Introduction of WireCell Tomography Reconstruction Xin Qian BNL

Introduction of Wire-Cell Tomography Reconstruction Xin Qian BNL 1

Outline • Challenges in LAr. TPC Reconstruction and Wire -Cell concept • LAr. TPC Signal Processing • Wire-Cell Imaging • Wire-Cell Pattern Recognition 2

Principle of Single-Phase LAr. TPC time • LAr. TPC has mm scale position resolution • Energy deposition and topology can be used to do PID 3

Comparison with Existing Fine-Grain Tracking Detectors • Wire readout is necessary due to external constraints – Heat consumption, cost … • Wire plane is in general parallel to the beam direction 4

Challenges in LAr. TPC Reconstruction (I) • LAr. TPC is required to have high signal efficiency (~80%) and low backgrounds over a wide neutrino energy range – Complicated nuclear physics: QE + RES + DIS • NOνA: focused on 2 Ge. V, 35% signal efficiency relative to the containment cut DUNE 5

Challenges in LAr. TPC Reconstruction (I) • High resolution of LAr. TPC should result high efficiency and low background • Also help in reducing systematics due to nuclear response with excellent hadron detection from π+ μ+ e+ p e p from π6

Challenges in LAr. TPC Reconstruction (II) LAr. TPC • High density (Z ~ 18) Liquid Scintillator • Low density (Z ~ 6) – Event are more compact • Parallel wire readout w. r. t. the beam direction • Perpendicular wire readout w. r. t. the beam direction – More ambiguities • Slow detector response (~ms) • Fast detector response (~10 ns) – Challenges in rejecting cosmics for detector on surface • Ultra-high resolution – A layer ~ 3. 5% X 0 (14 cm R. L. ) • Higher physics requirement – ~ 80% efficiency • High resolution – A layer ~ 15% X 0 (44 cm) • ~35% efficiency in NOνA 7

Challenges in Reconstruction with Wire Readout u 2 u 1 At fixed time v 3 True Hits v 2 Fake Hits • Use two-plane as an example • Red points are true hits • Blue ones are fake hits • At u 1, there are two hits, so u 1 will see the total change of both hits 8

Traditional Solution: • Use the time information first – Track should be continuous in time • Do cluster/tracking in 2 -D (time vs. wire number) • Combine three planes into 3 -D tracking • Difficult for Shower, when there are many tracks • 3 D reconstruction is crucial for direction reconstruction, energy reconstruction as well as PID Time Wire Number 9

New input from Charge • We can in principle remove faked hit by looking at the charge information – Find out all potential hits including faked hits (Hi) – We can then form a matrix, which represents the geometry knowledge v 3 u 2 True Hits u 1 At fixed time v 2 H 1 H 2 H 4 v 1 Fake Hits H 3 H 5 H 6 With charge in each point solved, fake hits would naturally have small (close to 10 zero) charge

Wire-Cell 3 D Reconstruction • Wire-Cell Imaging: – 2 D images at fixed time slice are reconstructed – 2 D images are then stitched together to form 3 D object • Wire-Cell Pattern Recognition: – 3 D objects are identified before calculation of physics quantities 11

Strategy Comparison (Xin’s View) Traditional 2 D Reconstruction • Start with 2 D (time + wire) • 2 D pattern recognition – Particle track information • Matching 2 D patterns into 3 D objects Wire-Cell 3 D Tomography • Start with 2 D (at fixed time) • 2 D image reconstruction – Explicit Time + Charge information – Some connectivity information can be used – Time information (start/end of • 3 D image reconstruction clusters) – Straight forward – Some charge information to • 3 D Pattern recognition remove ambiguities in matching – Tracks – 3 D track-like objects for both – Showers tracks and showers • MC truth are needed to evaluate efficiency • Imaging vs. recognized pattern can be used to evaluate efficiency 12

