INFN GEM Cosmic Ray Analysis Status...INFN four-layer cosmic ray test stand, Nov. 2018 11/13/19 SBS GMN-GEM meeting 3 Trigger Scintillators y x z

INFN GEM Cosmic Ray Analysis Status

Andrew PuckettUniversity of Connecticut

GMN GEM Meeting12/12/2019

Outline

• Decoded data format: “Hit” ROOT files• Hit reconstruction: Clustering algorithm• Tracking• Alignment• Spatial Resolution• Track-based efficiency• Event display• Path forward

11/13/19 SBS GMN-GEM meeting 2

INFN four-layer cosmic ray test stand, Nov. 2018


Trigger Scintillators

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Decoded Data Format—”Hit” ROOT Files


• “evtID” = event ID number• “nch” = number of strips fired, AFTER common-mode subtraction, zero suppression• “detID” = module number• “planeID” (0 or 1): 0 (1) = Y (X) strips (measuring horizontal (vertical) coordinate)• “strip” = strip fired• adc0,1,2,3,4,5: ADC samples

Hit Reconstruction: Clustering algorithm


1. Filter strips by requiring the max. ADC sample on a strip and the sum of all samples on a strip to be above some user-adjustable thresholds.

2. From remaining strips, select candidate “pixels” (combinations of one X and Y strip) based on Pearson correlation coefficient between individual ADC samples on X and Y strips, which ranges between -1 and 1

a) This statistic measures the degree of ADC and time correlation between X and Y strips, and seems to have good efficiency and discrimination

3. Using the “pixel” with largest correlation coefficient as a seed, add nearest neighbor X (Y) strips to the (2D) cluster, provided their best matches in Y (X) are also within +/- 2 strips of the current “pixel” and their correlation coefficients with their “best matching” strips exceed some user-adjustable threshold. Repeat this process left/right/up/down from the current pixel until we run out of new strips. Increment “pixels” in the order in which they are added to the cluster

4. Mark strips added to the cluster as used and repeat until we run out of unused strips

5. Once we are done adding strips, compute the “cluster correlation coefficient” which is the same as the strip correlation coefficient, except that we sum the ADC values of all X/Y strips in the cluster for each sample, then compute 𝜌 for the “cluster summed samples”.

6. Optionally filter clusters based on ADC asymmetry and X-Y time difference.

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INFN GEM events, cosmic run 3805 (450k events)


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Strips fired and clusters per layer per event


• These plots are for events with at least 3/4 layers with at least one X and Y strip firing (in the same module)

Cluster sizes


• These cluster size distributions are obtained for clusters on good tracks

ADC and Time correlations, I


• These distributions are for all clusters on good tracks, without any explicit cuts applied.

Time and ADC correlations, II


• Bottom left: cluster correlation coefficient between X and Y time samples, summed over all strips in cluster sample-by-sample, clusters on good tracks

• Bottom right: correlation coefficient between X and Y strips used to “seed” the cluster (based on local maximum of correlation coefficient)

Tracking• Cosmic ray tracking is done by “educated brute force”, “Kalman Filter-like” approach:

• Consider all possible reconstructed 2D hits in first layer• For each hit in first layer, consider all possible hits in second layer compatible with a straight-line track with "#

"$≤ 1, "(

"$≤ 1 (or other user-adjustable maximum slope along x and y).

• Third and subsequent layers: for each potentially valid hit combination from the first N-1 layers, consider all hits in layer N falling within some reasonable distance from straight-line projection based on the first N-1 layers; update track parameters ”on the fly” with each new hit added (i.e., “evolve the state”)

• Prefer four-plane tracks initially, if no four-plane track is found with acceptable 𝜒2, reduce number of required hits to 3 and try again: • When number of layers required on current tracking iteration is less than the total number of layers with

available hits, we test all possible combinations of k<N layers chosen from among N layers so that we don’t bias the search in favor of some tracking layers over others.

• Analysis rate on INFN cosmic data ~1-2 kHz, depending on thresholds/cuts applied at the clustering stage; • Based on experience so far, analysis time for cosmic data is dominated by the clustering algorithm, NOT by

track-finding. • However, I don’t have quantitative analysis to back this up; need to measure time spent in clustering and

track-finding routines.

