S
    1
    13D
    1
    11S
    0
    21S
    0
    31S
    0
    41S
    0
    11P
    1
    21P
    1
    13P
    1
    23P
    1
    23P
    0
    13P
    0
    13P
    2
    23P
    2
    13F
    2
    11D
    2
    13D
    2
    13D
    3
    23D
    3
    23D
    2
    21D
    2
    33S
    1
    23D
    1
    43S
    1
    33D
    1
    53S
    1
    Y(4260)
    Z(3940)
    Y(4660)
    Y(4350)
    Y(4008)
    Z+(4430)
    Z
    1
    (4050)
    X(3872)
    X(3940)
    Y(3940)
    Z
    2
    (4250)
    X(4160)
    Y(4140)
    D D
    D D
    Y(4630)
    2
    DD
    DD*
    DD
    DD
    D D
    D D
    D D
    D D
    s s
    *
    *
    s s
    *
    D D
    D D
    s s
    *
    *
    D D
    D D
    1
    D D , D D
    D D , D D
    s s1 s s0
    *
    D D
    D D
    *
    2
    D D
    D D
    *
    s s2
    s s
    re 2.
    (Left) The Ds
    meson spectrum as predicted by Godfrey and Igsur [12] (solid line) and by Di Pierro and Eichten [13] (dotted li
    rimental values are shown by points; black points refer to old measured states, red ones to newly discovered. (Right) The charmoni
    rum. The solid lines are CQM predictions [12], the shaded lines are the observed conventional charmonium states, the horizontal
    ed lines represent various thresholds. The red dots are the newly discovered charmonium-like states placed in the column of the mo
    able spin assignment. The states in the last column do not fit elsewhere and appear to be truly exotic.
    ng list of states, with mass in the range 1–2 GeV/c2,
    which an exotic interpretation has been claimed.
    been found, allowing us to check the hyperfine contributi
    to the q ¯
    q potential. Taking the PDG11 [4] value for
    Mitglied der Helmholtz-Gemeinschaft
    28
    D Mesons Spectrum
    Godfrey (2009) »Topics in Hadron Spectroscopy in 2009«
    arXiv:0910.3409
    Predictions
    Observed
    New Discoveries
    Many D(S) and old/new charmonium states decay via D meson
    → Good reconstruction important!
    Predictions
    Observed
    Gianotti (2012) »Results and perspectives in hadron spectroscopy «
    Phys. Scr. 2012 014014

    View Slide

  47. Mitglied der Helmholtz-Gemeinschaft
    29
    D Hadronic Decay
    K∗
    2
    (1430)0 → K− π+
    K− π+ e+ νe nonresonant < 7 × 10−3 CL=90% 864
    K− π+ µ+ νµ ( 3.8 ±0.4 ) % 851
    K∗(892)0 µ+ νµ ,
    K∗(892)0 → K− π+
    ( 3.52±0.10) % 717
    K− π+ µ+ νµ nonresonant ( 2.0 ±0.5 ) × 10−3 851
    K− π+ π0 µ+ νµ < 1.6 × 10−3 CL=90% 825
    π0 e+ νe ( 4.05±0.18) × 10−3 930
    ηe+ νe ( 1.14±0.10) × 10−3 855
    ρ0 e+ νe ( 2.18+0.17
    −0.25) × 10−3 774
    ρ0 µ+ νµ ( 2.4 ±0.4 ) × 10−3 770
    ωe+ νe ( 1.82±0.19) × 10−3 771
    η′(958)e+ νe ( 2.2 ±0.5 ) × 10−4 689
    φe+ νe < 9 × 10−5 CL=90% 657
    Fractions of some of the following modes with resonances have already
    appeared above as submodes of particular charged-particle modes.
    K∗(892)0 e+ νe ( 5.52±0.15) % 722
    K∗(892)0 µ+ νµ ( 5.28±0.15) % 717
    K∗
    0
    (1430)0 µ+ νµ < 2.4 × 10−4 CL=90% 380
    K∗(1680)0 µ+ νµ < 1.5 × 10−3 CL=90% 105
    Hadronic modes with a K or K K K
    Hadronic modes with a K or K K K
    Hadronic modes with a K or K K K
    Hadronic modes with a K or K K K
    K0
    S
    π+ ( 1.47±0.07) % S=2.0 863
    K0
    L
    π+ ( 1.46±0.05) % 863
    K− 2π+ [c] ( 9.13±0.19) % 846
    (K− π+)S−wave π+ ( 7.32±0.19) % 846
    K∗
    0
    (1430)0 π+ ,
    K∗
    0
    (1430)0 → K− π+
    [d] ( 1.21±0.06) % 382
    HTTP://PDG.LBL.GOV Page 3 Created: 8/21/2014 13:13
    D+
    D-
    K-
    +
    +
    K+
    -
    -
    p p
    100 m
    pBeam = 6.5 GeV/c

    View Slide

  48. D+
    D-
    K-
    +
    +
    K+
    -
    -

    R
    p p
    100 m
    2015-01-15 19:08:40
    R| / mm

    |
    0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
    counts
    10
    2
    10
    3
    10
    4
    10
    5
    10 Entries 1000000
    Mean 0.5471
    RMS 0.5424
    R|

    |
    -
    D
    +
    D
    2015-01-15 19:08:42
    / mm
    xy
    R)

    (
    0 0.05 0.1 0.15 0.2 0.25 0.3
    counts
    0
    10000
    20000
    30000
    40000
    50000
    Entries 1000000
    Mean 0.04196
    RMS 0.03302
    xy
    R)

    (
    -
    D
    +
    D
    2015-01-15 19:08:41
    / mm
    z
    R)

    (
    5
    − 4
    − 3
    − 2
    − 1
    − 0 1 2 3 4 5
    counts
    0
    10000
    20000
    30000
    40000
    50000
    60000
    70000
    80000
    Entries 1000000
    Mean 0.001421

    RMS 0.7685
    z
    R)

    (
    -
    D
    +
    D
    Mitglied der Helmholtz-Gemeinschaft
    D Decay Vertex Distances
    30

    View Slide

  49. D+
    D-
    K-
    +
    +
    K+
    -
    -
    p p
    100 m
    CHAPTER 4. APPLICATION TO THE RECONSTRUCTION OF D+ ! K ⇡+⇡+
    2015-01-15 19:08:22
    )
    4
    /c
    2
    / (GeV
    (1+2)
    +
    π
    -
    K
    2
    M
    0.5 1 1.5 2 2.5 3
    )
    4
    /c
    2
    counts / 0.03 (GeV
    0
    10000
    20000
    30000
    40000
    50000
    Entries 2000000
    Daughters Invariant Mass
    +
    D
    (a) m2(K ⇡+). Two entries per event, as the two final
    state ⇡ are indistinguishable.
    2015-01-15 19:08:23
    )
    4
    /c
    2
    / (GeV
    (2)
    +
    π
    (1)
    +
    π
    2
    M
    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
    )
    4
    /c
    2
    counts / 0.02 (GeV
    0
    2000
    4000
    6000
    8000
    10000
    12000
    14000
    Entries 1000000
    Daughters Invariant Mass
    +
    D
    (b) m2(⇡+⇡+)
    Figure 4.7: Squared masses of the two two-particle-combinations of the D+ daughter particles.
    4.6. BACKGROUND STUDIES
    Figure 4.5: Momenta Plots from CLEO-c. The corresponding plots of EvtGen’s implementation are Figure
    4.6, Figure 4.7(a), and Figure 4.7(b).
    NOTE: Ref!
    )
    4
    /c
    2
    ) / (GeV
    )
    2.5
    3
    Entries 1000000
    350
    400
    450
    Entries 1000000
    +
    π
    +
    π
    -
    K

    +
    Dalitz plot for D
    CHAPTER 4. APPLICATION TO THE RECONSTRUCTION OF D+ ! K ⇡+⇡
    2015-01-15 19:08:22
    )
    4
    /c
    2
    / (GeV
    (1+2)
    +
    π
    -
    K
    2
    M
    0.5 1 1.5 2 2.5 3
    )
    4
    /c
    2
    counts / 0.03 (GeV
    0
    10000
    20000
    30000
    40000
    50000
    Entries 2000000
    Daughters Invariant Mass
    +
    D
    (a) m2(K ⇡+). Two entries per event, as the two final
    state ⇡ are indistinguishable.
    2015-01-15 19:08:23
    )
    4
    /c
    2
    / (GeV
    (2)
    +
    π
    (1)
    +
    π
    2
    M
    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
    )
    4
    /c
    2
    counts / 0.02 (GeV
    0
    2000
    4000
    6000
    8000
    10000
    12000
    14000
    Entries 1000000
    Daughters Invariant Mass
    +
    D
    (b) m2(⇡+⇡+)
    Figure 4.7: Squared masses of the two two-particle-combinations of the D+ daughter particles.
    Mitglied der Helmholtz-Gemeinschaft
    Decay Model: EvtGen / CLEO
    31
    CLEO-c
    EvtGen
    4.6. BACKGROUND STUDIES
    Figure 4.5: Momenta Plots from CLEO-c. The corresponding plots of EvtGen’s implementation are Figure
    4.6, Figure 4.7(a), and Figure 4.7(b).
    NOTE: Ref!
    2014-12-21 20:29:11
    )
    4
    /c
    2
    ) / (GeV
    (1)
    +
    π
    -
    (K
    2
    m
    0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
    )
    4
    /c
    2
    ) / (GeV
    (2)
    +
    π
    -
    (K
    2
    m
    1
    1.5
    2
    2.5
    3
    Entries 1000000
    0
    50
    100
    150
    200
    250
    300
    350
    400
    450
    Entries 1000000
    +
    π
    +
    π
    -
    K

    +
    Dalitz plot for D
    Figure 4.6: Dalitz plot for D+ ! K ⇡+⇡+. Since the two ⇡ in the final state are indistinguishable, the
    distribution is symmetric around the diagonal y = x. K ⇡+
    (1)
    is the lighter combination, plotted on
    x.