Discussions • Wire-Cell uses more (explicitly) Time+Charge information than traditional 2 D reconstruction • Wire-Cell uses less particle track information – Less powerful in track reconstruction (i. e. dealing with gaps in detectors due to dead channels) – Advantages in reconstructing showers • Wire-Cell delays the pattern recognition – Errors from imperfect pattern recognition will propagate in the entire reconstruction chain • Wire-Cell does not use Gaussian hit information (will discuss more later) 13

Potential Advantages of Wire-Cell Concept • Note: some of these have not been demonstrated yet • 3 D reconstruction of shower will provide better information in its – – Direction: 3 D direction fit Energy: 3 D clustering PID: profile likihood My prediction: better photon rejection and better pi 0 peak resolution • Imaging and pattern recognition are separated: – 3 D imaging vs. pattern recognition can be used to evaluate efficiency – 3 D imaging can take advantages of human’s superior capability in pattern recognition (Bee 2. 0) 14

Outline • Challenges in LAr. TPC Reconstruction and Wire -Cell concept • LAr. TPC Signal Processing • Wire-Cell Imaging • Wire-Cell Pattern Recognition 15

Overview of Signal Processing Number of ionized electrons V. Radeka Field Response Signal on Wire Plane Electronics Response Signal to be digitized by ADC (Deconvolution) High-level tracking … time • TPC signal consists of time and charge information from induction and collection planes • Same amount charge was seen by all the wire planes • The goal of signal processing is to extract both time and charge information reliably 16

What will affect TPC signal? • E-field: – Electron drift velocity – Recombination factor d. E/dx fluctuations MPV: ~ 1. 8 Me. V/cm • Electron lifetime – Drift distance drift time signal size • Track angle – Time structure of signal • d. E/dx – Recombination etc. • Diffusion 17

Field and Electronics Response Leon, SLAC • Charge vs. Time averaged for a single electron Cold electronics: • Difference between simulation and data • 4 shaping time (0. 5, 1. 0, 2. 0, 3. 0 us) (bigger signal in Long. Bo ar. Xiv: 1504: 00398) • 4 gain (4. 7, 7. 8, 14, 25 m. V/f. C) 18

Convolution of Field and Electronics Response for Single Electron (4. 7 m. V/f. C) • Now, we can consider tracks – – Define beam direction to be z (parallel to the wire plane) Polar angle Θ and azimuthal angle φ W-wire is thus cos Θ=0 and φ=π/2 Beam direction is thus cos Θ=1 19

MIP (100 cm) + 3 ms Tele + 3. 5 m drift distance Strong angular dependence for signal height • The charge per tick is the highest when the track is parallel to the wire • The charge per tick is the smallest when the track is perpendicular to the wire, and travelling toward the wire • One tick = 0. 8 mm @ 0. 5 k. V/cm vs. wire pitch of 5 mm 20

MIP (100 cm) + 3 ms Tele + 3. 5 m drift distance Strong angular dependence for signal length • The signal length is the highest when the track is perpendicular to the wire, and travelling toward the wire • The minimum signal length is due to the longitudinal diffusion • Both signal height (# of electrons) and signal length would contribute to signal to noise ratio for the digitized signal 21

Deconvolution Frequency Content Time domain Fourier transformation Frequency domain Back to time domain Anti-Fourier transformation Deconvoluted Signals The goal of deconvolution is to help extract charge and time information from TPC signals Time Domain 22

Deconvolution and Matrix Inversion Time domain • We can also write the formula in a discrete manner Fourier transformation • If there is no filter function in the deconvolution process , the FFT deconvolution is Frequency domain basically equivalent to the matrix inversion problem Anti-Fourier transformation Back to time domain 23

Matrix Inversion and Chi-square • Matrix inversion can be derived through Chi-square Now, we recovered the solution in the previous slice The last equation is in matrix format 24

Adding a Penalty in Chi-square • Let’s use the second derivative to penalty • The second derivative can be written as • , in this case 25

Continue • The solution is thus • So, we have an additional term of applied to the original solution 26