• This approach should scale to high-rate tracking, assuming the implementation of constraints from other detectors (calorimeters, CDET, GRINCH, hodoscope, etc) to limit the search region for clusters/tracks before 2D clustering. Such constraints are natural to implement within this approach


Alignment


(xg, yg, zg) = Global hit coordinates

(xl, yl, zl = 0) = Local hit coordinates (internal to module)

(x0, y0, z0) = Global coordinates of module center

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• Linearized equations for local/global coordinate transformation:

• Assume rotational offsets of modules are small enough that we can treat all cosines as 1, sines as the angles themselves

• Determine offsets and rotations for each module by solving a (linear) system of equations for the offsets that minimize 𝜒2 defined in terms of track residuals

• Set up and invert a matrix, easy-peasy. • Iterate the process until the changes on subsequent iterations are smaller than the stat.

uncertainties. • Re-run reconstruction with new offsets, tighter 𝜒2 cut for tracking, lather, rinse, repeat.

Example Good Alignment Result


• Fixed some bugs in alignment code to improve quality of solutions: • On each iteration, fit the changes in each parameter relative to

the previous iteration (or starting solution), which improves convergence, stability of solutions.

• Previous alignment found a false solution that gave small tracking residuals while having the modules within the same layer too close to each other; not enough “dead area” between adjacent modules within the same layer; unphysical overlap along the “X” axis.

• Good starting point is essential for convergence to a “correct” solution

Tracking results after alignment


• Naïve, global average per-layer detection efficiency based on ratio of 3-hit/4-hit tracks is ~84%. Local efficiency in ”good” regions of active area is close to 100%.

• Global average track reconstruction efficiency for events with at least one 2D hit reconstructed in at least 3/4 tracking layers is ~86%.

𝜎 = 0.15 𝑚𝑚assumed in 𝜒0calculation

Tracking residuals


• After software alignment, Gaussian fit to FWHM of tracking residuals gives (𝝈𝒙, 𝝈𝒚) = (𝟏𝟑𝟒 𝝁𝒎 , 𝟏𝟐𝟑 𝝁𝒎). Some additional improvement possible with more sophisticated hit position reconstruction (currently just simple ADC-weighted average strip position). Modest additional analysis needed to derive “intrinsic” spatial resolution from tracking residuals and details of detection geometry

Track-Based Efficiency (INFN cosmic run 3805)


• Divide each layer into coarse XY binning so that we have on average ~few hundred events/bin• Then for each track falling in that bin, ask if there was a hit on that track in that bin. • Ratio of “Did hit”/”Should hit” gives local efficiency• After bug fixes and improved alignment, ”good” regions of GEM active area are >95% efficient, and “dead areas” between modules are more

clearly visible. • Fourth (top) layer shows clearly lower efficiency, could be related to gas flow issue during this run…

Hit Maps, Run 3805


• Distribution within each layer of reconstructed hit coordinates, showing dead areas/shorted sectors/etc.

• “Stripe” at y = 100 mm in layer 3 is caused by trigger bias; gap between trigger scintillators above GEMs.

Cosmic Ray Event display examples, I


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• Pink “x” = reconstructed hit position

• Black “+” = reconstructed track position at layer

• Stripes = all strips fired by module, color-coded by ADC value

Cosmic Ray Event display examples, II





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Cosmic Ray Event display examples, III





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Cosmic Ray Event display examples, IV





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Cosmic Ray Event display examples, V





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Path forward

• Put all this code into “production” software tools (SBS-offline repo) for UVA EEL cosmic setup, other test data, for final experiment setup.• Deploy, test, and optimize these algorithms for

high-rate tracking in BigBite/GMN/GEN-RP with simulated, digitized data.• Eric already has the digitization machinery and

simulation output; should be able to test the performance of my tracking algorithms under various background conditions.• First test case: GMN


INFN GEM Cosmic Ray Analysis Status...INFN four-layer cosmic ray test stand, Nov. 2018 11/13/19 SBS GMN-GEM meeting 3 Trigger Scintillators y x z

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