    View Slide

  50. 2015-01-07 14:34:50
    / GeV/c
    z
    p
    0 0.5 1 1.5 2 2.5 3 3.5
    / GeV/c
    t
    p
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1 Entries 2000000
    0
    200
    400
    600
    800
    1000
    1200
    1400
    Entries 2000000
    Momentum Distribution
    (1+2)
    +
    π
    Mitglied der Helmholtz-Gemeinschaft
    K, π Momentum Distributions
    32
    2015-01-07 14:34:42
    / GeV/c
    z
    p
    0 0.5 1 1.5 2 2.5 3 3.5
    / GeV/c
    t
    p
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1 Entries 1000000
    0
    100
    200
    300
    400
    500
    Entries 1000000
    Momentum Distribution
    -
    K

    View Slide

  51. Mitglied der Helmholtz-Gemeinschaft
    D± → K∓ π± π±
    33
    Description & EvtGen
    Detector Response
    Tracking Performance
    Event Reconstruction

    View Slide

  52. 2015-01-27 14:49:51
    #Hits
    0 10 20 30 40 50 60 70 80
    counts
    0
    10000
    20000
    30000
    40000
    50000
    60000
    Entries 200000
    Mean 0.02411
    ±
    12.23
    RMS 0.01705
    ±
    10.78
    Underflow 0
    Overflow 0
    : #STT Hits
    -
    K
    2015-01-28 20:29:58
    #Hits
    0 10 20 30 40 50 60
    counts
    1
    10
    2
    10
    3
    10
    4
    10
    5
    10
    Entries 200000
    Mean 0.02405
    ±
    3.443
    RMS 0.01701
    ±
    10.76
    Underflow 0
    Overflow 0
    : #FTS Hits
    -
    K
    Mitglied der Helmholtz-Gemeinschaft
    Sub-Detector Hit Counting
    34
    2015-01-24 16:10:55
    #Hits
    0 1 2 3 4 5 6 7 8
    counts
    0
    20
    40
    60
    80
    100
    3
    10
    ×
    Entries 200000
    Mean 0.006149
    ±
    2.342
    RMS 0.004348
    ±
    2.75
    Underflow 0
    Overflow 0
    : #GEM Hits
    -
    K
    2015-01-24 16:10:54
    #Hits
    0 1 2 3 4 5 6 7 8 9
    counts
    0
    10000
    20000
    30000
    40000
    50000
    60000
    Entries 200000
    Mean 0.003445
    ±
    3.671
    RMS 0.002436
    ±
    1.541
    Underflow 0
    Overflow 0
    : #MVD Hits
    -
    K
    K-
    MVD STT
    GEM FTS

    View Slide

  53. 2015-01-28 20:39:59
    #GEM Hits
    0 1 2 3 4 5 6 7 8
    #STT Hits
    0
    5
    10
    15
    20
    25
    30
    Entries 200000
    Mean x 0.006153
    ±
    2.343
    Mean y 0.02403
    ±
    12.2
    RMS x 0.004351
    ±
    2.751
    RMS y 0.01699
    ±
    10.74
    0 185 0
    0 199815 0
    0 0 0
    0
    5000
    10000
    15000
    20000
    25000
    30000
    Entries 200000
    Mean x 0.006153
    ±
    2.343
    Mean y 0.02403
    ±
    12.2
    RMS x 0.004351
    ±
    2.751
    RMS y 0.01699
    ±
    10.74
    0 185 0
    0 199815 0
    0 0 0
    : #GEM Hits vs. #STT Hits
    -
    K
    Mitglied der Helmholtz-Gemeinschaft
    Sub-Detector Hit Counting
    35
    K-
    STT
    GEM

    View Slide

  54. 2015-01-24 16:11:25
    #Hits
    0 1 2 3 4 5 6 7 8
    counts
    0
    50
    100
    150
    200
    250
    3
    10
    ×
    Entries 400000
    Mean 0.003999
    ±
    1.647
    RMS 0.002828
    ±
    2.529
    Underflow 0
    Overflow 8
    : #GEM Hits
    +
    π
    2015-01-24 16:11:24
    #Hits
    0 1 2 3 4 5 6 7 8 9
    counts
    0
    20
    40
    60
    80
    100
    120
    3
    10
    ×
    Entries 400000
    Mean 0.002305
    ±
    3.815
    RMS 0.00163
    ±
    1.458
    Underflow 0
    Overflow 41
    : #MVD Hits
    +
    π
    Mitglied der Helmholtz-Gemeinschaft
    Sub-Detector Hit Counting
    36
    π+
    2015-01-28 20:30:27
    #Hits
    0 10 20 30 40 50 60 70 80
    counts
    0
    10000
    20000
    30000
    40000
    50000
    60000
    70000
    Entries 400000
    Mean 0.01823
    ±
    17.59
    RMS 0.01289
    ±
    11.51
    Underflow 0
    Overflow 1132
    : #STT Hits
    +
    π
    2015-01-28 20:33:00
    #Hits
    0 10 20 30 40 50 60
    counts
    1
    10
    2
    10
    3
    10
    4
    10
    5
    10
    Entries 400000
    Mean 0.0152
    ±
    2.582
    RMS 0.01075
    ±
    9.612
    Underflow 0
    Overflow 12
    : #FTS Hits
    +
    π
    MVD STT
    GEM FTS

    View Slide

  55. 2015-01-25 17:09:12
    / GeV/c
    z
    p
    0 0.5 1 1.5 2 2.5 3 3.5
    / GeV/c
    t
    p
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1
    Entries 70379
    Mean x 0.003239
    ±
    1.435
    Mean y 0.0007536
    ±
    0.3081
    RMS x 0.00229
    ±
    0.8592
    RMS y 0.0005329
    ±
    0.1999
    0 0 0
    0 70379 0
    0 0 0
    0
    20
    40
    60
    80
    100
    120
    Entries 70379
    Mean x 0.003239
    ±
    1.435
    Mean y 0.0007536
    ±
    0.3081
    RMS x 0.00229
    ±
    0.8592
    RMS y 0.0005329
    ±
    0.1999
    0 0 0
    0 70379 0
    0 0 0
    for no #STT Hits
    z
    vs. p
    t
    : p
    +
    π
    2015-01-25 17:09:13
    / GeV/c
    z
    p
    0 0.5 1 1.5 2 2.5 3 3.5
    / GeV/c
    t
    p
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1
    Entries 34085
    Mean x 0.004096
    ±
    0.962
    Mean y 0.001204
    ±
    0.3999
    RMS x 0.002896
    ±
    0.7562
    RMS y 0.0008514
    ±
    0.2223
    0 0 0
    0 34085 0
    0 0 0
    0
    20
    40
    60
    80
    100
    Entries 34085
    Mean x 0.004096
    ±
    0.962
    Mean y 0.001204
    ±
    0.3999
    RMS x 0.002896
    ±
    0.7562
    RMS y 0.0008514
    ±
    0.2223
    0 0 0
    0 34085 0
    0 0 0
    for no #STT, #GEM, #FTS Hits
    z
    vs. p
    t
    : p
    +
    π
    2015-01-25 17:09:13
    #FTS Hits
    0 10 20 30 40 50 60
    #GEM Hits
    0
    1
    2
    3
    4
    5
    6
    7
    8
    Entries 70379
    Mean x 0.06796
    ±
    12.04
    Mean y 0.01082
    ±
    2.685
    RMS x 0.04805
    ±
    18.03
    RMS y 0.007649
    ±
    2.869
    0 1 0
    0 70376 2
    0 0 0
    0
    5000
    10000
    15000
    20000
    25000
    30000
    Entries 70379
    Mean x 0.06796
    ±
    12.04
    Mean y 0.01082
    ±
    2.685
    RMS x 0.04805
    ±
    18.03
    RMS y 0.007649
    ±
    2.869
    0 1 0
    0 70376 2
    0 0 0
    : #Hits FTS vs. #Hits GEM for no #Hits STT
    +
    π
    Mitglied der Helmholtz-Gemeinschaft
    Sub-Detector Hit Counting
    37
    π+: No STT hits
    2015-01-28 20:30:27
    #Hits
    0 10 20 30 40 50 60 70 80
    counts
    0
    10000
    20000
    30000
    40000
    50000
    60000
    70000
    Entries 400000
    Mean 0.01823
    ±
    17.59
    RMS 0.01289
    ±
    11.51
    Underflow 0
    Overflow 1132
    : #STT Hits
    +
    π
    STT
    GEM
    FTS
    STT
    STT STT
    GEM
    FTS
    MVD

    View Slide

  56. 2015-01-30 11:41:07
    θ
    0 0.5 1 1.5 2 2.5 3
    #Hits per track
    0
    5
    10
    15
    20
    25
    30
    35
    40
    Sub-Detectors
    MVD
    STT
    GEM
    FTS
    ALL
    for Different Sub-Detectors
    θ
    : Profile of #Hits vs.
    +
    π
    2015-01-30 11:40:42
    θ
    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
    #Hits per track
    0
    5
    10
    15
    20
    25
    30 Sub-Detectors
    MVD
    STT
    GEM
    FTS
    ALL
    for Different Sub-Detectors
    θ
    : Profile of #Hits vs.
    -
    K
    Mitglied der Helmholtz-Gemeinschaft
    Sub-Detector Hit Counting
    38
    π & K: Profile histogram comparison

    View Slide

  57. 2015-02-01 20:24:34
    θ
    0 0.5 1 1.5 2 2.5 3
    #Hits > 6 / #Hits
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    (All Sub-Detectors)
    θ
    : Efficiency vs.
    +
    π
    2015-02-01 20:24:03
    θ
    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
    #Hits > 6 / #Hits
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    (All Sub-Detectors)
    θ
    : Efficiency vs.
    -
    K
    Mitglied der Helmholtz-Gemeinschaft
    Sub-Detector Hit Counting
    39
    π: Efficiency estimation
    Tracks with more than 6 hits
    All tracks
    All All

    View Slide

  58. Mitglied der Helmholtz-Gemeinschaft
    Decay Positions
    40
    K
    2015-02-01 20:37:11
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    K: Decay Positions r vs. z
    All

    View Slide

  59. 2015-02-01 20:37:11
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    K: Decay Positions r vs. z
    Mitglied der Helmholtz-Gemeinschaft
    Decay Positions
    41
    2015-02-01 20:37:17
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 762146
    Mean x 0.203
    ±
    161.2
    Mean y 0.03335
    ±
    60.81
    RMS x 0.1436
    ±
    177.2
    RMS y 0.02358
    ±
    29.11
    0 59 3
    163 761890 31
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 762146
    Mean x 0.203
    ±
    161.2
    Mean y 0.03335
    ±
    60.81
    RMS x 0.1436
    ±
    177.2
    RMS y 0.02358
    ±
    29.11
    0 59 3
    163 761890 31
    0 0 0
    : Decay Positions r vs. z
    π
    K & π
    All
    All

    View Slide

  60. 2015-02-01 20:37:11
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    K: Decay Positions r vs. z
    Mitglied der Helmholtz-Gemeinschaft
    Decay Positions
    41
    2015-02-01 20:37:17
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 762146
    Mean x 0.203
    ±
    161.2
    Mean y 0.03335
    ±
    60.81
    RMS x 0.1436
    ±
    177.2
    RMS y 0.02358
    ±
    29.11
    0 59 3
    163 761890 31
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 762146
    Mean x 0.203
    ±
    161.2
    Mean y 0.03335
    ±
    60.81
    RMS x 0.1436
    ±
    177.2
    RMS y 0.02358
    ±
    29.11
    0 59 3
    163 761890 31
    0 0 0
    : Decay Positions r vs. z
    π
    2015-02-01 20:37:13
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    K: Decay Positions r vs. z
    2015-02-01 20:37:18
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 762146
    Mean x 0.203
    ±
    161.2
    Mean y 0.03335
    ±
    60.81
    RMS x 0.1436
    ±
    177.2
    RMS y 0.02358
    ±
    29.11
    0 59 3
    163 761890 31
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 762146
    Mean x 0.203
    ±
    161.2
    Mean y 0.03335
    ±
    60.81
    RMS x 0.1436
    ±
    177.2
    RMS y 0.02358
    ±
    29.11
    0 59 3
    163 761890 31
    0 0 0
    : Decay Positions r vs. z
    π
    K & π
    All
    All

