Identification and reconstruction of low-energy electrons in the ProtoDUNE-SP detector

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Identification and reconstruction of low-energy electrons in the ProtoDUNE-SP detector © 2023 the Authors Published version DUNE Collaboration DUNE Collaboration. (2023). Identification and reconstruction of low-energy electrons in the ProtoDUNE-SP detector. Physical Review D, 107(9), Article 092012. https://doi.org/10.1103/PhysRevD.107.092012 2023 Identification and reconstruction of low-energy electrons in the ProtoDUNE-SP detector A. Abed Abud et al.* (DUNE Collaboration) (Received 3 November 2022; accepted 27 April 2023; published 30 May 2023) Measurements of electrons from νeinteractions are crucial for the Deep Underground Neutrino Experiment (DUNE) neutrino oscillation program, as well as searches for physics beyond the standard model, supernova neutrino detection, and solar neutrino measurements. This article describes the selection and reconstruction of low-energy (Michel) electrons in the ProtoDUNE-SP detector. ProtoDUNE-SP is one of the prototypes for the DUNE far detector, built and operated at CERN as a charged particle test beam experiment. A sample of low-energy electrons produced by the decay of cosmic muons is selected with a purity of 95%. This sample is used to calibrate the low-energy electron energy scale with two techniques. An electron energy calibration based on a cosmic ray muon sample uses calibration constants derived from measured and simulated cosmic ray muon events. Another calibration technique makes use of the theoretically well-understood Michel electron energy spectrum to convert reconstructed charge to electron energy. In addition, the effects of detector response to low-energy electron energy scale and its resolution including readout electronics threshold effects are quantified. Finally, the relation between the theoretical and reconstructed low-energy electron energy spectra is derived, and the energy resolution is characterized. The low-energy electron selection presented here accounts for about 75% of the total electron deposited energy. After the addition of lost energy using a Monte Carlo simulation, the energy resolution improves from about 40% to 25% at 50 MeV. These results are used to validate the expected capabilities of the DUNE far detector to reconstruct low-energy electrons. DOI: 10.1103/PhysRevD.107.092012 I. INTRODUCTION Discoveries over the past half-century have positioned neutrinos, one of the most abundant matter particles in the Universe, at the center stage of fundamental physics. Neutrinos are now being studied to answer open questions about the nature of matter and the evolution of the Universe. In particular, the measurement of CP violation in the lepton sector [1,2] will help probe the possibility that early-Universe CP violation involving leptons might have led to the present dominance of matter over antimatter. DUNE [3,4] is a next-generation long-baseline accelerator neutrino experiment, designed to be sensitive to neutrino oscillations. The DUNE experiment will consist of a far detector [5] to be located about 1.5 km underground at the Sanford Underground Research Facility (SURF) in South Dakota, USA, at a distance of 1300 km from Fermilab, and a near detector [6] to be located at Fermilab. DUNE uses liquid argon time projection chamber (LArTPC) technology, which permits the reconstruction of neutrino interactions with mm-scale precision. CP violation will be tested in νμ→νeoscillations and the corresponding antineutrino channel, which are sensitive to the CP-violating phase and the neutrino mass ordering [7]. In addition, the large underground LArTPC detectors planned for DUNE will enable a rich physics program beyond the acceleratorbased neutrino oscillation program, including searches beyond the standard model [8], supernova neutrino detection [9], and solar neutrino measurements [10]. To achieve the planned DUNE physics program, it is critically important to accurately reconstruct the energies of electrons and positrons originating from MeV-scale solar and supernova burst νe’s as well as GeV-scale neutrinos from the Long-Baseline Neutrino Facility beam. Calorimetric energy reconstruction requires efficient charge collection, calibration corrections to account for liquid argon impurities and electronics response, and a recombination correction to account for charge loss due to electronion recombination. The goal of this article is to demonstrate the capability to reconstruct low-energy electrons in the single-phase ProtoDUNE (ProtoDUNE-SP) [11] LArTPC. This work presents techniques and results on the selection and energy reconstruction of the low-energy (Michel) *Full author list given at end of the article. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. PHYSICAL REVIEW D 107, 092012 (2023) 2470-0010=2023=107(9)=092012(22) 092012-1 Published by the American Physical Society electrons [12], originating from the decay at rest of cosmic ray muons. With a well-understood energy spectrum, these low-energy electrons are ideal for evaluating the electron selection and energy reconstruction in ProtoDUNE-SP and demonstrating the capability of the DUNE far detector to identify and reconstruct these lowenergy electron events. Although there are other studies of low-energy electrons in LArTPCs [13–17], the unique features of this study include the data-driven determination of the recombination correction, evaluation of the lost energy due to the TPC readout threshold, a comparison of the electron energy calibration based on muonderived calibration corrections with that based on the Michel electron true energy spectrum, and a characterization of the electron energy resolution. II. DUNE FIRST FAR DETECTOR AND ITS PROTOTYPE Central to the realization of the DUNE physics program is the construction and operation of LArTPC detectors that combine a many-kiloton fiducial mass necessary for rareevent searches with the ability to image those events with mm-scale spatial resolution, providing the capability to identify the signatures of the physics processes