protodune pds michel tagging august 2020...how does this look in my case? – then, finally, τ 1 is...

ProtoDUNE PDS Michel TaggingAugust 2020

Erin EwartIndiana University

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Introduction

Erin Ewart | ProtoDUNE PDS Michel Tagging | August 2020

• Goal is to see how well we can tag Michel electrons using only the PDS● Gives complementary result to TPC● Calibration of PDS● Contributes to muon charge ID

• Other work:● Kyle Spurgeon did the initial work on this project- more on that later● Aleena Rafique has been doing Michel tagging using primarily the TPC

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General idea


• Reminder: scintillation light can be roughly divided into fast and slow components● The slow component has most of the integrated light, but a time constant of

1.5 microseconds● However, the fast component has a time constant of around 8 nanoseconds

• The PDS has a fast response time● Michel’s prompt light arrives within a few time bins (bin = tick = 6.67ns)● Sharp rise can be used to distinguish the michel from late light● Late light is spread out, so coincident clusters will have slower apparent rises

• I want to find a filter that is good at finding this signal in the noise and late light

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Previous Results


• Kyle Spurgeon performed a first analysis using the ROOT default peak-finder to find the largest peak in the waveform- the “muon”, and the second-largest, the “electron”

• This study was performed on ProtoDUNE data- see Kyle’s January collaboration meeting presentation for details

• This peak-finder performs poorly when the michel is (temporally) close to the muon

• I want to write a better peak-finder that works at short(er) times

Muon decay time in units of microseconds, fitted to an exponential with flat backgroundSource: Kyle Spurgeon

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Event Selection


• Can run over either ProtoDUNE data or monte carlo● For data, we use the TPC to select candidate muon decay events to test our

method● For monte carlo we select on waveforms time-coincident with true decays

● I use Prod 2, specifically PDSPProd2_MC_1GeV_reco_sce_datadriven● This data set has one beam particle and one cosmic shower per event● Because of this, most of the candidates are cosmics (but I do not

discriminate)● Either way, sum waveforms from all eligible channels near the selected time

and perform the analysis on the composite waveform● Eligible channels: non-”bad” channels from IU bars

• For this presentation, I will only consider monte carlo: data analysis is pending

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A note on backgrounds


• Any PDS signal coincident with the muon flash is a possible background● In particular, radiological signals are very common

● However, because they are low-energy, they must occur close to the bar to be detectable, and therefore could be eliminated by looking for bar coincidence

● Other events with energy comparable to a Michel electron would be harder to distinguish● Could attempt to do broad spacial localization with the PDS● Probably better to incorporate TPC information

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First Attempt


• “Modified matched template” method• Convolve the signal with the expected

signal (“template”), subtract off the result of the template convolved with itself, and then peak-find on the remainder (details in backup)

• For the template I use a single-PE waveform convolved with the illumination function given by Denver et al’s Tallbo paper (docdb 696)

• Issue: extremely sensitive to signal shape, and signal shape not consistent enough

Source: “Resolution of overlapping echoes and constrained matched filter”, Huaijin Gu and R. Gao

Distortion example: long component enhanced by 10%. Subtraction results in a fake signal near the muon time.

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Next Ideas


• “First derivative test”: one characteristic of a peak on a monotonically decreasing background (up to noise) is that the first derivative will have rapid rise then fall over the peak. Several methods to detect this:● Do the matched template, take the first derivative, potentially re-smooth,

apply test● Smooth the waveform, take the derivative, re-smooth, apply test● Use a derivative filter (e.g. sawtooth), apply test● Use a Savitzky-Golay (SG) filter

● Equivalent to a least-squares polynomial fit, can “automatically” take the derivative of a function

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Results


• All methods able to achieve decent ID rate of 30-40%● Full details in the backups● Format- Method:percent good/passedCuts filter1_bins filter2_bins

• Examining missed events by hand, I estimate that the maximum any peakfinder could have achieved is 86%, and that a more realistic best figure is 60%

Single-pass methods Double-pass methods

These numbers are from a slightly older algorithm than the examples

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Results


• The following examples use a matched filter with 300 bins

• This first example is “good”, in that the calculated peak is 2 bins away from the “true” michel time

Sample raw waveform. Green lozenges are the true times of the muon and michel, the pink and red triangles are the peak-finder’s results up to a constant offset.