    View Slide

  61. 2015-02-01 20:37:11
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    K: Decay Positions r vs. z
    Mitglied der Helmholtz-Gemeinschaft
    Decay Positions
    41
    2015-02-01 20:37:17
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 762146
    Mean x 0.203
    ±
    161.2
    Mean y 0.03335
    ±
    60.81
    RMS x 0.1436
    ±
    177.2
    RMS y 0.02358
    ±
    29.11
    0 59 3
    163 761890 31
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 762146
    Mean x 0.203
    ±
    161.2
    Mean y 0.03335
    ±
    60.81
    RMS x 0.1436
    ±
    177.2
    RMS y 0.02358
    ±
    29.11
    0 59 3
    163 761890 31
    0 0 0
    : Decay Positions r vs. z
    π
    2015-02-01 20:37:13
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 382674
    Mean x 0.306
    ±
    205.9
    Mean y 0.05362
    ±
    54.9
    RMS x 0.2164
    ±
    189.3
    RMS y 0.03791
    ±
    33.16
    0 66 4
    0 382551 53
    0 0 0
    K: Decay Positions r vs. z
    2015-02-01 20:37:18
    z / cm
    0 200 400 600 800 1000
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 762146
    Mean x 0.203
    ±
    161.2
    Mean y 0.03335
    ±
    60.81
    RMS x 0.1436
    ±
    177.2
    RMS y 0.02358
    ±
    29.11
    0 59 3
    163 761890 31
    0 0 0
    1
    10
    2
    10
    3
    10
    Entries 762146
    Mean x 0.203
    ±
    161.2
    Mean y 0.03335
    ±
    60.81
    RMS x 0.1436
    ±
    177.2
    RMS y 0.02358
    ±
    29.11
    0 59 3
    163 761890 31
    0 0 0
    : Decay Positions r vs. z
    π
    K & π
    2015-02-01 20:37:16
    θ
    0 0.5 1 1.5 2 2.5 3
    ratio of counts inside / all
    0
    0.2
    0.4
    0.6
    0.8
    1
    K: Ratio of IN / ALL of DIRC/EMC
    2015-02-01 20:37:22
    θ
    0 0.5 1 1.5 2 2.5 3
    ratio of counts inside / all
    0.2
    0.4
    0.6
    0.8
    1
    : Ratio of IN / ALL of DIRC/EMC
    π
    All
    All

    View Slide

  62. 2015-01-25 18:00:32
    z / cm
    100
    − 0 100 200 300 400 500 600
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 33385
    Mean x 0.3767
    ±
    38.3
    Mean y 0.1691
    ±
    17.86
    RMS x 0.2664
    ±
    68.8
    RMS y 0.1196
    ±
    30.88
    0 12 0
    16 33354 3
    0 0 0
    0
    200
    400
    600
    800
    1000
    1200
    1400
    Entries 33385
    Mean x 0.3767
    ±
    38.3
    Mean y 0.1691
    ±
    17.86
    RMS x 0.2664
    ±
    68.8
    RMS y 0.1196
    ±
    30.88
    0 12 0
    16 33354 3
    0 0 0
    : Decay Positions r vs. z for no #STT, #GEM, #FTS Hits
    +
    π
    Mitglied der Helmholtz-Gemeinschaft
    Decay Positions
    42
    π+: Positions for no STT, no GEM, no FTS hits
    Particles go through
    uncovered slits!
    STT
    GEM
    FTS
    MVD

    View Slide

  63. 2015-01-25 18:00:32
    z / cm
    100
    − 0 100 200 300 400 500 600
    r / cm
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180
    200
    220 Entries 33385
    Mean x 0.3767
    ±
    38.3
    Mean y 0.1691
    ±
    17.86
    RMS x 0.2664
    ±
    68.8
    RMS y 0.1196
    ±
    30.88
    0 12 0
    16 33354 3
    0 0 0
    0
    200
    400
    600
    800
    1000
    1200
    1400
    Entries 33385
    Mean x 0.3767
    ±
    38.3
    Mean y 0.1691
    ±
    17.86
    RMS x 0.2664
    ±
    68.8
    RMS y 0.1196
    ±
    30.88
    0 12 0
    16 33354 3
    0 0 0
    : Decay Positions r vs. z for no #STT, #GEM, #FTS Hits
    +
    π
    Mitglied der Helmholtz-Gemeinschaft
    Decay Positions
    42
    π+: Positions for no STT, no GEM, no FTS hits
    Particles go through
    uncovered slits!
    STT
    GEM
    FTS
    MVD

    View Slide

  64. Mitglied der Helmholtz-Gemeinschaft
    D± → K∓ π± π±
    43
    Description & EvtGen
    Detector Response
    Tracking Performance
    Event Reconstruction

    View Slide

  65. 2015-02-02 14:42:50
    θ
    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
    ε
    0
    0.2
    0.4
    0.6
    0.8
    1
    Particles
    All
    ±
    K
    ±
    π
    θ
    vs.
    ε
    Reconstruction efficiency
    2015-02-02 14:46:07
    θ
    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
    ε
    0
    0.2
    0.4
    0.6
    0.8
    1
    Particles
    All
    ±
    K
    ±
    π
    θ
    vs.
    ε
    Reconstruction efficiency
    Mitglied der Helmholtz-Gemeinschaft
    Circle Hough Benchmark
    44
    εAll = 97 %
    εK = 82 %
    επ = 95 %
    K, π: Efficiency of reconstructable tracks
    εAll = 81 %
    εK = 71 %
    επ = 82 %
    PANDA
    default
    tracking
    Circle
    Hough

    View Slide

  66. 2015-01-28 19:29:48
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    50
    100
    150
    200
    250
    300 Entries 2076
    Mean 0.002905
    ±
    0.01168

    RMS 0.002054
    ±
    0.1323
    / ndf
    2
    χ 306.5 / 64
    Constant 8.6
    ±
    213.9
    Mean 0.001599
    ±
    0.008731

    Sigma 0.00213
    ±
    0.06589
    Particles
    ±
    Transverse Momentum Relative: #K
    2015-01-28 19:29:46
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    100
    200
    300
    400
    500
    600
    700
    800
    900 Entries 5268
    Mean 0.001937
    ±
    0.02164

    RMS 0.001369
    ±
    0.14
    / ndf
    2
    χ 865 / 83
    Constant 17.0
    ±
    682
    Mean 0.00078
    ±
    0.01069

    Sigma 0.00101
    ±
    0.05104
    Particles
    ±
    π
    Transverse Momentum Relative:
    2015-01-28 19:27:47
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    100
    200
    300
    400
    500
    600
    Entries 2396
    Mean 0.004085
    ±
    0.04415

    RMS 0.002889
    ±
    0.1973
    / ndf
    2
    χ 526.1 / 87
    Constant 21.0
    ±
    611.8
    Mean 0.000558
    ±
    0.004154

    Sigma 0.00059
    ±
    0.02356
    Particles
    ±
    Transverse Momentum Relative: #K
    2015-01-28 19:27:46
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    200
    400
    600
    800
    1000
    1200
    1400
    1600
    1800 Entries 6118
    Mean 0.002647
    ±
    0.03134

    RMS 0.001872
    ±
    0.2032
    / ndf
    2
    χ 1447 / 96
    Constant 39.8
    ±
    1846
    Mean 0.000288
    ±
    0.001895

    Sigma 0.00030
    ±
    0.01922
    Particles
    ±
    π
    Transverse Momentum Relative:
    Mitglied der Helmholtz-Gemeinschaft
    Circle Hough Benchmark
    45
    K, π: pt resolution
    σAll = 5.5 %
    σK = 6.5 % σπ = 5.1 %
    σAll = 2.1 %
    σK = 2.3 % σπ = 1.9 %
    σAll = 5.4 %
    σK = 5.6 % σπ = 5.2 %
    PANDA
    default
    tracking
    Circle
    Hough
    PANDA
    tracking
    w/o Kalman

    View Slide

  67. Spurious found tracks:
    Partially found tracks
    Mitglied der Helmholtz-Gemeinschaft
    Circle Hough Benchmark
    46
    pt resolution of differently well-found tracks
    Fully found tracks
    • All hits of reconstructed track
    come from one MC track
    • ≥ 50 % of hits of MC track are in
    reconstructed track
    • ≥ 50 % hits of reconstructed
    track come from one MC track
    • All hits of reconstructed track
    come from one MC track
    • All hits of MC track are in
    reconstructed track
    2015-01-28 19:29:49
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    100
    200
    300
    400
    500
    600 Entries 3153
    Mean 0.001133
    ±
    0.005316

    RMS 0.000801
    ±
    0.06361
    / ndf
    2
    χ 261.2 / 33
    Constant 14.1
    ±
    487.3
    Mean 0.000882
    ±
    0.008452

    Sigma 0.00105
    ±
    0.04735
    Transverse Momentum Relative: All, fully
    2015-01-28 19:29:49
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    10
    20
    30
    40
    50
    Entries 617
    Mean 0.006823
    ±
    0.002804

    RMS 0.004825
    ±
    0.1691
    / ndf
    2
    χ 95.64 / 50
    Constant 2.26
    ±
    34.85
    Mean 0.00568
    ±
    0.01461

    Sigma 0.0057
    ±
    0.1187
    Transverse Momentum Relative: All, Partially
    2015-01-28 19:29:50
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    50
    100
    150
    200
    250
    300
    350
    400
    450
    Entries 2807
    Mean 0.002806
    ±
    0.01998

    RMS 0.001984
    ±
    0.1478
    / ndf
    2
    χ 497.5 / 79
    Constant 11.8
    ±
    351.8
    Mean 0.00108
    ±
    0.01299

    Sigma 0.00134
    ±
    0.05168
    Transverse Momentum Relative: All, Spurious (>0.7)
    7 %
    2.1 %
    13.7 %
    PANDA
    default
    tracking
    Circle
    Hough
    PANDA
    tracking
    w/o Kalman
    σpt
    N
    11.9 %
    11 %
    11 %
    41 %
    5.1 %
    7.4 %
    σpt
    N
    5.1 %
    36 %
    36 %
    34 %
    1.8 %
    4.1 %
    σpt
    N
    4.7 %
    47 %
    47 %