of interest. The DUNE far detector will consist of four detector modules, each with an equivalent LAr fiducial mass of 10 kt, installed approximately 1.5 km underground. Each LArTPC will be installed inside a cryostat of internal dimensions 15.1mðwÞ×14 mðhÞ×62 mðlÞcontaining a total LAr mass of about 17.5 kt. Charged particles passing through the TPC ionize the argon, and the ionization electrons drift to the anode planes under the influence of an applied electric field. DUNE is actively developing two LArTPC technologies: a horizontal-drift (HD) LArTPC in which the ionization electrons drift horizontally between a vertical cathode and anode planes, and a vertical-drift LArTPC, in which the ionization electrons drift vertically between a horizontal cathode and anode planes. The focus of this article is on the HD LArTPC [18] technology as the first DUNE far detector module will be based on this technology. Figure 1(top) shows the configuration of a DUNE HD module. Each of the four LAr drift volumes is subjected to an electric field of 500 V=cm [19], corresponding to a Cathode Plane Assembly (CPA) high voltage of −180 kV relative to the anode, which will be grounded. The pattern of ionization collected on the grid of anode wires enables reconstruction in the two coordinates perpendicular to the drift direction. Novel photon detectors (PDs) called X-ARAPUCAs [20] will be placed behind the Anode Plane Assembly (APA) collection wire planes. The PDs are used to provide a timestamp of the interaction, thus giving an estimate of the drift distances traveled by the ionization electrons to reconstruct the third event coordinate. The DUNE Collaboration has constructed and operated a large horizontal drift prototype detector, known as ProtoDUNE-SP. The detector has been assembled and tested at the CERN Neutrino Platform [21]. ProtoDUNESP was operated from 2018 to 2020, and its large samples of high-quality beam data have been used to demonstrate the effectiveness of the single-phase far detector design. Results on the performance of the ProtoDUNE-SP liquid argon TPC in the test beam can be found in Ref. [22] including noise and gain measurements; dE=dx calibration for muons, protons, pions, and electrons; drift electron lifetime measurements; and photon detector noise, signal sensitivity, and time resolution measurements. The measured values meet or exceed the specifications for the DUNE far detector. Figure 1(bottom) shows the components of the ProtoDUNE-SP LArTPC, which is approximately one-twentieth the size of the planned far detector HD module but uses anode and cathode components identical in size to those of the full-scale module. ProtoDUNE-SP has the same 3.6 m maximum drift length as the full far detector HD module. It consists of two drift volumes with a common central cathode surrounded by two anode planes and a field cage that surrounds the entire active volume. The active volume is 6 m high FIG. 1. Configuration of the 10 kt DUNE far detector horizontal drift module (top); configuration of ProtoDUNE-SP LArTPC (bottom). A. ABED ABUD et al. PHYS. REV. D 107, 092012 (2023) 092012-2 (y-coordinate), 7.2 m wide (x-coordinate, along the drift direction), and 7 m deep (z-coordinate, along the beam direction). Each anode plane consists of three adjacent APAs that are each 6 m high by 2.3 m wide. The wire planes and their wire orientations are the U layer (þ35.7° from vertical, also called the first induction plane), the V layer (−35.7° from vertical, also called the second induction plane), and the X layer (vertical, also called the collection plane). Each successive wire plane is built 4.75 mm above the previous layer. As they drift, ionization electrons first pass the induction planes and then are collected on the collection plane. The U and V plane wires are wrapped around the APA frame (and hence see the charge arriving from both sides of the APA) while each side has a separate X layer, as sketched in Fig. 3 of [22]. The distance between two consecutive wires in the same layer, also known as wire pitch, is 4.67 mm for U and V layers, and 4.79 mm for X layer wires. Signals from the wires of each APA are read out via a total of 2560 electronic channels. Uniformity of the electric field is provided by the surrounding field cage. The cold electronics mounted onto the APA frame, and thus immersed in LAr, amplify and continuously digitize the induced signals on the sense wires at 2 MHz during the entire data-taking period, and transmit these waveforms to the Data Acquisition system. The modular PD system is integrated into the APAs, as further described in [22]. The PD was not used in the analysis described here. III. ELECTRONS IN LARTPCS For the DUNE physics program it is critical to understand the far detector response to electromagnetic showers since DUNE will measure electrons produced in νe interactions, where the νeare from νμoscillations, the Sun, and possibly supernova explosions. In addition, DUNE will search for proton decay signatures, as event identification may proceed via the detection of a lowenergy electron. ProtoDUNE-SP has collected data samples of test-beam electrons and data samples of electrons from cosmic ray muon decays [22]. Data from ProtoDUNE-SP beam runs with 1GeV=c beam momentum, including a sample of beam positrons, were used for the initial classification of trackand showerlike energy deposits using a convolutional neural network technique [23]. Studies of electron selection and identification in ProtoDUNE-SP TPC lead to a more accurate understanding of the calorimetric response to electrons and offer an opportunity for a precise understanding of the electron energy resolution parameters for electron neutrino reconstruction in future DUNE far detectors. This work focuses on studies of the ProtoDUNE-SP LArTPC response to low-energy electrons. As the electrons propagate in the LAr, they deposit energy either through ionization or through radiative losses (bremsstrahlung). The energy loss via ionization is continuous and results in tracklike topologies. Radiative losses are also present at all electron energies leading to the