AD

CTicks

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Results


• Same plot of the waveform as before, but the red histogram shows photon arrival times

• This is for ALL photons, not only those specifically involved in this composite waveform


AD

CTicks

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Results


Previous waveform after initial processing with the matched filter

Final result after taking derivative

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Results


• Another example, this time of a failure

• I classified this example as “should get”, since the peak is obvious by eye

• Moral: matched filter is good, but still requires significant separation

• I’m looking into more sophisticated methods


AD

CTicks

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Results


Previous waveform after initial smoothing with a matched filter

Final result after taking derivative

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Results


Measured time minus true time for all monte carlo events that pass basic quality cuts (i.e. detected michel after the muon and correctly matched the muon) Fraction given is the number of detected michels within 20 ticks of the true value.

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Aside- The Cliff


• A property of these composite waveforms• Presumably also a property of single

waveforms, but unnoticeable due to noise• Occurs 120-140 ticks after the initial rise• We currently believe this is due to truncation

of the photon template in the simulation• This could be confirmed by changing the

PulseLength fhicl parameter and then generating a small sample● In module OpDetDigitizerDUNE● I have not done this yet

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Next Steps


• See how the current method performs on data to reproduce Kyle’s plot

• Try new peak-finding methods?

• Experiment with significance measures and cuts

• Test performance for NOT finding michels in a muon capture event● Or use beam protons as a proxy

• Include ARAPUCAs● And then look at DUNE FD monte carlo

Backups

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Jon suggested I look at “matched filters”– These days, often used in 2D image

processing– However, is also the provably ideal

method for finding a single signal in Gaussian noise

– I found a paper (DOI: 10.1109/78.599959) that adapts the matched filter for finding overlapping signals

Method

Input Matched filter

Full algorithm

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How does this look in my case?– First step: construct a template

signal, s(t)– Data from the PDS calibration

runs- LED flashes at maximum amplitude

– VERY heavy cuts to remove extraneous peaks

– What you see here has been normalized, but the peak was around 4.5x10^7, while the noise width was something like 2x10^4

Implementation

template

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How does this look in my case?– At the start of the analysis, we

compute two “helper” functions for use later in the algorithm

– Convolve the template with itself and re-normalize:

Implementation

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How does this look in my case?– Also calculate this weird

normalization function– This bit is important to

compensate for the shape distortion that happens during peak subtraction

Implementation

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How does this look in my case?– Start with some signal– In this example, all non-bad

channels have been added together

– Unfortunately this is actually a weird example- usually the muon is at the beginning, but this one triggered on the small peak to the far left

Implementation

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How does this look in my case?– Pass it through the standard

matched filter by convolving with the template and normalizing

– τ0 is determined by the maximum bin- we assume the “best” signal is the muon

Implementation

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How does this look in my case?– Then subtract off the peak you

expect from a pure signal– Note the changed scale

Implementation

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How does this look in my case?– Finally, normalize by that weird

shape from before– I’ve included the previous step for

comparison

Implementation

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How does this look in my case?– Then, finally, τ1 is the maximum

of the new histograms, and the muon lifetime is τ1–τ0

– In the future, will have more complex requirements:

● Run the algorithm for an arbitrary number of peaks

● Consider peaks above a certain threshold to be “main”

● Consider peaks below a certain threshold to be noise

● In between are Michel candidates

Implementation

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The words indicate the type of filter used:– Templ: matched template– Tri: triangular– Rect: rectangular– Saw: Sawtooth– Bip: rectangular bipolar– SG N: Savitsky-Golay first-derivative filter of degree N– For two pass methods, the second filter name is applied after manually taking the first derivative

The decimal number and the fraction indicate the same thing– The numerator is the number of michels ID’d within 20 time bins– The denominator is the number passing basic quality cuts– The numerator alone is a better indicator of performance. Use 143 for normalization

The final one or two numbers are the size, in bins, of the filter(s) that performed the best and whose performance is indicated by the preceding quantities

Parameter Search Explanation

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Parameter Search Results

Single-pass methods, “mode 1”

Single-pass methods, “mode 2”

Double-pass methods, “mode 1” Double-pass methods, “mode 2”

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The version of the algorithm used for the above is slightly different than for the earlier examples, but this search is somewhat time-consuming to perform (I have not parallelized it)

“Mode 1”– Find all local maxima and minima– Find the biggest and second-biggest difference between a max and its consecutive

min, call those the muon and the electron “Mode 2”

– Use a sliding window of fixed bin size– Within this window, find the maximum bin– Find the minimum bin from the start of the window to the maximum bin– Take the difference– After scanning window over entire filtered waveform, find the biggest and second-

biggest such differences such that their corresponding windows do not overlap, and call them the muon and the electron

Parameter Search Additional Details

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Random Waveforms

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Random Waveforms

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Random Waveforms

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Random Waveforms

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Random Waveforms

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Random Waveforms

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Random Waveforms

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Random Waveforms

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Random Waveforms

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protodune pds michel tagging august 2020...how does this look in my case? – then, finally, τ 1 is...

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