    View Slide

  68. Spurious found tracks:
    Mitglied der Helmholtz-Gemeinschaft
    Circle Hough Benchmark
    47
    pt resolution of differently well-found tracks
    • ≥ 50 % hits of reconstructed
    track come from one MC track
    2015-01-28 19:29:50
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    50
    100
    150
    200
    250
    300
    350
    400
    450
    Entries 2807
    Mean 0.002806
    ±
    0.01998

    RMS 0.001984
    ±
    0.1478
    / ndf
    2
    χ 497.5 / 79
    Constant 11.8
    ±
    351.8
    Mean 0.00108
    ±
    0.01299

    Sigma 0.00134
    ±
    0.05168
    Transverse Momentum Relative: All, Spurious (>0.7)
    PANDA
    default
    tracking
    Circle
    Hough
    PANDA
    tracking
    w/o Kalman
    41 %
    5.1 %
    7.4 %
    σpt
    N
    5.1 %
    36 %
    36 %
    2015-01-28 19:29:50
    fraction (a.u.)
    0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
    counts
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180 Entries 3821
    Mean 0.002095
    ±
    0.7873
    RMS 0.001481
    ±
    0.1295
    Fraction of Hits of a MC Track in Assoc. Reco Track

    View Slide

  69. Spurious found tracks:
    Mitglied der Helmholtz-Gemeinschaft
    Circle Hough Benchmark
    47
    pt resolution of differently well-found tracks
    • ≥ 50 % hits of reconstructed
    track come from one MC track
    2015-01-28 19:29:50
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    50
    100
    150
    200
    250
    300
    350
    400
    450
    Entries 2807
    Mean 0.002806
    ±
    0.01998

    RMS 0.001984
    ±
    0.1478
    / ndf
    2
    χ 497.5 / 79
    Constant 11.8
    ±
    351.8
    Mean 0.00108
    ±
    0.01299

    Sigma 0.00134
    ±
    0.05168
    Transverse Momentum Relative: All, Spurious (>0.7)
    PANDA
    default
    tracking
    Circle
    Hough
    PANDA
    tracking
    w/o Kalman
    41 %
    5.1 %
    7.4 %
    σpt
    N
    5.1 %
    36 %
    36 %
    2015-01-28 19:29:50
    fraction (a.u.)
    0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
    counts
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180 Entries 3821
    Mean 0.002095
    ±
    0.7873
    RMS 0.001481
    ±
    0.1295
    Fraction of Hits of a MC Track in Assoc. Reco Track
    2015-01-28 19:29:51
    fraction reco'd hits (a.u.)
    0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1

    0.8

    0.6

    0.4

    0.2

    0
    0.2
    0.4
    0.6
    0.8
    1
    Entries 3821
    Mean x 0.002086
    ±
    0.7925
    Mean y 0.003193
    ±
    0.03289
    RMS x 0.001475
    ±
    0.1269
    RMS y 0.002258
    ±
    0.1942
    0
    5
    10
    15
    20
    25
    30
    35
    40
    45
    Entries 3821
    Mean x 0.002086
    ±
    0.7925
    Mean y 0.003193
    ±
    0.03289
    RMS x 0.001475
    ±
    0.1269
    RMS y 0.002258
    ±
    0.1942
    res.
    t
    Fraction of Hits of a MC Track in Assoc. Reco Track vs. p

    View Slide

  70. Spurious found tracks:
    Mitglied der Helmholtz-Gemeinschaft
    Circle Hough Benchmark
    47
    pt resolution of differently well-found tracks
    • ≥ 50 % hits of reconstructed
    track come from one MC track
    2015-01-28 19:29:50
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    50
    100
    150
    200
    250
    300
    350
    400
    450
    Entries 2807
    Mean 0.002806
    ±
    0.01998

    RMS 0.001984
    ±
    0.1478
    / ndf
    2
    χ 497.5 / 79
    Constant 11.8
    ±
    351.8
    Mean 0.00108
    ±
    0.01299

    Sigma 0.00134
    ±
    0.05168
    Transverse Momentum Relative: All, Spurious (>0.7)
    PANDA
    default
    tracking
    Circle
    Hough
    PANDA
    tracking
    w/o Kalman
    41 %
    5.1 %
    7.4 %
    σpt
    N
    5.1 %
    36 %
    36 %
    2015-01-28 19:29:50
    fraction (a.u.)
    0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
    counts
    0
    20
    40
    60
    80
    100
    120
    140
    160
    180 Entries 3821
    Mean 0.002095
    ±
    0.7873
    RMS 0.001481
    ±
    0.1295
    Fraction of Hits of a MC Track in Assoc. Reco Track
    2015-01-28 19:29:51
    fraction reco'd hits (a.u.)
    0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    1

    0.8

    0.6

    0.4

    0.2

    0
    0.2
    0.4
    0.6
    0.8
    1
    Entries 3821
    Mean x 0.002086
    ±
    0.7925
    Mean y 0.003193
    ±
    0.03289
    RMS x 0.001475
    ±
    0.1269
    RMS y 0.002258
    ±
    0.1942
    0
    5
    10
    15
    20
    25
    30
    35
    40
    45
    Entries 3821
    Mean x 0.002086
    ±
    0.7925
    Mean y 0.003193
    ±
    0.03289
    RMS x 0.001475
    ±
    0.1269
    RMS y 0.002258
    ±
    0.1942
    res.
    t
    Fraction of Hits of a MC Track in Assoc. Reco Track vs. p
    2015-02-02 16:06:04
    fraction reco'd hits (a.u.)
    0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
    MC
    t
    ) / p
    MC
    t
    - p
    RECO
    t
    (p
    0.1

    0.05

    0
    0.05
    0.1
    0.15
    0.2
    0.25
    0.3 Entries 3699
    Mean 0.002084
    ±
    0.7925
    Mean y 0.003193
    ±
    0.03276
    RMS 0.001474
    ±
    0.1267
    RMS y 0.002258
    ±
    0.1942
    res.
    t
    Fraction of Hits of a MC Track in Assoc. Reco Track vs. p

    View Slide

  71. 2015-02-02 14:36:57
    / GeV/c
    MC
    t
    p
    0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
    ratio
    ε
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1
    Algorithms
    Default
    Circle Hough
    Efficiency of All MC Tracks vs. Transv. Mom.
    2015-02-02 14:36:58
    / GeV/c
    MC
    t
    p
    0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
    ratio
    ε
    0
    0.2
    0.4
    0.6
    0.8
    1
    Algorithms
    Default
    Circle Hough
    Efficiency of MC Tracks Possible to Find vs. Transv. Mom.
    Mitglied der Helmholtz-Gemeinschaft
    Circle Hough Benchmark
    48
    Efficiencies vs. pt
    PANDA
    default
    tracking
    Circle
    Hough
    Found tracks
    All tracks
    Found tracks
    Findable tracks

    View Slide

  72. Mitglied der Helmholtz-Gemeinschaft
    D± → K∓ π± π±
    49
    Description & EvtGen
    Detector Response
    Tracking Performance
    Event Reconstruction

    View Slide

  73. Mitglied der Helmholtz-Gemeinschaft
    Offline Event Analysis
    • PandaRoot: scrut14
    • Beam Momentum: pBeam = 6.5 GeV/c
    • PID algorithm: PidAlgoIdealCharged
    • PID selection: {Kaon,Pi}Best{Plus,Minus}
    • Initial signal dataset: 200 000 events produced
    • Mass window cut: Δmcut = 0.15 GeV/c2 around mD
    50

    View Slide

  74. 2015-02-01 16:42:18
    Mesons
    -
    #D
    0 1 2 3 4 5 6
    ratio (a.u.)
    0
    0.05
    0.1
    0.15
    0.2
    0.25
    0.3 Entries 83512
    / event
    -
    # D
    / event
    +
    # D
    D: Percentage of Reconstructed Mesons (before cuts)
    Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — D Mesons / Event
    51
    • 25 % (30 %) of all events: 1 D+(-) is found
    • 9 % (12 %) of all events: >1 D+(-) is found
    no cuts

    View Slide

  75. Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — Daughter Momenta
    52
    2015-02-01 16:42:19
    / GeV/c
    z
    p
    0 0.5 1 1.5 2 2.5 3 3.5
    / GeV/c
    t
    p
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1
    Entries 69987
    Mean x 0.002427
    ±
    1.236
    Mean y 0.0008045
    ±
    0.4365
    RMS x 0.001716
    ±
    0.6412
    RMS y 0.0005689
    ±
    0.2126
    1 85 37
    43 69809 12
    0 0 0
    0
    5
    10
    15
    20
    25
    30
    35
    40
    45
    Entries 69987
    Mean x 0.002427
    ±
    1.236
    Mean y 0.0008045
    ±
    0.4365
    RMS x 0.001716
    ±
    0.6412
    RMS y 0.0005689
    ±
    0.2126
    1 85 37
    43 69809 12
    0 0 0
    ): Momentum Distribution
    +
    (from D
    -
    K
    2015-02-01 16:42:20
    / GeV/c
    z
    p
    0 0.5 1 1.5 2 2.5 3
    / GeV/c
    t
    p
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1
    Entries 139974
    Mean x 0.001737
    ±
    0.9904
    Mean y 0.0004872
    ±
    0.4571
    RMS x 0.001229
    ±
    0.6485
    RMS y 0.0003445
    ±
    0.1818
    0 308 137
    105 139299 125
    0 0 0
    0
    10
    20
    30
    40
    50
    60
    70
    80
    90
    100
    Entries 139974
    Mean x 0.001737
    ±
    0.9904
    Mean y 0.0004872
    ±
    0.4571
    RMS x 0.001229
    ±
    0.6485
    RMS y 0.0003445
    ±
    0.1818
    0 308 137
    105 139299 125
    0 0 0
    ): Momentum Distribution (2 Entries per D)
    +
    (from D
    +
    Pi
    no cuts

    View Slide

  76. Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — D Candidate Mass
    53
    no cuts
    2015-02-01 17:42:20
    2
    m / GeV/c
    1.7 1.75 1.8 1.85 1.9 1.95 2 2.05
    counts
    0
    500
    1000
    1500
    2000
    2500
    3000
    3500
    4000
    Entries 69987
    Mean 0.0001896
    ±
    1.862
    RMS 0.0001341
    ±
    0.05016
    Underflow 0
    Overflow 0
    : Invariant Mass
    +
    D

    View Slide

  77. Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — Vertex Fit
    54
    no cuts
    2015-02-01 17:42:21
    2
    χ
    0 1 2 3 4 5 6 7 8 9 10
    counts
    0
    200
    400
    600
    800
    1000
    1200
    1400
    Entries 69987
    Mean 0.009761
    ±
    2.521
    RMS 0.006902
    ±
    2.142
    Underflow 744
    Overflow 2.11e+04
    2
    χ
    : Vertex Fit
    +
    D
    2015-02-01 17:42:21
    )
    2
    χ
    Prob(
    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
    counts
    0
    2000
    4000
    6000
    8000
    10000
    12000
    14000
    16000
    18000
    20000
    22000
    Entries 69987
    Mean 0.001346
    ±
    0.3888
    RMS 0.0009516
    ±
    0.3556
    Underflow 0
    Overflow 146
    )
    2
    χ
    : Vertex Fit Prob(
    +
    D
    PndKinVtxFit