production of electromagnetic shower cascades of secondary electrons and photons. Bremsstrahlung photons may Compton scatter or convert to eþe−pairs, resulting in signatures with secondary energy deposits disconnected from the primary ionization tracks. The typical attenuation length for photons in liquid argon in the energy range of interest for Michel electrons is 20–30 cm [24]. The event reconstruction takes into account the charge released by both primary particle ionization and radiative processes. IV. SELECTION OF STOPPING MUONS AND MICHEL ELECTRONS The generation of cosmic ray muons is performed with CORSIKA v7.4 [25], while the simulation of particle propagation and interaction in ProtoDUNE-SP is performed by GEANT 4 v4.10.3 by using the QGSP BERT physics list [26] with the detector response described within LA r S oft [27].In all ProtoDUNE simulations, the delta-ray threshold (and the electron transport threshold) is set to 455 keV (corresponding to an electron range of about 1.5 mm) [28].Allμþ decay into Michel positrons, whereas only 25% of μ− undergo decay to Michel electrons since the other 75% are captured by the argon atoms inside the TPC. Therefore, the Michel electron sample described in this analysis includes both electrons and positrons. In this article, “electrons” refers to both electrons and positrons unless indicated otherwise. The reconstruction of charged particles in the ProtoDUNE-SP LArTPC follows the technique described elsewhere [22], and in this section the procedure is briefly described. The TPC readout electronics collect a waveform that represents the current on the APAwire as a function of time. Each waveform is processed in an offline data processing chain to produce a collection of ionization charge deposition arrival times and charge integrals at each readout wire. Signal processing starts with a deconvolution of measured charge from signals induced by the drifting ionization electrons, followed by noise removal. In order to make use of deconvolved waveforms to reconstruct individual events, it is necessary to apply three-dimensional (3D) hit finding and pattern recognition algorithms. The 3D-hit (called “hit”from now on) is an ionization charge released in space and time by through-going charged particles and detected by three layers of anode plane wires, and collected by a collection plane wire alone in the analysis described here. A collection of hits is merged together to form a particle track or a shower that belongs to an event. The hit finding algorithm searches for candidate hits based on charge deposits in the waveform on a single wire as a function of time, and fits them to a Gaussian shape. Pattern recognition and event reconstruction are performed by the PANDORA software package [29], which is IDENTIFICATION AND RECONSTRUCTION OF LOW-ENERGY …PHYS. REV. D 107, 092012 (2023) 092012-3 a collection of reconstruction algorithms that focus on specific hit topology patterns. The first step in the reconstruction procedure is the two-dimensional clustering of observed charge pulses in each of the three detector readout planes separately. In the second step, sets of twodimensional clusters are matched between the three views to produce 3D hits and to create particle interaction hierarchies. As described in [22], one important feature of the cosmic ray reconstruction step is the “stitching”of tracks across the boundaries between neighboring drift volumes bounded by a CPA or an APA. In the analysis performed here the stitching procedure is applied when two 3D clusters are reconstructed in neighboring drift volumes with consistent direction vectors and an equal but opposite shift in the drift direction from the CPA. These two clusters present segments of a single muon track that is penetrated through the CPA. When the clusters are shifted toward each other as expressed in time-tick units (1time tick ¼500 ns), a single muon track of two initially separate tracks is produced with a known absolute position and time (T0) relative to the trigger time [22]. The reconstruction of electrons below 50 MeV is very different from the reconstruction of GeV-scale electromagnetic showers [30]. For this reason, a dedicated algorithm has been developed to reconstruct and identify the Michel electrons presented in this study. Figure 2shows two Michel electron candidate events from ProtoDUNE-SP data, with muons entering from the top. The event selection starts by searching for a candidate muon that decayed to an electron. A set of conditions is initially applied to ensure a high quality muon track candidate. Finally, additional selection criteria are implemented to make sure that a Michel electron candidate is identified around the end position of the candidate muon by selecting and summing up charge hits that represent the Michel electron. While all three anode planes are used for track reconstruction, the collection plane provides the best signal-to-noise performance and charge resolution [22]. Therefore, only the collection plane charge is used to reconstruct the electron energy. A. Muon track selection (i) Only the T0-tagged candidate muon tracks are selected from muon tracks reconstructed by PANDORA . These are the tracks that cross the cathode or anode plane boundaries, and the two pieces of the track from the two volumes help determine the correct end position of the track in the drift direction. The fraction of tracks having a T0assigned to them is 2% from the data sample. Since this requirement selects most of the events and the corresponding charge coming from locations farther away from the anode in ProtoDUNE-SP, it is expected that the DUNE far detector will perform equally or better in terms of charge reconstruction. This is because there will be less ionization charge attenuation as events, on average, will be closer to the anode plane wires and that may slightly affect the energy reconstruction. (ii) Selected tracks are required to have one reconstructed endpoint within 30 cm from one or more of the detector boundaries. The cut is applied to all six faces of the detector. This step improves the selection of cosmic ray muon