A in Matrix vs. Filter in Deconvolution • A in matrix format is multiplied to the original solution effective a smearing function • Filter in deconvolution is effective a smearing function • Therefore, we can conclude that they are equivalent! – Filter is equivalent to a penalty in the chi-square – Filter is equivalent to a smearing function 27

A new Challenge: Dynamic Induced Charge V. Radeka Ann. Rev. Nucl. Part. Sci. 38, 217, 1988 v: velocity Ew: weighting field qm: charge Bo Yu for Micro. Boo. NE configuration 28

Dynamic Induced Charge • In reality, we know that the signal strength depends on the distance between electrons and wires • Diffusion will help to average electron’s position • Intrinsic d. E/dx fluctuation and track angle will lead to difference • This is why the TPC wire-planes are placed 29 parallel w. r. t beam direction

Bo’s Garfield Simulation 1. 7 deg 45 deg • Due to this induced signal on adjacent wire, the digitized signal on wires becomes more complicated and have stronger dependence on the track angle etc • This becomes a new challenge in the signal processing 30

Deconvolution with Induced Signal i. e. a 45 degree track • If there is a discrepancy between the convolution kernel and deconvolution kernel, the deconvoluted signal will not be correct (i. e. charge and time) 31

Double Deconvolution • With induced signals, the signal is still linear sum of direct signal and induced signal – R 1 represents the induced signal from i+1 th wire signal to ith wire – Si and Si+1 are not directly related The inversion of matrix R can again be done with deconvolution through 2 -D FFT 32

Outline • Challenges in LAr. TPC Reconstruction and Wire -Cell concept • LAr. TPC Signal Processing • Wire-Cell Imaging • Wire-Cell Pattern Recognition 33

Wire-Cell 3 D Reconstruction • Wire-Cell Imaging: – 2 D images at fixed time slice are reconstructed – 2 D images are then stitched together to form 3 D object • Wire-Cell Pattern Recognition: – 3 D objects are identified before calculation of physics quantities 34

Steps of Wire-Cell Imaging • Tiling: – Create Cells from Wires • Merging: – Significantly reduce number of unknowns at the cost of reducing knowns • Solving: – Matrix Inversion • Searching: – Advanced techniques are used to find the optimal solution 35

Signal Processing (I) • Currently, 1 D deconvolution is used – No treatment of dynamic induced charge yet (existing in toy model study) – How to calibrate 2 D response function with point source? • Raw signal are deconvoluted twice – Normalized Wiener filters (one for each plane) • Best signal to noise ratio • To judge if a wire is fired or not – Gaussian filter (same for all planes) • Gaussian smearing function • To obtain charge information 36

Signal Processing (II) Time (us) Frequency (A. U. ) • Wiener filters negative component in the smearing function necessary for the best signal to noise ratio • Gaussian filter no-negative component in the smearing function good for charge matching among three planes, but worse signal to noise ratio 37

Definition of Time Slice Signal Processing, Jyoti Joshi • Wire-Cell abandon the concept of “hit” in order to avoid complications in fitting waveform • A time slice is currently taken as 2 us (4 ticks) to match the electronic shaping time (2 us) • Wire in a time slice is fired judging by deconvoluted signals (Wiener filter) • Charge in a time slice is the sum of its deconvoluted signals (Gaussian filter) 38

Tiling • Wire: wire +- pitch/2 • Cell: overlap of three wires (each in U, V, and W) • Tiling: form cells from wires • W: measured charge in a wire • C: expected charge in a cell • G: a matrix containing geometry information connecting wire and cell Mike Mooney Cell. Maker 39

Merging • Merged cell all cells that are connected • Merged wire associated with merged cell 40

Solving C: charge in each (merged) cell G: Geometry matrix connecting cells and wires W: charge in each single wire B: Geometry matrix connecting merged wires and single wires • VBW: Covariance matrix describing uncertainty in wire charge • • 41