    View Slide

  78. Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — Vertex Fit
    54
    no cuts
    2015-02-01 17:42:21
    2
    χ
    0 1 2 3 4 5 6 7 8 9 10
    counts
    0
    200
    400
    600
    800
    1000
    1200
    1400
    Entries 69987
    Mean 0.009761
    ±
    2.521
    RMS 0.006902
    ±
    2.142
    Underflow 744
    Overflow 2.11e+04
    2
    χ
    : Vertex Fit
    +
    D
    2015-02-01 17:42:21
    )
    2
    χ
    Prob(
    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
    counts
    0
    2000
    4000
    6000
    8000
    10000
    12000
    14000
    16000
    18000
    20000
    22000
    Entries 69987
    Mean 0.001346
    ±
    0.3888
    RMS 0.0009516
    ±
    0.3556
    Underflow 0
    Overflow 146
    )
    2
    χ
    : Vertex Fit Prob(
    +
    D
    Require Prob(χ2) > 0.01
    PndKinVtxFit

    View Slide

  79. Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — Vertex After Vertex Fit
    55
    Vertex Fit
    2015-02-01 17:42:25
    z / cm
    0.1
    − 0.05
    − 0 0.05 0.1 0.15 0.2 0.25
    counts
    0
    200
    400
    600
    800
    1000
    1200
    1400
    1600
    1800
    2000
    2200
    2400 Entries 69987
    Mean 0.0002301
    ±
    0.05153
    RMS 0.0001627
    ±
    0.05695
    Underflow 5395
    Overflow 3341
    Entries 42207
    Mean 0.0002513
    ±
    0.05143
    RMS 0.0001777
    ±
    0.05111
    Underflow 222
    Overflow 605
    : z Position After Vtx Fit (Comparison)
    +
    D
    2015-02-01 17:42:23
    x / cm
    0.1
    − 0.08
    − 0.06
    − 0.04
    − 0.02
    − 0 0.02 0.04 0.06 0.08 0.1
    counts
    0
    1000
    2000
    3000
    4000
    5000
    6000
    Entries 69987
    Mean 05

    8.289e
    ±
    06

    3.428e
    RMS 05

    5.861e
    ±
    0.02081
    Underflow 3384
    Overflow 3590
    Entries 42207
    Mean 05

    5.393e
    ±
    05

    1.866e

    RMS 05

    3.814e
    ±
    0.01106
    Underflow 87
    Overflow 96
    : x Position After Vtx Fit (Comparison)
    +
    D
    2015-02-01 17:42:24
    y / cm
    0.1
    − 0.08
    − 0.06
    − 0.04
    − 0.02
    − 0 0.02 0.04 0.06 0.08 0.1
    counts
    0
    1000
    2000
    3000
    4000
    5000
    6000
    Entries 69987
    Mean 05

    8.361e
    ±
    05

    1.227e
    RMS 05

    5.912e
    ±
    0.02101
    Underflow 3434
    Overflow 3395
    Entries 42207
    Mean 05

    5.304e
    ±
    06

    4.617e
    RMS 05

    3.75e
    ±
    0.01087
    Underflow 99
    Overflow 110
    : y Position After Vtx Fit (Comparison)
    +
    D
    no cuts

    View Slide

  80. Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — Mass After Vertex Fit
    56
    no cuts
    Vertex Fit
    2015-02-01 18:13:26
    2
    ) / GeV/c
    MC
    (m - m
    0.15
    − 0.1
    − 0.05
    − 0 0.05 0.1 0.15
    counts
    0
    500
    1000
    1500
    2000
    2500
    3000
    3500
    4000
    Entries 69987
    Mean 0.0001858
    ±
    0.007714

    RMS 0.0001314
    ±
    0.04639
    Underflow 1468
    Overflow 6176
    / ndf
    2
    χ 1.241e+04 / 97
    Constant 24.8
    ±
    3255
    Mean 0.000100
    ±
    0.002007

    Sigma 0.00014
    ±
    0.02204
    Entries 42207
    Mean 0.0001669
    ±
    0.003508

    RMS 0.000118
    ±
    0.03381
    Underflow 98
    Overflow 1055
    / ndf
    2
    χ 4654 / 94
    Constant 22.4
    ±
    2882
    Mean 0.000098
    ±
    0.001167

    Sigma 0.00010
    ±
    0.01814
    : Relative Invariant Mass After Vertex Fit Comparison
    +
    D
    2015-02-01 18:16:44
    ) / GeV/c
    MC
    t
    - p
    t
    (p
    1
    − 0.8
    − 0.6
    − 0.4
    − 0.2
    − 0 0.2 0.4 0.6 0.8 1
    counts
    0
    2000
    4000
    6000
    8000
    10000
    12000
    14000
    16000
    18000
    20000
    22000 Entries 69987
    Mean 0.0005834
    ±
    0.0542
    RMS 0.0004125
    ±
    0.1531
    Underflow 0
    Overflow 1106
    / ndf
    2
    χ 1.764e+04 / 55
    Constant 1.520e+02
    ±
    2.379e+04
    Mean 0.000077
    ±
    0.001102
    Sigma 0.00008
    ±
    0.01719
    Entries 42207
    Mean 0.0009259
    ±
    0.01594
    RMS 0.0006547
    ±
    0.1873
    Underflow 0
    Overflow 1284
    / ndf
    2
    χ 5474 / 97
    Constant 23.3
    ±
    2732
    Mean 0.000551
    ±
    0.003463
    Sigma 0.0007
    ±
    0.1035
    : Relative Transverse Momentum After Vertex Fit Comparison
    +
    D

    View Slide

  81. 2015-02-01 18:16:45
    2
    χ
    0 1 2 3 4 5 6 7 8 9 10
    counts
    0
    2000
    4000
    6000
    8000
    10000
    12000
    Entries 69987
    Mean 0.008903
    ±
    1.501
    RMS 0.006295
    ±
    2.094
    Underflow 219
    Overflow 1.443e+04
    2
    χ
    : Mass Fit
    +
    D
    2015-02-01 18:16:45
    )
    2
    χ
    Prob(
    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
    counts
    0
    2000
    4000
    6000
    8000
    10000
    12000
    14000
    16000
    18000
    Entries 69987
    Mean 0.001257
    ±
    0.3587
    RMS 0.0008885
    ±
    0.3321
    Underflow 0
    Overflow 142
    )
    2
    χ
    : Mass Fit Prob(
    +
    D
    Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — Mass Constraint Fit
    57
    no cuts
    PndKinFitter with D+ mass constraint

    View Slide

  82. 2015-02-01 18:16:45
    2
    χ
    0 1 2 3 4 5 6 7 8 9 10
    counts
    0
    2000
    4000
    6000
    8000
    10000
    12000
    Entries 69987
    Mean 0.008903
    ±
    1.501
    RMS 0.006295
    ±
    2.094
    Underflow 219
    Overflow 1.443e+04
    2
    χ
    : Mass Fit
    +
    D
    2015-02-01 18:16:45
    )
    2
    χ
    Prob(
    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
    counts
    0
    2000
    4000
    6000
    8000
    10000
    12000
    14000
    16000
    18000
    Entries 69987
    Mean 0.001257
    ±
    0.3587
    RMS 0.0008885
    ±
    0.3321
    Underflow 0
    Overflow 142
    )
    2
    χ
    : Mass Fit Prob(
    +
    D
    Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — Mass Constraint Fit
    57
    no cuts
    Require Prob(χ2) > 0.01
    PndKinFitter with D+ mass constraint

    View Slide

  83. 2015-02-01 18:35:24
    2
    ) / GeV/c
    MC
    (m - m
    0.15
    − 0.1
    − 0.05
    − 0 0.05 0.1 0.15
    counts
    0
    500
    1000
    1500
    2000
    2500
    3000
    3500
    4000
    4500 Entries 69987
    Mean 0.0001816
    ±
    0.007284

    RMS 0.0001284
    ±
    0.04597
    Underflow 0
    Overflow 5940
    / ndf
    2
    χ 1.312e+04 / 81
    Constant 25.5
    ±
    3265
    Mean 0.000101
    ±
    0.002073

    Sigma 0.0001
    ±
    0.0224
    Entries 42207
    Mean 0.0001669
    ±
    0.003508

    RMS 0.000118
    ±
    0.03381
    Underflow 98
    Overflow 1055
    / ndf
    2
    χ 4654 / 94
    Constant 22.4
    ±
    2882
    Mean 0.000098
    ±
    0.001167

    Sigma 0.00010
    ±
    0.01814
    Entries 45375
    Mean 0.0001155
    ±
    0.001035

    RMS 05

    8.169e
    ±
    0.024
    Underflow 117
    Overflow 2095
    / ndf
    2
    χ 1609 / 93
    Constant 22.1
    ±
    3388
    Mean 0.0000866
    ±
    0.0009225

    Sigma 0.00008
    ±
    0.01762
    Entries 35182
    Mean 0.0001144
    ±
    0.0006527

    RMS 05

    8.09e
    ±
    0.02126
    Underflow 50
    Overflow 583
    / ndf
    2
    χ 969.4 / 90
    Constant 21.3
    ±
    2940
    Mean 0.0000897
    ±
    0.0007204

    Sigma 0.00008
    ±
    0.01641
    : Relative Mass After Fits Comparison
    +
    D
    Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — Mass Constraint Fit
    58
    • In 17.5 % (20.5 %) of all events: D+ (D-) is found
    • In 8.6 % of all events: D+D- are found
    • DPM: Of 1M events, 100 survive these fits
    → more cuts!
    no cuts
    Vertex Fit
    Mass Fit
    2015-02-02 11:24:43
    2
    ) / GeV/c
    MC
    (m - m
    0.15
    − 0.1
    − 0.05
    − 0 0.05 0.1 0.15
    counts
    0
    500
    1000
    1500
    2000
    2500
    3000
    3500
    4000
    4500 Entries 69987
    Mean 0.0001816
    ±
    0.007284

    RMS 0.0001284
    ±
    0.04597
    Underflow 0
    Overflow 5940
    / ndf
    2
    χ 1.312e+04 / 81
    Constant 25.5
    ±
    3265
    Mean 0.000101
    ±
    0.002073

    Sigma 0.0001
    ±
    0.0224
    Entries 42207
    Mean 0.0001669
    ±
    0.003508