candidates entering the detector. By requiring this, the next steps in the selection can focus on the other end of the track to search for the Michel electron signatures. (iii) Only the muons that stop within the detector fiducial volume are considered. The fiducial volume is a rectangular volume shaped as follows: the boundary from the anode planes is 51 cm, the boundary from the upstream and downstream ends is 80 cm, and the boundaries from the top and bottom of the TPC are 43 cm and 80 cm, respectively. These values are obtained from an optimization based on Monte Carlo (MC) simulation. This step specifies the end of the contained track from which evidence of Michel electrons can be sought. (iv) Muon tracks that stop within a region that is close to a boundary between two adjacent APAs (∼10 cm from each APA side) are removed. This cut removes all those tracks that appear to stop in the gaps between two APA planes. Candidate muon Candidate Michel electron Cosmic ray muon Candidate muon Candidate Michel electron Cosmic ray muon FIG. 2. Two Michel electron candidates observed in the ProtoDUNE-SP data. The parent muons enter the images from the top before stopping and decaying. A. ABED ABUD et al. PHYS. REV. D 107, 092012 (2023) 092012-4 (v) Broken tracks, for which the reconstruction algorithm does not connect track segments correctly at detector boundaries or anode gaps, are removed from further analysis. In order to reject broken candidate muon tracks, the algorithm looks for any additional track that starts within <30 cm of the reconstructed end position of the candidate muon track, and is nearly parallel (<14°or>165°) with respect to the candidate muon track. If this condition is satisfied, the candidate muon is removed from the event selection. (vi) It is required that candidate muon tracks are at least 75 cm long [31], i.e., those that have crossed the cathode with track segments reconstructed in both drift volumes. Since cosmic muons generally have long track lengths, this cut improves the quality of the candidate cosmic muon track reconstruction. (vii) Every reconstructed hit is associated with a time counted in ticks, known as the hit time with respect to T0. The peak of the reconstructed hit time distribution is known as the hit peak time. For every track, a cut is placed on the value of the minimum and maximum hit peak time. Only those candidate muon tracks that have a minimum hit peak time to be >200 time ticks and a maximum hit peak time to be <5800 time ticks are kept. The peak time cuts ensure that the candidate muon is contained within the event readout window. About 28% of the T0-tagged muons satisfy the above selection criteria, and simulation studies indicate that the selected muon sample has a purity of 99.7%. The purity here corresponds to the fraction of the true muons out of all the selected tracks. The determination of the selection cut values for different quantities is based on the MC simulation studies for which the maximum sample purity is obtained. B. Michel electron selection (i) The first step in the identification of Michel electrons is to select nearby hits, i.e. hits within 10 cm of the end position of the candidate muon. In the collection plane view, these hits must not belong to either the candidate muon or any other track having length >10 cm. Nearby hits are counted, and events that have between 5 and 40 hits around the endpoint of the candidate muon track are considered. These values are optimized to deliver a high sample purity. Furthermore, the reconstructed electron shower around the candidate muon track endpoint is required to start within 10 cm from the candidate muon track end position. The Michel electron candidate is formed from these selected electron shower hits. (ii) The direction of the candidate Michel electron (obtained by a linear fit to the nearby hits) is compared to the direction of the muon (measured using the last 10 hits in the trajectory). The angle between the directions is required to be less than 130° such that events where the candidate Michel electron goes back along the muon are rejected. (iii) In the next step, the angle between the collection plane wires and the direction of the candidate Michel electron is calculated. Only those events where the value of this angle is >10° and <170° are selected so that Michel electron candidates that are parallel to the collection plane wires are not included in the data sample. This cut is applied to reject Michel electrons that are parallel to the collection plane wires and therefore may not have well-reconstructed hits. (iv) The final selection criterion, the cone cut, separates Michel electron hits from nearby cosmic rays that may interact in the TPC close to the candidate Michel electron event. A cone around the endpoint of the candidate muon is defined such that any hit that lies within that cone is assumed to belong to the candidate Michel electron. It is required that those hits are not a part of the parent muon or any other track longer than 10 cm. A straight line is fit along the nearby collection plane hit distribution (hits within 10 cm distance from the muon endpoint in the collection plane). The cone cut is illustrated in Fig. 3, where the red points represent the Michel electron hits, and the black points are other (nonMichel candidate) hits of the event excluding the hits of the parent muon or any other long (>10 cm) tracks. Using simulation, the cone opening angle θis optimized at 70° and the cone length dis 20 cm in order to maximize the value of Michel electron hit purity (83%) and hit completeness (74%). The hit purity is defined as the fraction of hits in the reconstructed cone that actually belong to the true Michel electron. The hit completeness is defined as the fraction of true Michel electron hits inside the reconstructed cone. FIG. 3. Illustration of the cone containment that separates Michel electron hits (red dots) from nearby cosmic ray background events (black dots). The Michel electron is defined by the hits starting within 10 cm from the end position of the candidate muon. All the hits contained inside the cone