Same formulism for DUNE Wrapped Wire • C: charge in each (merged) cell • G: Geometry matrix connecting cells and channels • W: charge in each single channel • B: Geometry matrix connecting merged channels and single channels • VBW: Covariance matrix describing uncertainty in channel charge Xiaoyue Li (Stony Brook) 42

Searching (I) • Sometimes, the matrix can not be inverted – The number of constraints is larger than the number of unknowns – There are infinite amount of solutions can give ~ zero χ2 • We need a unique solution to proceed the remaining reconstruction chain • We need to find the “optimal” solution (more in the next few slides) 43

Searching (II) • To obtain a unique solution: 1. One of the merged cells is chosen to be eliminated 2. All matrices including “M” are updated 3. If the number of zero eigenvalues are not reduced, go back to 1. and switch to another merged cell 4. If the number of zero eigenvalues are reduced, go to 1. and pick one more merged cell 5. Stop till there are no zero eigenvalues. Since the matrix can be inverted, we thus reach a unique solution 6. This solution can plug back into the χ2 formula to calculate its value • The optimal solution is a unique solution which gives rise to the smallest χ2 44

Challenges in Reconstruction with Wire Readout u 2 u 1 v 3 True Hits v 2 v 1 At fixed time Fake Hits • Use two-plane as an example • Red points are true hits • Blue ones are fake hits • At u 1, there are two hits, so u 1 will see the total change of both hits 45

Example u 2 u 1 v 3 True Hits v 2 v 1 At fixed time Fake Hits Eigenvalues: 5, 3, 2, 2, 0, 0 • We need to remove two hits to solve • For each combination, we can calculate a χ2 • The unique solution with minimal χ2 is defined as the final optimal solution 46

About Searching Speed • In the previous example, we need to remove two out of six possible hit locations. Naively, we have combinations • This number can increase quickly. For example, • It is thus not practical to go through all possible combinations to find the optimal solution • We use Markov-Chain Monte Carlo (MCMC) to speed up the searching 47

Markov-Chain Monte Carlo • Start with a solution – Calculate charge residual for all merged cell • Assign a probability threshold for each merged cell – High probability for high charge merged cell – High probability for low residual charge merged cell – High probability for merged cell which connected to good merged cells from adjacent time slice • Use Monte Carlo to judge if a merged cell is included in the solution or not • Need to make sure the matrix can be inverted for a set of merged cells • Need to make sure all the merged cells are either added or removed when matrix can not be inverted – Maximal set of merged cell • Repeat the procedure and save the better solution (smaller 48 χ2 )

Performance 49

For 3 D demo, visit http: //www. phy. bnl. gov/wirecell/examples/mvd/nue-cc-v 2/#/1 Electron Shower Hadronic Shower Details about “Bee” can be found at Chao Zhang db-4494 50

For 3 D demo, visit http: //www. phy. bnl. gov/wire-cell/examples/list/ Neutral pion Neutrino interaction buried under cosmics Details about “Bee” can be found at Chao Zhang db-4494 51

The Usage of Connectivity • The requirement of “unique” solution is very strong – It is possible that the matrix can not be inverted given the truth information (i. e. it is possible that we lost too much information) • When we solve for one time slice, we do not really know the other time slice, so sometimes the track can be broken 52

Examples • http: //www. phy. bnl. gov/wirecell/bee/set/451 b 9 c 39 -3312 -4 aec-a 07 c 9376 ba 6 b 12 c 8/event/0/ • http: //www. phy. bnl. gov/wirecell/bee/set/ee 2 fd 0 e 7 -98 e 7 -49 b 5 -951 ea 724 a 10395 df/event/0/ • http: //www. phy. bnl. gov/wirecell/bee/set/8/event/7/ 53

The Usage of Connectivity • We can add penalty to χ2 based on connectivity and single channel assumption – For example, if we remove a merged cell that are connected to good cells in the adjacent time slice, we can add penalty in χ2 to increase the chi-square value less chance to be chosen as the optimal solution • For later pattern recognition, we can also cluster with all merged cell, and then remove bad ones taking into account connectivity 54