    RMS 0.000118
    ±
    0.03381
    Underflow 98
    Overflow 1055
    / ndf
    2
    χ 4654 / 94
    Constant 22.4
    ±
    2882
    Mean 0.000098
    ±
    0.001167

    Sigma 0.00010
    ±
    0.01814
    Entries 45375
    Mean 0.0001155
    ±
    0.001035

    RMS 05

    8.169e
    ±
    0.024
    Underflow 117
    Overflow 2095
    / ndf
    2
    χ 1609 / 93
    Constant 22.1
    ±
    3388
    Mean 0.0000866
    ±
    0.0009225

    Sigma 0.00008
    ±
    0.01762
    Entries 35182
    Mean 0.0001144
    ±
    0.0006527

    RMS 05

    8.09e
    ±
    0.02126
    Underflow 50
    Overflow 583
    / ndf
    2
    χ 969.4 / 90
    Constant 21.3
    ±
    2940
    Mean 0.0000897
    ±
    0.0007204

    Sigma 0.00008
    ±
    0.01641
    : Relative Mass After Fits Comparison
    +
    D
    Mass & Vtx

    View Slide

  84. Mitglied der Helmholtz-Gemeinschaft
    Offline Analysis — Inclusive Event
    59
    • When a D+ is found, the invariant missing mass is at:
    µ = (1.870 ± 0.0009) GeV/c2 ,
    σ = (0.01676 ± 0.00009) GeV/c2
    • PDG: 1.869 GeV/c2
    no cuts
    Vertex Fit
    2015-02-02 11:24:48
    2
    m / GeV/c
    1.7 1.75 1.8 1.85 1.9 1.95 2 2.05
    counts
    0
    500
    1000
    1500
    2000
    2500
    3000
    3500
    4000
    Entries 69987
    Mean 0.0001811
    ±
    1.871
    RMS 0.0001281
    ±
    0.04629
    Underflow 4485
    Overflow 169
    / ndf
    2
    χ 1.262e+04 / 93
    Constant 24.4
    ±
    3066
    Mean 0.000
    ±
    1.872
    Sigma 0.000
    ±
    0.024
    Entries 42207
    Mean 0.0001673
    ±
    1.871
    RMS 0.0001183
    ±
    0.03388
    Underflow 1086
    Overflow 117
    / ndf
    2
    χ 4516 / 96
    Constant 21.4
    ±
    2741
    Mean 0.000
    ±
    1.871
    Sigma 0.00011
    ±
    0.01858
    Entries 35182
    Mean 0.0001217
    ±
    1.869
    RMS 05

    8.606e
    ±
    0.02265
    Underflow 472
    Overflow 68
    / ndf
    2
    χ 1159 / 96
    Constant 20.5
    ±
    2790
    Mean 0.00
    ±
    1.87
    Sigma 0.00008
    ±
    0.01676
    : Inclusive Missing Mass After Fits Comparison
    +
    D
    Mass & Vtx

    View Slide

  85. Mitglied der Helmholtz-Gemeinschaft
    Summary
    • GPU Algorithms:
    – Different algorithms in development
    – Triplet Finder: Max performance 12 MHit/s
    – Circle Hough: ≥ 70 % reconstruction performance
    • Benchmark channel D → K π π
    – 17.5 % D+ can be reconstructed (37 % before fits)
    ~1300 D+ / h (σ = 100 nb)
    → Continue studies (Background, Circle Hough)
    60

    View Slide

  86. Thank you!
    Andreas Herten
    [email protected]
    Mitglied der Helmholtz-Gemeinschaft
    Summary
    • GPU Algorithms:
    – Different algorithms in development
    – Triplet Finder: Max performance 12 MHit/s
    – Circle Hough: ≥ 70 % reconstruction performance
    • Benchmark channel D → K π π
    – 17.5 % D+ can be reconstructed (37 % before fits)
    ~1300 D+ / h (σ = 100 nb)
    → Continue studies (Background, Circle Hough)
    60

    View Slide

  87. Mitglied der Helmholtz-Gemeinschaft
    BACKUP
    61

    View Slide

  88. Mitglied der Helmholtz-Gemeinschaft
    STT — Drift Tubes and t0
    62

    View Slide

  89. Mitglied der Helmholtz-Gemeinschaft
    STT — Drift Tubes and t0
    62
    Particle ionizes gas atoms in drift tubes

    View Slide

  90. Mitglied der Helmholtz-Gemeinschaft
    STT — Drift Tubes and t0
    62
    Particle ionizes gas atoms in drift tubes
    Electrons drift to anode wire, ions to wall

    View Slide

  91. Mitglied der Helmholtz-Gemeinschaft
    STT — Drift Tubes and t0
    62
    Particle ionizes gas atoms in drift tubes
    Electrons drift to anode wire, ions to wall
    Signal only when electrons arrive at wire
    No information about drift duration!
    For that, start time (t0) needed:
    t0 - tarrival ≈ tdrift
    vdrift = const → tdrift • vdrift = risochrone

    View Slide

  92. Mitglied der Helmholtz-Gemeinschaft
    STT — Drift Tubes and t0
    62
    Particle ionizes gas atoms in drift tubes
    Electrons drift to anode wire, ions to wall
    Signal only when electrons arrive at wire
    No information about drift duration!
    For that, start time (t0) needed:
    t0 - tarrival ≈ tdrift
    vdrift = const → tdrift • vdrift = risochrone
    risochrone

    View Slide

  93. Mitglied der Helmholtz-Gemeinschaft
    STT — Drift Tubes and t0
    62
    Particle ionizes gas atoms in drift tubes
    Resolution without t0: (0.1 cm)
    Resolution with t0: (0.015 cm)
    Electrons drift to anode wire, ions to wall
    Signal only when electrons arrive at wire
    No information about drift duration!
    For that, start time (t0) needed:
    t0 - tarrival ≈ tdrift
    vdrift = const → tdrift • vdrift = risochrone
    risochrone

    View Slide

  94. Mitglied der Helmholtz-Gemeinschaft
    STT — Drift Tubes and t0
    62
    Particle ionizes gas atoms in drift tubes
    Resolution without t0: (0.1 cm)
    Resolution with t0: (0.015 cm)
    Usual HEP experiment: t0 by trigger
    But PANDA has no trigger…
    Electrons drift to anode wire, ions to wall
    Signal only when electrons arrive at wire
    No information about drift duration!
    For that, start time (t0) needed:
    t0 - tarrival ≈ tdrift
    vdrift = const → tdrift • vdrift = risochrone
    risochrone

    View Slide

  95. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    63
    STT
    More

    View Slide

  96. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    63
    STT
    More

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  97. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    63
    STT
    More

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  98. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    63
    STT
    More

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  99. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    • STT hit in pivot straw
    63
    STT
    More

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  100. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    • STT hit in pivot straw
    • Find surrounding hits
    → Create virtual hit (triplet)
    at center of gravity (cog)
    63
    STT
    More

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  101. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    • STT hit in pivot straw
    • Find surrounding hits
    → Create virtual hit (triplet)
    at center of gravity (cog)
    • Combine with
    63
    STT
    More

    View Slide

  102. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    • STT hit in pivot straw
    • Find surrounding hits
    → Create virtual hit (triplet)
    at center of gravity (cog)
    • Combine with
    1.Second STT pivot-cog virtual hit
    63
    STT
    More

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  103. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    • STT hit in pivot straw
    • Find surrounding hits
    → Create virtual hit (triplet)
    at center of gravity (cog)
    • Combine with
    1.Second STT pivot-cog virtual hit
    63
    STT
    More

    View Slide

  104. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    • STT hit in pivot straw
    • Find surrounding hits
    → Create virtual hit (triplet)
    at center of gravity (cog)
    • Combine with
    1.Second STT pivot-cog virtual hit
    63
    STT
    More

    View Slide

  105. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    • STT hit in pivot straw
    • Find surrounding hits
    → Create virtual hit (triplet)
    at center of gravity (cog)
    • Combine with
    1.Second STT pivot-cog virtual hit
    2.Interaction point
    63
    Interaction Point
    STT
    More

    View Slide

  106. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    • STT hit in pivot straw
    • Find surrounding hits
    → Create virtual hit (triplet)
    at center of gravity (cog)
    • Combine with
    1.Second STT pivot-cog virtual hit
    2.Interaction point
    • Calculate circle through three
    points
    63
    Interaction Point
    STT
    More

    View Slide

  107. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Method
    • STT hit in pivot straw
    • Find surrounding hits
    → Create virtual hit (triplet)
    at center of gravity (cog)
    • Combine with
    1.Second STT pivot-cog virtual hit
    2.Interaction point
    • Calculate circle through three
    points
    → Track Candidate
    63
    Interaction Point
    STT
    More

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  108. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Animation
    64
    Triplet
    Isochrone early
    Isochrone early & skewed
    Isochrone close
    Isochrone late
    MVD hit
    Track timed out
    Track current

    View Slide

  109. Dynamic
    Parallelism
    Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Optimizations
    • Compare data processing strategies
    65
    1 thread/bunch
    Calling
    kernel
    1 thread/bunch
    Calling
    kernel
    Triplet
    Finder
    1 thread/bunch
    Calling
    kernel
    1 block/bunch
    Joined
    kernel
    1 block/bunch
    Joined
    kernel
    1 block/bunch
    Joined
    kernel
    TF Stage #1
    TF Stage #2
    TF Stage #3
    TF Stage #4
    1 stream/bunch
    Combining
    stream
    1 stream/bunch
    Combining
    stream
    1 stream/bunch
    Calling
    stream
    Joined
    Kernel
    Host
    Streams
    Triplet
    Finder
    Triplet
    Finder
    CPU
    GPU
    TF Stage #1
    TF Stage #2
    TF Stage #3
    TF Stage #4
    TF Stage #1
    TF Stage #2
    TF Stage #3
    TF Stage #4

    View Slide

  110. Mitglied der Helmholtz-Gemeinschaft
    66
    Triplet Finder — Data Processing
    Explanation
    K20X

    View Slide

  111. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Binning: Sector Rows
    67
    • Sector Row testing
    – After found track:
    Hit association not with all hits of current window,
    but only with subset
    (first test rows of sector, then hits of row)
    More

    View Slide

  112. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Binning: Sector Rows
    67
    • Sector Row testing
    – After found track:
    Hit association not with all hits of current window,
    but only with subset
    (first test rows of sector, then hits of row)
    More

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  113. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Binning: Sector Rows
    67
    • Sector Row testing
    – After found track:
    Hit association not with all hits of current window,
    but only with subset
    (first test rows of sector, then hits of row)
    More

    View Slide

  114. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Binning: Sector Rows
    67
    • Sector Row testing
    – After found track:
    Hit association not with all hits of current window,
    but only with subset
    (first test rows of sector, then hits of row)
    More

    View Slide

  115. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Binning: Sector Rows
    67
    • Sector Row testing
    – After found track:
    Hit association not with all hits of current window,
    but only with subset
    (first test rows of sector, then hits of row)
    More