cuts are taken to be the candidate Michel electron hits. IDENTIFICATION AND RECONSTRUCTION OF LOW-ENERGY …PHYS. REV. D 107, 092012 (2023) 092012-5 C. Event selection summary Table Ilists the muon passing rates and corresponding statistical uncertainties with respect to thewell-reconstructed muon tracks and candidate Michel electrons passing rates with respect to the well-reconstructed muons that satisfy the muon selection criteria for the simulation and data samples. As the focus of this analysis was to select a pure sample of Michel electrons, an estimation of the systematic uncertainties on the passing cosmic ray muon rates was not performed here.Thetotalnumberofdataeventsinthisstudy thatpassall the selection steps is ∼8300. The total event purity of the selected electron sample from the simulation is found to be 95%. The purity here corresponds to the fraction of the true Michel electron events out of all the selected events. The remaining 5% of events represent different types of background events including those that have a tagged electromagnetic activity from muons (delta rays or bremsstrahlung photons), in which some random noise hits appear to be reconstructed as candidate Michel electron hits or those in which protons are emitted from argon nuclei because of the muon capture on argon. Isolating background events in the simulation, their energy spectrum is found to be monotonically decreasing, with a low-end cutoff at ∼10 MeV. These secondary background events have been characterized elsewhere [30,32]. It is important to point out that the DUNE far detector data will be dominated by single νμor single νeevents, where the event selection and reconstruction efficiencies will improve in the absence of nearby cosmic ray background activity, as opposed to the ProtoDUNE-SP case studied in this article. It is expected that the muon flux inside ProtoDUNE-SP is on the order of one per cm2=min [33]. The event selection criteria will be revisited and optimized for the DUNE far detector analyses. An expected muon rate in four modules of DUNE being underground will be about 0.2 Hz with an average muon energy of 283 GeV [34]. V. TEST AND VERIFICATION OF THE MICHEL ELECTRON RECOMBINATION CORRECTION A through-going charged particle will deposit energy in LAr by creating both ionization and excitation. Electron-ion pairs will be produced (e−,Ar þ), along with excited argon atoms (Ar). These excited atoms (Ar) will form excited molecular argon ions, so-called short-lived excimers (Ar 2), through collisions of Arwith neutral Ar atoms. In addition, the Ar 2will also be formed by free electrons recombining with surrounding molecular argon ions (Arþ 2). These excimers (Ar 2) undergo dissociative decay to their ground state by emitting the vacuum ultraviolet photons known as argon scintillation light [14,32,35]. When the deposited energy is reconstructed using charge alone, as done in the work presented here, only the electrons that escape electronion recombination and successfully drift to anode collection wires will be accounted for. Note that Ris the recombination factor that describes the fraction of ionization electrons that survive prompt recombination with argon ions before the drift towards the anode plane. The value of Ris critical to energy reconstruction from collected ionization charge, as later described in Eq. (3). In this subsection the data-driven recombination correction factor is derived by following the Modified Box model [36]. The Michel electron candidates in this study are selected with the cuts described in Sec. IV B. The electron energy loss per unit length is calculated on an event-by-event basis. The value of dQ=dx per event is computed as dQ=dx ¼Qtotal L;ð1Þ whereQtotal is thetotal charge deposited determined from the candidate Michel electron hits and Lis the 3D displacement from the first to the last hit of the candidate Michel electron. In both data and MC, raw dQ=dx is converted to corrected dQ=dx based on calibration constants derived with the cosmic ray muons [22], as described later by Eq. (3). With the Modified Box model [36], the calibrated dQ=dx value is converted to an average dE=dx for every Michel electron candidate. The average dE=dx distribution of Michel electron candidates is shown in Fig. 4(top). The mean value of the dE=dx distribution is 3.25 MeV=cm. Finally, the agreement of simulation with data is tested using the recombination correction factor distribution. The recombination factor Ris calculated as R¼lnðdE dx ×β0=ρEfþαÞ dE dx ×β0=ρEf ;ð2Þ where αand β0arethe ModifiedBoxmodelparameterswhich were measured by the ArgoNeuT experiment at an electric fieldstrengthof0.481 kV=cm [36].Thevaluesofαandβ0are 0.93 0.02 and 0.212 0.002ðkV=cmÞðg=cm2Þ=MeV, respectively. The liquid argon density ρat a pressure of 124.11kPa is 1.38 g=cm3,andEfistheapplied electric field. Using Eq. (2),Ris computed for each event using dE=dx for the event and assuming a constant electric field of 0.5kV=cm [19].TheRdistribution of Michel electron candidates is shown in Fig. 4(bottom). TABLE I. Passing rates for event selection criteria applied to ProtoDUNE simulation and data samples. Quantities with statistical uncertainties for muon selection present the percentage with respect to well-reconstructed muons. Quantities with statistical uncertainties for Michel electron selection present the percentage with respect to well-reconstructed muons that satisfy the muon selection criteria. Passing rates Simulation Data Muon selection ð27.90.1Þ%ð25.50.1Þ% Michel electron selection ð16.30.1Þ%ð14.50.2Þ% A. ABED ABUD et al. PHYS. REV. D 107, 092012 (2023) 092012-6 The mean values of the recombination factor obtained from the reconstructed data and MC distributions in Fig. 4 (bottom) are 0.625 0.020ðstatÞand 0.626 0.020ðstatÞ, respectively. Independent of the analysis performed above, the average recombination factor of 0.644 0.014ðsystÞ was evaluated based on the ProtoDUNE-SP GEANT 4electron simulation [26], which incorporates the Modified Box model of the ionization electron recombination and its systematic uncertainty as described in [36]. The recombination