Comparison of One Event Without Connectivity With Connectivity 55

Another Event with Wrapped Wire • Before: – http: //www. phy. bnl. gov/wirecell/bee/set/ee 2 fd 0 e 7 -98 e 7 -49 b 5 -951 ea 724 a 10395 df/event/0/ • After: – http: //www. phy. bnl. gov/wirecell/bee/set/288 d 120 e-91 b 4 -4 b 15 -b 29 ed 56260 e 8 fc 32/event/0/

Another Event with Wrapped Wire • Before: – http: //www. phy. bnl. gov/wirecell/bee/set/451 b 9 c 39 -3312 -4 aec-a 07 c 9376 ba 6 b 12 c 8/event/0/ • After: – http: //www. phy. bnl. gov/wirecell/bee/set/afa 6 b 1 cb-149 a-4458 -9 a 3 af 19 c 6 eebc 9 b 2/event/0/ 57

Outline • Challenges in LAr. TPC Reconstruction and Wire -Cell concept • LAr. TPC Signal Processing • Wire-Cell Imaging • Wire-Cell Pattern Recognition 58

What’s the challenge of Tracking/Clustering? • Operations are all at “low-level” i. e. Hough transformation, Crawler, Vertex fitting/merging … • Too many different topologies many corner cases • There is no silver bullet, and has to accumulate experience gradually and patiently 59

Current Pattern Recognition Chain • 3 D Clustering – Categorize the merged cells • (non-parallel) Track and Vertex Identification – Find out non-parallel tracks • Parallel Track Identification • Shower Identification (not finished) • Short-track identification 60

Clustering • Clusters are made based on connectivity • Seed of track finding and vertex fitting • Clusters sometimes are merged based on angles (Hough Transformation) 61

Clusters (II) 62

(Non-Parallel) Track Reconstruction • Three categories: – Tracks not parallel to wire-plane (Done) – Red: Vertices – Magenta: tracks 63

Track Reconstruction • Three categories: – Tracks not parallel to wire-plane (Done) – Tracks parallel to the wire-plane (Done) • Objects are thin in the 2 -D projected view • Showers are generally fat in the 2 -D projected view 64

More on tracks Magenta: regular tracks or parallel tracks Red: bad tracks Blue: short tracks 65

Shower Identification • Showers are objects – Extended object in 3 D (i. e. fat in the projected 2 D view) – This is different from parallel tracks • Showers’ topology is very different from tracks – Can contain many isolated pieces • Program need to separate showers from tracks – Single shower like – Shower + tracks • For a shower, the important information are – Primary vertex, initial track for d. E/dx, angle, and energy 66

Progress on Shower Reconstruction 67

Another Shower 68

Reconstructed Image 3 D Pattern Recognition Monte-Carlo Truth • Reasonable performance, but very difficult to get everything correctly 69

Cosmic Identification (Micro. Boo. NE) • Stitch small tracks together 70

Neutrino Identification (Micro. Boo. NE) • With TPC information only 71

Recent Progress on Lar. Soft Integration • Tingjun implemented a new Lar. Soft module to take Wire. Cell 3 D output (space points with wire hits associations) and write as space points and hits, so that the existing reconstruction alg. can try on Wire-Cell output (3 D images) – Will reported separately at some points trackkalmanhit 72

Future Milestones • Dealing with gaps in the wire-cell imaging and improve wrapped wire imaging (done) • Evaluate efficiencies for single muons – How to stich small tracks together? • • • Finish shower reconstruction Find primary neutrino interaction vertex Implement fine tracking (e. g. PMA) Reconstruction neutral pion mass d. E/dx for e/gamma separation 73

Summary • (Automated) LAr. TPC reconstruction is still an open question and very challenging – Wire-Cell concept has many advantages and may hold the key in solving this problem • LAr. TPC signal processing is important to provide a solid foundation for reconstruction • Wire-Cell Imaging is well developed • Wire-Cell Pattern Recognition is still difficult and under rapid development 74