    View Slide

  116. Mitglied der Helmholtz-Gemeinschaft
    68
    Triplet Finder — Binning: Sector Rows
    K20X
    All Tubes (No Binning)
    Sector-Row Binning

    View Slide

  117. Mitglied der Helmholtz-Gemeinschaft
    69
    Triplet Finder — Binning: Skewlets
    K20X
    Skewlet Binning
    All Skewlets (No Binning)

    View Slide

  118. Mitglied der Helmholtz-Gemeinschaft
    70
    Triplet Finder — AoS vs. SoA
    K20X
    struct  {
           int  r,  g,  b;
    }  AoS[N];
    struct  {
           int  r[N];
           int  g[N];
           int  b[N];
    }  SoA;

    View Slide

  119. Mitglied der Helmholtz-Gemeinschaft
    71
    Triplet Finder — CUDA Versions
    K20X

    View Slide

  120. Mitglied der Helmholtz-Gemeinschaft
    72
    Triplet Finder — Clock Speed / GPU
    K40 3004 MHz, 745 MHz / 875 MHz
    K20X 2600 MHz, 732 MHz / 784 MHz
    Memory Clock Core Clock GPU Boost

    View Slide

  121. Mitglied der Helmholtz-Gemeinschaft
    73
    Triplet Finder — Comparison to Kepler
    K20X 750 Ti
    Kepler
    Performance: 3.95 TFLOPSsingle
    Price: 3600 €
    Maxwell
    Performance: 1.3 TFLOPSsingle
    Price: 130 €

    View Slide

  122. Mitglied der Helmholtz-Gemeinschaft
    74
    Triplet Finder — Kepler vs. Maxwell
    K20X 750 Ti

    View Slide

  123. Mitglied der Helmholtz-Gemeinschaft
    75
    Triplet Finder — Kepler vs. Maxwell
    Performance per multiprocessor
    K20X
    750 Ti

    View Slide

  124. Mitglied der Helmholtz-Gemeinschaft
    75
    Triplet Finder — Kepler vs. Maxwell
    Performance per multiprocessor
    K20X
    750 Ti

    View Slide

  125. Tesla K40 Tesla K20X GeForce GTX 760 Ti
    Peak double
    performance
    Peak single
    performance
    GPU Chipset
    # CUDA Cores
    Memory size
    Memory
    bandwidth
    1.46 TFLOPS 1.31 TFLOPS 0.04 TFLOPS
    4.29 TFLOPS 3.95 TFLOPS 1.3 TFLOPS
    GK110B GK110 GM107
    2880 2688 640
    12 GB 6 GB 2 GB
    288 GByte/s 250 GByte/s 192 GByte/s
    Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Optimizations
    • Impact of chipset
    76
    Source: http://www.nvidia.com/content/tesla/pdf/NVIDIA-Tesla-Kepler-Family-Datasheet.pdf

    View Slide

  126. Mitglied der Helmholtz-Gemeinschaft
    Triplet Finder — Kernel Launch Strategies
    • Joined Kernel (JK): slowest
    – High # registers → low occupancy
    • Dynamic Parallelism (DP) / Host Streams (HS): comparable performance
    – Performance
    • HS faster for small # processed hits, DP faster for > 45000 hits
    • HS stagnates there, while DP continues rising
    – Limiting factor
    • High # of required kernel calls
    • Kernel launch latency
    • Memcopy
    – HS more affected by this, because
    • More PCI-E transfers (launch configurations for kernels)
    • Less launch throughput, kernel launch latency gets more important
    • False dependencies of launched kernels
    – Single CPU thread handles all CUDA streams (Multi-thread possible, but
    synchronization overhead too high for good performance)
    – Grid scheduling done on hardware (Grid Management Unit) (DP: software)
    » False dependencies when N(streams) > N(device connections)=323.5
    77
    Back

    View Slide

  127. Mitglied der Helmholtz-Gemeinschaft
    78
    ALGORITHMS #2
    Hough Transform
    Riemann Track Finder
    Triplet Finder

    View Slide

  128. Mitglied der Helmholtz-Gemeinschaft
    79
    Riemann Track Finder — Method
    • Idea: Don‘t fit lines (in 2D), fit planes (in 3D)!
    • Create seeds
    – All possible three hit combinations
    • Grow seeds to tracks
    Continuously test next hit if it fits
    – Use mapping to Riemann paraboloid (+ s-z fit, det. layer)
    x
    x
    x
    x
    y
    z‘
    x
    x
    x
    y
    x
    x
    x
    x
    y
    x
    More on: Seeds; Growing
    1
    2

    View Slide

  129. Mitglied der Helmholtz-Gemeinschaft
    80
    1 2 3 4 5
    1
    2
    3
    4
    5
    Riemann Algorithm — 1 Triplets
    1
    Layer number

    View Slide

  130. Mitglied der Helmholtz-Gemeinschaft
    80
    1 2 3 4 5
    1
    2
    3
    4
    5
    Riemann Algorithm — 1 Triplets
    1
    Layer number

    View Slide

  131. Mitglied der Helmholtz-Gemeinschaft
    80
    1 2 3 4 5
    1
    2
    3
    4
    5
    Riemann Algorithm — 1 Triplets
    1
    Layer number

    View Slide

  132. Mitglied der Helmholtz-Gemeinschaft
    80
    1 2 3 4 5
    21
    11 31
    1
    2
    3
    4
    5
    Riemann Algorithm — 1 Triplets
    1
    Layer number

    View Slide

  133. Mitglied der Helmholtz-Gemeinschaft
    80
    1 2 3 4 5
    21
    11 31
    31
    11 41
    1
    2
    3
    4
    5
    Riemann Algorithm — 1 Triplets
    1
    Layer number

    View Slide

  134. Mitglied der Helmholtz-Gemeinschaft
    80
    1 2 3 4 5
    21
    11 31
    31
    11 41
    31
    11 32
    1
    2
    3
    4
    5
    Riemann Algorithm — 1 Triplets
    1
    Layer number

    View Slide

  135. Mitglied der Helmholtz-Gemeinschaft
    80
    1 2 3 4 5
    21
    11 31
    31
    11 41
    31
    11 32
    1
    2
    3
    4
    5
    Riemann Algorithm — 1 Triplets
    1
    Layer number

    View Slide

  136. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2

    View Slide

  137. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘

    View Slide

  138. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘
    x
    x
    x
    y
    x
    Riemann Surface
    (paraboloid)

    View Slide

  139. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘
    x
    x
    x
    y
    x
    Riemann Surface
    (paraboloid)

    View Slide

  140. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘
    x
    x
    x
    y
    x
    Riemann Surface
    (paraboloid)

    View Slide

  141. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘
    x
    x
    x
    y
    x
    Riemann Surface
    (paraboloid)

    View Slide

  142. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘
    x
    x
    x
    y
    x
    Riemann Surface
    (paraboloid)

    View Slide

  143. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘
    x
    x
    x
    y
    x
    Riemann Surface
    (paraboloid)
    x

    View Slide

  144. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘
    x
    x
    x
    y
    x
    Riemann Surface
    (paraboloid)
    x

    View Slide

  145. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘
    x
    x
    x
    y
    x
    Riemann Surface
    (paraboloid)
    x

    View Slide

  146. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘
    x
    x
    x
    y
    x
    Riemann Surface
    (paraboloid)
    x

    View Slide

  147. Mitglied der Helmholtz-Gemeinschaft
    81
    Riemann Algorithm — 1 Expansion
    2
    x
    x
    x
    x
    y
    z‘
    Expand to z‘
    x
    x
    x
    y
    x
    Riemann Surface
    (paraboloid)
    x

    View Slide

  148. Mitglied der Helmholtz-Gemeinschaft
    82
    Riemann Track Finder — GPU Adaptations
    CPU GPU

    View Slide

  149. Mitglied der Helmholtz-Gemeinschaft
    82
    Riemann Track Finder — GPU Adaptations
    CPU GPU
    3 loops to generate seeds
    serially
    for (int i = 0; i < hitsInLayerOne.size(); i++) {
    for (int j = 0; j < hitsInLayerTwo.size(); j++) {
    for (int k = 0; k < hitsInLayerThree.size(); k++) {
    /* Triplet Generation */
    }
    }
    }
    Needed: Mapping of
    inherent GPU indexing
    variable to triplet index
    int ijk = threadIdx.x + blockIdx.x * blockDim.x;
    nLayerx
    = 1
    2
    ⇣p
    8x
    +
    1 1

    pos
    (
    nLayerx
    ) =
    3
    pp
    3
    p
    243x2 1
    +
    27x
    32
    /
    3
    + 1
    3
    p
    3
    3
    pp
    3
    p
    243x2 1
    +
    27x
    1
    1

    View Slide

  150. Mitglied der Helmholtz-Gemeinschaft
    82
    Riemann Track Finder — GPU Adaptations
    CPU GPU
    3 loops to generate seeds
    serially
    for (int i = 0; i < hitsInLayerOne.size(); i++) {
    for (int j = 0; j < hitsInLayerTwo.size(); j++) {
    for (int k = 0; k < hitsInLayerThree.size(); k++) {
    /* Triplet Generation */
    }
    }
    }
    Needed: Mapping of
    inherent GPU indexing
    variable to triplet index
    int ijk = threadIdx.x + blockIdx.x * blockDim.x;
    nLayerx
    = 1
    2
    ⇣p
    8x
    +
    1 1

    pos
    (
    nLayerx
    ) =
    3
    pp
    3
    p
    243x2 1
    +
    27x
    32
    /
    3
    + 1
    3
    p
    3
    3
    pp
    3
    p
    243x2 1
    +
    27x
    1
    1
    2
    Port of CPU code;
    parallelism on seed base
    Only easy computations;
    e.g. 3x3 matrices

    View Slide

  151. Mitglied der Helmholtz-Gemeinschaft
    82
    Riemann Track Finder — GPU Adaptations
    CPU GPU
    → 100 × faster than CPU version: ~0.6 ms/event
    Still needs merging into PandaRoot
    3 loops to generate seeds
    serially
    for (int i = 0; i < hitsInLayerOne.size(); i++) {
    for (int j = 0; j < hitsInLayerTwo.size(); j++) {
    for (int k = 0; k < hitsInLayerThree.size(); k++) {
    /* Triplet Generation */
    }
    }
    }
    Needed: Mapping of
    inherent GPU indexing
    variable to triplet index
    int ijk = threadIdx.x + blockIdx.x * blockDim.x;
    nLayerx
    = 1
    2
    ⇣p
    8x
    +
    1 1

    pos
    (
    nLayerx
    ) =
    3
    pp
    3
    p
    243x2 1
    +
    27x
    32
    /
    3
    + 1
    3
    p
    3
    3
    pp
    3
    p
    243x2 1
    +
    27x
    1
    1
    2
    Port of CPU code;
    parallelism on seed base
    Only easy computations;
    e.g. 3x3 matrices