factor R¼0.644 derived with the simulation comes with a small uncertainty and agrees well with the datadriven value described in this subsection, verifying the simulation-based recombination factor applied in the analysis described in this article. VI. MICHEL ELECTRON LOST ENERGY STUDIES The lost energy is a fraction of energy that is not reconstructed. It corresponds to ionization charge deposits that are missed by either being left below the anode charge readout threshold or left outside the selection cone. This subsection describes the Michel electron lost energy studies performed to quantify the containment of Michel electron events within the applied cone cut and to evaluate the effects of TPC readout thresholds using MC simulation. A. Michel electron hit completeness Figure 5shows the fraction of true Michel electron energy left outside the cone as a function of true Michel electron energy per event. The average value of the energy loss due to hit incompleteness for the Michel electron sample is 13 1ðstatÞ%. It is also evident that the energy loss by hits not captured within the reconstruction cone increases with the Michel electron energy due to the increase of radiative losses. B. Michel electron hit reconstruction threshold In order to avoid random noise from being reconstructed as a particle hit, there is an intrinsic threshold applied to the energy deposited in a given readout channel (wire) per time tick, the value of which is set to ∼100 keV/tick. To quantify the impact of the threshold on the Michel electron energy distribution, a study was performed to look at all simulated channels and to estimate the lost energy due to the abovementioned threshold. Figure 6shows the true Michel electron lost energy fraction as a function of true Michel electron energy per event from this threshold; on average 50 100 150 200 250 300 350 400 DUNE:ProtoDUNE-SP MC sig+bkg Data 1 2 100 200 300 400 500 600 700 800 900 DUNE:ProtoDUNE-SP MC sig+bkg Data 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 0 3 3 0 # Entries data/MC # Entries Recombination factor data/MC 012345678910 dE/dx [MeV/cm] FIG. 4. Computed Michel electron dE=dx (top) and recombination correction factor (bottom): Data (black points) and MC simulation (red histogram) are compared. 0 1020304050607080 True Michel electron energy [MeV] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Outside cone missing energy fraction 1 10 10 DUNE:ProtoDUNE-SP Simulation FIG. 5. True Michel electron energy fraction left outside the selection cone as a function of true Michel electron energy. 0 1020304050607080 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 10 10 DUNE:ProtoDUNE-SP Simulation True Michel electron energy [MeV] Below threshold missing energy fraction FIG. 6. True Michel electron energy fraction left below the charge readout threshold as a function of true Michel electron energy. IDENTIFICATION AND RECONSTRUCTION OF LOW-ENERGY …PHYS. REV. D 107, 092012 (2023) 092012-7 11 1ðstatÞ%of the ionization from Michel electrons is lost due to this threshold. Therefore, a total of about 24% of the true energy is not reconstructed from hits outside the cone and below threshold, so only 76 1ðstatÞ%of the total energy is captured. VII. MICHEL ELECTRON ENERGY RECONSTRUCTION This section describes the procedure of Michel electron energy reconstruction. In the first method (also called nominal reconstruction) cosmic ray muon data are used to derive calibration constants and corrections [22], which are then applied to reconstructed Michel electron hits. The second approach is based on the well-understood theoretical Michel electron energy spectrum [12] where the energy calibration is independent of the muon-based calibration. Finally, the energy resolution effects important for understanding the electron energy in the 5–50 MeV range in LArTPCs are discussed. It should be clarified that the nominal energy reconstruction presented here does not include the lost energy because it cannot be captured in the data with the existing event selection and charge readout threshold. However, potential energy reconstruction improvements with some or all of the lost energy recovered are studied with the simulation to indicate opportunities that might be realized with future DUNE far detector LArTPCs. A. Muon-based energy reconstruction of the Michel electron energy scale The electron energy, E, is calculated from the sum of charges deposited by the corresponding ionization electron hits on the anode plane wires. The total reconstructed energy of the Michel electron is given as E¼Cnorm Wion RCcalib X N i¼1½εðXiÞεðYi;Z iÞdQið3Þ where dQi(in ADC tick) corresponds to the charge deposited in the ith hit, and Ncorresponds to the total number of candidate Michel electron hits. Note that dQ=dx values along the drift direction are affected by attenuation due to electronegative impurities and by longitudinal diffusion. Here, Cnorm is the factor that normalizes the reconstructed dQ=dx values to the average dQ=dx value across anode planes in both drift volumes; εðXiÞrepresents the drift electron lifetime and the space charge corrections, and εðYi;Z iÞdescribes the dead wire correction that is used to remove the nonuniformity in dQ=dx values [22].In addition, Wionð¼ 23.6eVÞis the ionization work function of argon [37]. A highly pure sample of stopping muons is used in ProtoDUNE to correct for space charge effects and to determine dQ=dx [22]. From the calibrated dQ=dx values (in ADC=cm) along the muon track in its MIP region, the dE=dx (in MeV=cm) values are fitted using the Modified Box model [36] function to correct for the recombination effect with the charge calibration constant Ccalib as a free parameter in the χ2minimization. Therefore, Ccalib (ADC tick/electron) represents the calibration constant that is used to convert the corrected charge deposition (in ADC) on a hit to energy deposition (in MeV) on a hit. It accounts for the electronics gain of the collection-plane wires, the signal processing, as well as detector effects that convert the deposited energy into collected electrons on the wire planes. Note that R¼0.644 is