    View Slide

  152. Mitglied der Helmholtz-Gemeinschaft
    Algorithm: Hough Transform
    • Idea: Transform (x,y)i → (α,r)ij, find lines via (α,r) space
    • Solve rij line equation for
    – Lots of hits (x,y,ρ)i
    and
    – Many αj ∈ [0°,360°) each
    • Fill histogram
    • Extract track parameters
    83
    x
    y
    x
    y
    Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Princip
    → Bin
    giv
    r
    α

    View Slide

  153. Mitglied der Helmholtz-Gemeinschaft
    Algorithm: Hough Transform
    • Idea: Transform (x,y)i → (α,r)ij, find lines via (α,r) space
    • Solve rij line equation for
    – Lots of hits (x,y,ρ)i
    and
    – Many αj ∈ [0°,360°) each
    • Fill histogram
    • Extract track parameters
    83
    rij =
    cos
    ↵j
    ·
    xi +
    sin
    ↵j
    ·
    yi + ⇢i
    i: ~100 hits/event (STT)
    j: every 0.2° rij: 180 000
    x
    y
    x
    y
    Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Princip
    → Bin
    giv
    r
    α

    View Slide

  154. Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Granularity
    84
    • Line Hough around point
    α = 0°, 2°, 4°, …
    α = 0°, 2°, 4°, …
    rij = cos(αj) ⋅ xi + sin(αj) ⋅ yi static slide

    View Slide

  155. Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Granularity
    84
    • Line Hough around point
    α = 0°, 2°, 4°, …
    α = 0°, 2°, 4°, …
    rij = cos(αj) ⋅ xi + sin(αj) ⋅ yi static slide

    View Slide

  156. Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Granularity
    84
    • Line Hough around point
    α = 0°, 2°, 4°, …
    α = 0°, 2°, 4°, …
    rij = cos(αj) ⋅ xi + sin(αj) ⋅ yi static slide

    View Slide

  157. Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Variations
    85
    • Line Hough with isochrones
    α = 0°, 10°, 20°, …
    α = 0°, 10°, 20°, …
    rij
    ± = cos(αj) ⋅ xi + sin(αj) ⋅ yi ± ρi static slide

    View Slide

  158. Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Variations
    85
    • Line Hough with isochrones
    α = 0°, 10°, 20°, …
    α = 0°, 10°, 20°, …
    rij
    ± = cos(αj) ⋅ xi + sin(αj) ⋅ yi ± ρi static slide

    View Slide

  159. Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Variations
    85
    • Line Hough with isochrones
    α = 0°, 10°, 20°, …
    α = 0°, 10°, 20°, …
    rij
    ± = cos(αj) ⋅ xi + sin(αj) ⋅ yi ± ρi static slide

    View Slide

  160. Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Remarks
    86
    °
    /
    α
    0 20 40 60 80 100 120 140 160 180
    r
    -30
    -20
    -10
    0
    10
    20
    30
    40
    HoughHist
    Entries 9000
    Mean x 89.33
    Mean y 6.66
    RMS x 51.8
    RMS y 19.2
    0
    2
    4
    6
    8
    10
    12
    14
    16
    18
    HoughHist
    Entries 9000
    Mean x 89.33
    Mean y 6.66
    RMS x 51.8
    RMS y 19.2
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    Hill Climber
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  161. Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Remarks
    86
    °
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    Mean y 6.66
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    Mean x 89.6
    Mean y 9.719
    RMS x 51.78
    RMS y 18.09
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  162. 2015-01-24 16:11:25
    #Hits
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    Entries 400000
    Mean 0.0152
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    RMS 0.01075
    ±
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    Underflow 0
    Overflow 12
    : #FTS Hits
    +
    π
    2015-01-24 16:11:25
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    Mean 0.003999
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    RMS 0.002828
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    Underflow 0
    Overflow 8
    : #GEM Hits
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    π
    2015-01-24 16:11:27
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    counts
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    Entries 29006
    Mean 0.0003544
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    RMS 0.0002506
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    Underflow 0
    Overflow 1768
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    θ
    :
    +
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    Mitglied der Helmholtz-Gemeinschaft
    Sub-Detector Hit Counting
    87
    π+: θ for no GEM hits and for no FTS hits
    2015-01-25 17:09:14
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    Mean 0.0003124
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    RMS 0.0002209
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  163. 2015-01-25 17:22:23
    θ
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    Mitglied der Helmholtz-Gemeinschaft
    Sub-Detector Hit Counting
    88
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    2015-01-25 17:22:22
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  164. Mitglied der Helmholtz-Gemeinschaft
    89
    D Meson Production Cross Section
    6.0 6.5 7.0 7.5 8.0
    p
    lab
    (GeV/c)
    6.0 6.5 7.0 7.5 8.0
    p
    lab
    (GeV/c)
    10-3
    10-2
    10-1
    100
    σ
    tot
    (µb)
    pp -> D+
    D-
    FIG. 3: Total reaction cross sections for ¯
    pp → D ¯
    D as a func-
    tion of plab
    , based on baryon-exchange (shaded band) and
    the quark model (grid). Results obtained in Born approx-
    imation are indicated by the dotted (baryon-exchange) and
    Baryon Exchange Model
    Quark Model
    p
    lab
    (GeV/c)
    6.0 6.5 7.0 7.5 8.0
    p
    lab
    (GeV/c)
    10-3
    10-2
    10-1
    100
    σ
    tot
    (µb)
    pp -> D+
    D-
    3: Total reaction cross sections for ¯
    pp → D ¯
    D as a func-
    of plab
    , based on baryon-exchange (shaded band) and
    uark model (grid). Results obtained in Born approx-
    on are indicated by the dotted (baryon-exchange) and
    dotted (quark model) lines, respectively.
    lab
    6.0 6.5 7.0 7.5 8.0
    p
    lab
    (GeV/c)
    10-3
    10-2
    10-1
    100
    σ
    tot
    (µb)
    pp -> D+
    D-
    3: Total reaction cross sections for ¯
    pp → D ¯
    D as a func-
    of plab
    , based on baryon-exchange (shaded band) and
    uark model (grid). Results obtained in Born approx-
    on are indicated by the dotted (baryon-exchange) and
    dotted (quark model) lines, respectively.
    J. Haidenbauer, G. Krein; Production of charmed pseudoscalar mesons
    in antiproton-proton annihilation; arXiv:1404.4174 [hep-ph] (04-2014)
    from Foley et al. [43], Berglund et al. [47], Russ et al. [48],
    Λ,Σ,
    Σ(1385)
    K K
    N N
    ✉ ✉ ↔
    Λc
    ,Σc
    ,
    Σc
    (2520)
    D D
    N N
    ✉ ✉
    FIG. 2: Transition potential for ¯
    NN → D ¯
    D (right) and
    ¯
    NN → ¯
    KK (left), respectively.
    D ¯
    D, ¯
    NN = V D ¯
    D, ¯
    NN
    + V D ¯
    D, ¯
    NN G ¯
    NN T ¯
    NN, ¯
    NN , (5)
    he ¯
    NN potential described in Sect. II.
    Eq. (5) implies that the ¯
    NN → D ¯
    D transition
    s effectively evaluated in a DWBA.
    with inclusion of ISI effects are presented as
    ig. 3 because we consider several variants of
    otential as discussed in the previous section.
    s that the results change drastically once the
    ded in the calculation. The cross sections for
    trongly reduced while at the same time those
    are enhanced. Indeed now both D ¯
    D channels
    d at a comparable rate. In fact, the predicted
    n for D+D− appears to be even somewhat
    the one for D0 ¯
    D0.
    the reduction in the D0 ¯
    D0 case is in line
    arable effects observed in the previous stud-
    annihilation processes [23, 25–27], as men-
    ve, the enhancement seen for D+D− may be
    6.0 6.5 7.0 7.
    p
    lab
    (GeV/c)
    10-3
    10-2
    10-1
    100
    σ
    tot
    (µb)
    FIG. 3: Total reaction cross sections for ¯
    pp
    tion of plab
    , based on baryon-exchange (s
    the quark model (grid). Results obtained
    imation are indicated by the dotted (bary
    dash-dotted (quark model) lines, respective
    Q Q
    q q q q
    FIG. 4: Microscopic quark-model mechanism for the
    tion potential: annihilation of two pairs of light quark

    u, d ¯
    d, and creation of a pair of heavier quarks, Q ¯
    Q =

    cc) is created – see Fig. 4. We base our study
    model of Kohno and Weise (KW) [28] for the ¯
    pp
    reaction; we replace parameters corresponding
    s−quark and K−meson of that model by those
    c−quark and D−meson. The quark-model ¯
    NN
    transition potential V ¯
    NN→D ¯
    D
    Q
    (t) can be written
    V ¯
    NN→D ¯
    D
    Q
    (t) = χ†
    ¯
    N
    [h1
    (t) σ · p + h2
    (t) σ · p] χN
    cutoff mass below.
    us now focus on the effects of the initial state inter-
    Those effects are included by solving the formal
    d-channel equations
    T ¯
    NN, ¯
    NN = V ¯
    NN, ¯
    NN
    + V ¯
    NN, ¯
    NN G ¯
    NN T ¯
    NN, ¯
    NN , (4)
    T D ¯
    D, ¯
    NN = V D ¯
    D, ¯
    NN
    + V D ¯
    D, ¯
    NN G ¯
    NN T ¯
    NN, ¯
    NN , (5)
    ng the ¯
    NN potential described in Sect. II.
    rse, Eq. (5) implies that the ¯
    NN → D ¯
    D transition
    ude is effectively evaluated in a DWBA.
    ults with inclusion of ISI effects are presented as
    in Fig. 3 because we consider several variants of
    N potential as discussed in the previous section.
    bvious that the results change drastically once the
    ncluded in the calculation. The cross sections for
    are strongly reduced while at the same time those
    +D− are enhanced. Indeed now both D ¯
    D channels
    oduced at a comparable rate. In fact, the predicted
    section for D+D− appears to be even somewhat
    than the one for D0 ¯
    D0.
    ereas the reduction in the D0 ¯
    D0 case is in line
    omparable effects observed in the previous stud-
    ¯
    NN annihilation processes [23, 25–27], as men-
    above, the enhancement seen for D+D− may be
    6.0 6.5 7.0 7.5
    p
    lab
    (GeV/c)
    10-3
    10-2
    6.0 6.5 7.0 7.5
    p
    lab
    (GeV/c)
    10-3
    10-2
    10-1
    100
    σ
    tot
    (µb)
    p
    FIG. 3: Total reaction cross sections for ¯
    pp
    tion of plab
    , based on baryon-exchange (sh
    the quark model (grid). Results obtained
    imation are indicated by the dotted (baryo
    dash-dotted (quark model) lines, respectivel
    82

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