the average recombination correction evaluated by the ProtoDUNE-SP GEANT 4 simulation based on the Modified Box model [36], and it is verified above on an event-by-event basis by selected Michel electron events. The reconstructed Michel electron energy is evaluated on an event-by-event basis using Eq. (3) in which all the calibration corrections are derived from cosmic ray muon data and simulation samples. Therefore, the energy reconstruction applied to the Michel electron sample in this subsection is based on cosmic ray muon calibration. With the Michel electron energy reconstruction described in Eq. (3), it is appropriate to evaluate systematic uncertainty contributions to the energy scale. These contributions originate from charge hit (dQi) association efficiency, the recombination factor (R) uncertainty, the theoretical Michel electron versus positron uncertainty, and from the space-charge effects [εðXiÞ] uncertainty. These uncertainties quantify how well the absolute energy scale of Michel electrons is understood. Systematic uncertainty contributions from Ccalib,εðYi;Z iÞ) and Cnorm are negligible. Table II presents the systematic uncertainties on the reconstructed Michel electron energy spectrum. The uncertainties are expressed with respect to the mean energy of the reconstructed Michel electron energy spectrum. Individual contributions are added in quadrature. The hit association systematic uncertainty was evaluated by considering the number of candidate Michel electron hits within 10 cm of the muon stopping point in both data and simulation. The difference in the average number of hits in data and simulation was used to vary the MC Michel electron hit distribution. A shift in the mean value of the reconstructed Michel electron energy scale was determined TABLE II. Michel electron energy spectrum systematic uncertainties estimates from simulation. The uncertainties are expressed with respect to the mean energy of the reconstructed Michel electron energy spectrum. Sources of systematic uncertainties Uncertainty estimates Hit association efficiency 4.0% Recombination factor 2.2% Michel electron versus positron 1.7% Space charge effect 1.4% Total added in quadrature 5.1% A. ABED ABUD et al. PHYS. REV. 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Rincón,59 A. Ritchie-Yates,179 D. Rivera,132 R. Rivera,67 A. Robert,77 J. L. Rocabado Rocha,86 L. Rochester,187 M. Roda,131 P. Rodrigues,160 M. J. Rodriguez Alonso,35 J. Rodriguez Rondon,189 E. Romeo,100 S. Rosauro-Alcaraz,164 P. Rosier,164 M. Rossella,102,167 M. Rossi,35 M. Ross-Lonergan,132 J. Rout,117 P. Roy,213 A. Rubbia,60 C. Rubbia,75 B. Russell,129 D. Ruterbories,178 A. Rybnikov,119 A. Saa-Hernandez,87 R. Saakyan,206 S. Sacerdoti,165 N. Sahu,91 P. Sala,99,35 N. Samios,20 O. Samoylov,119 M. C. Sanchez,70 V. Sandberg,132 D. A. Sanders,147 D. Sankey,181 D. Santoro,99 N. Saoulidou,10 P. Sapienza,105 C. Sarasty,40 I. Sarcevic,8 G. Savage,67 V. Savinov,172 G. Scanavini,216 A. Scaramelli,102 A. Scarff,186 A. Scarpelli,20 T. Schefke,133 H. Schellman,159,67 S. Schifano,95,68 P. Schlabach,67 D. Schmitz,37 A. W. Schneider,138 K. Scholberg,56 A. Schukraft,67 E. Segreto,30 A. Selyunin,119 C. R. Senise,204 J. Sensenig,168 D. Sgalaberna,60 M. H. Shaevitz,45 S. Shafaq,117 F. Shaker,218 M. 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D 107, 092012 (2023) 092012-19 87Instituto Galego de Física de Altas Enerxías, University of Santiago de Compostela, Santiago de Compostela, 15782, Spain 88Illinois Institute of Technology, Chicago, Illinois 60616, USA 89Imperial College of Science Technology and Medicine, London SW7 2BZ, United Kingdom 90Indian Institute of Technology Guwahati, Guwahati, 781 039, India 91Indian Institute of Technology Hyderabad, Hyderabad, 502285, India 92Indiana University, Bloomington, Indiana 47405, USA 93Istituto Nazionale di Fisica Nucleare Sezione di Bologna, 40127 Bologna BO, Italy 94Istituto Nazionale di Fisica Nucleare Sezione di Catania, I-95123 Catania, Italy 95Istituto Nazionale di Fisica Nucleare Sezione di Ferrara, I-44122 Ferrara, Italy 96Istituto Nazionale di Fisica Nucleare Sezione di Genova, 16146 Genova GE, Italy 97Istituto Nazionale di Fisica Nucleare Sezione di Lecce, 73100—Lecce, Italy 98Istituto Nazionale di Fisica Nucleare Sezione di Milano Bicocca, 3—I-20126 Milano, Italy 99Istituto Nazionale di Fisica Nucleare Sezione di Milano, 20133 Milano, Italy 100Istituto Nazionale di Fisica Nucleare Sezione di Napoli, I-80126 Napoli, Italy 101Istituto Nazionale di Fisica Nucleare Sezione di Padova, 35131 Padova, Italy 102Istituto Nazionale di Fisica Nucleare Sezione di Pavia, I-27100 Pavia, Italy 103Istituto Nazionale di Fisica Nucleare Laboratori Nazionali di Pisa, Pisa PI, Italy 104Istituto Nazionale di Fisica Nucleare Sezione di Roma, 00185 Roma RM, Italy 105Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud, 95123 Catania, Italy 106Universidad Nacional de Ingeniería, Lima 25, Perú 107Institute for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia 108University of Insubria, Via Ravasi, 2, 21100 Varese VA, Italy 109University of Iowa, Iowa City, Iowa 52242, USA 110Iowa State University, Ames, Iowa 50011, USA 111Institut de Physique des 2 Infinis de Lyon, 69622 Villeurbanne, France 112Institute for Research in Fundamental Sciences, Tehran, Iran 113Instituto Superior T´ecnico—IST, Universidade de Lisboa, Portugal 114Instituto Tecnológico de Aeronáutica, Sao Jose dos Campos, Brazil 115Iwate University, Morioka, Iwate 020-8551, Japan 116University of Jammu, Jammu-180006, India 117Jawaharlal Nehru University, New Delhi 110067, India 118Jeonbuk National University, Jeonrabuk-do 54896, South Korea 119Joint Institute for Nuclear Research, Dzhelepov Laboratory of Nuclear Problems 6 Joliot-Curie, Dubna, Moscow Region, 141980 RU 120University of Jyvaskyla, FI-40014, Finland 121Kansas State University, Manhattan, Kansas 66506, USA 122Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa, Chiba 277-8583, Japan 123High Energy Accelerator Research Organization (KEK), Ibaraki, 305-0801, Japan 124Korea Institute of Science and Technology Information, Daejeon, 34141, South Korea 125K L University, Vaddeswaram, Andhra Pradesh 522502, India 126National Institute of Technology, Kure College, Hiroshima, 737-8506, Japan 127Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine 128Lancaster University, Lancaster LA1 4YB, United Kingdom 129Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 130Laboratório de Instrumentação e Física Experimental de Partículas, 1649-003 Lisboa and 3004-516 Coimbra, Portugal 131University of Liverpool, L69 7ZE, Liverpool, United Kingdom 132Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 133Louisiana State University, Baton Rouge, Louisiana 70803, USA 134University of Lucknow, Uttar Pradesh 226007, India 135Madrid Autonoma University and IFT UAM/CSIC, 28049 Madrid, Spain 136Johannes Gutenberg-Universität Mainz, 55122 Mainz, Germany 137University of Manchester, Manchester M13 9PL, United Kingdom 138Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 139Max-Planck-Institut, Munich, 80805, Germany 140University of Medellín, Medellín, 050026 Colombia 141University of Michigan, Ann Arbor, Michigan 48109, USA 142Michigan State University, East Lansing, Michigan 48824, USA 143Universit`a del Milano-Bicocca, 20126 Milano, Italy A. ABED ABUD et al. PHYS. REV. D 107, 092012 (2023) 092012-20 144Universit`a degli Studi di Milano, I-20133 Milano, Italy 145University of Minnesota Duluth, Duluth, Minnesota 55812, USA 146University of Minnesota Twin Cities, Minneapolis, Minnesota 55455, USA 147University of Mississippi, University, Mississippi 38677, USA 148Universit`a degli Studi di Napoli Federico II, 80138 Napoli NA, Italy 149University of New Mexico, Albuquerque, New Mexico 87131, USA 150H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 151Nikhef National Institute of Subatomic Physics, 1098 XG Amsterdam, Netherlands 152University of North Dakota, Grand Forks, North Dakota 58202-8357, USA 153Northern Illinois University, DeKalb, Illinois 60115, USA 154Northwestern University, Evanston, Illinois 60208, USA 155University of Notre Dame, Notre Dame, Indiana 46556, USA 156University of Novi Sad, 21102 Novi Sad, Serbia 157Occidental College, Los Angeles, California 90041, USA 158Ohio State University, Columbus, Ohio 43210, USA 159Oregon State University, Corvallis, Oregon 97331, USA 160University of Oxford, Oxford, OX1 3RH, United Kingdom 161Pacific Northwest National Laboratory, Richland, Washington 99352, USA 162Universt`a degli Studi di Padova, I-35131 Padova, Italy 163Panjab University, Chandigarh, 160014 U.T., India 164Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France 165Universit´e Paris Cit´e, CNRS, Astroparticule et Cosmologie, Paris, France 166University of Parma, 43121 Parma PR, Italy 167Universit`a degli Studi di Pavia, 27100 Pavia PV, Italy 168University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 169Pennsylvania State University, University Park, Pennsylvania 16802, USA 170Physical Research Laboratory, Ahmedabad 380 009, India 171Universit`a di Pisa, I-56127 Pisa, Italy 172University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA 173Pontificia Universidad Católica del Perú, Lima, Perú 174University of Puerto Rico, Mayaguez 00681, Puerto Rico, USA 175Punjab Agricultural University, Ludhiana 141004, India 176Queen Mary University of London, London E1 4NS, United Kingdom 177Radboud University, NL-6525 AJ Nijmegen, Netherlands 178University of Rochester, Rochester, New York 14627, USA 179Royal Holloway College London, TW20 0EX, United Kingdom 180Rutgers University, Piscataway, New Jersey 08854, USA 181STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom 182Universit`a del Salento, 73100 Lecce, Italy 183San Jose State University, San Jos´e, California 95192-0106, USA 184Sapienza University of Rome, 00185 Roma RM, Italy 185Universidad Sergio Arboleda, 11022 Bogotá, Colombia 186University of Sheffield, Sheffield S3 7RH, United Kingdom 187SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA 188University of South Carolina, Columbia, South Carolina 29208, USA 189South Dakota School of Mines and Technology, Rapid City, South Dakota 57701, USA 190South Dakota State University, Brookings, South Dakota 57007, USA 191Southern Methodist University, Dallas, Texas 75275, USA 192Stony Brook University, SUNY, Stony Brook, New York 11794, USA 193Sun Yat-Sen University, Guangzhou 510275, China 194Sanford Underground Research Facility, Lead, South Dakota 57754, USA 195University of Sussex, Brighton, BN1 9RH, United Kingdom 196Syracuse University, Syracuse, New York 13244, USA 197Universidade Tecnológica Federal do Paraná, Curitiba, Brazil 198Texas A&M University, College Station, Texas 77840, USA 199Texas A&M University—Corpus Christi, Corpus Christi, Texas 78412, USA 200University of Texas at Arlington, Arlington, Texas 76019, USA 201University of Texas at Austin, Austin, Texas 78712, USA 202University of Toronto, Toronto, Ontario M5S 1A1, Canada 203Tufts University, Medford, Massachusetts 02155, USA IDENTIFICATION AND RECONSTRUCTION OF LOW-ENERGY …PHYS. 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D 107, 092012 (2023) 092012-21 204Universidade Federal de São Paulo, 09913-030, São Paulo, Brazil 205Ulsan National Institute of Science and Technology, Ulsan 689-798, South Korea 206University College London, London, WC1E 6BT, United Kingdom 207Valley City State University, Valley City, North Dakota 58072, USA 208Variable Energy Cyclotron Centre, 700 064 West Bengal, India 209Virginia Tech, Blacksburg, Virginia 24060, USA 210University of Warsaw, 02-093 Warsaw, Poland 211University of Warwick, Coventry CV4 7AL, United Kingdom 212Wellesley College, Wellesley, Massachusetts 02481, USA 213Wichita State University, Wichita, Kansas 67260, USA 214William and Mary, Williamsburg, Virginia 23187, USA 215University of Wisconsin Madison, Madison, Wisconsin 53706, USA 216Yale University, New Haven, Connecticut 06520, USA 217Yerevan Institute for Theoretical Physics and Modeling, Yerevan 0036, Armenia 218York University, Toronto M3J 1P3, Canada †Corresponding author[email protected] ‡Corresponding author[email protected] A. ABED ABUD et al. PHYS. REV. D 107, 092012 (2023) 092012-22