Topological background discrimination in the PandaX-III neutrinoless double beta decay experiment
J Galan, X Chen, H Du, C Fu, K Giboni, F Giuliani, K Han, B Jiang, X Ji, H Lin, Y Lin, J Liu, K Ni, X Ren, S Wang, S Wu, C Xie, Y Yang, D Zhang, T Zhang, L Zhao, S Aune, Y Bedfer, E Berthoumieux, D Calvet, N d'Hose, E Ferrer-Ribas, F Kunne, B Manier, D Neyret, T Papaevangelou, L Chen, S Hu, S Jian, P Li, X Li, H Zhang, M Zhao, J Zhou, Y Mao, H Qiao, S Wang, Y Yuan, M Wang, Y Chen, A N Khan, N Raper, J Tang, W Wang, C Feng, C Li, J Liu, S Liu, X Wang, D Zhu, J F Castel, S Cebrián, T Dafni, I G Irastorza, G Luzón, H Mirallas, X Sun, A Tan, W Haxton, Y Mei, C Kobdaj, Y Yan
aa r X i v : . [ phy s i c s . i n s - d e t ] J u l Topological background discrimination in thePandaX-III neutrinoless double beta decayexperiment
J Galan , , X Chen , H Du , C Fu , K Giboni , F Giuliani ,K Han , B Jiang , X Ji , , H Lin , Y Lin , J Liu , K Ni ,X Ren , S Wang , S Wu , C Xie , Y Yang , D Zhang ,T Zhang , L Zhao , S Aune , Y Bedfer , E Berthoumieux ,D Calvet , N d’Hose , E Ferrer-Ribas , F Kunne , B Manier ,D Neyret , T Papaevangelou , L Chen , S Hu , S Jian , P Li ,X Li , H Zhang , M Zhao , J Zhou , Y Mao , H Qiao ,S Wang , Y Yuan , M Wang , Y Chen , A N Khan , N Raper ,J Tang , W Wang , C Feng , C Li , J Liu , S Liu , X Wang ,D Zhu , J F Castel , S Cebri´an , T Dafni , I G Irastorza ,G Luz´on , H Mirallas , , X Sun , A Tan , W Haxton ,Y Mei , C Kobdaj , Y Yan INPAC and School of Physics and Astronomy, Shanghai Jiao Tong University,Shanghai Laboratory for Particle Physics and Cosmology, Shanghai 200240, China IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France China Institute of Atomic Energy, Beijing 102413, China School of Physics, Peking University, Beijing 100871, China School of Physics and Key Laboratory of Particle Physics and Particle Irradiation(MOE), Shandong University, Jinan 250100, China School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275,China Department of Modern Physics, University of Science and Technology of China,Hefei 230026, China; State Key Laboratory of Particle Detection and Electronics,University of Science and Technology of China, Hefei 230026, China University of Zaragoza, C/P Cerbuna 12 50009, Zaragoza, Spain College of Physical Science and Technology, Central China Normal University,Wuhan 430079, China Department of Physics, University of Maryland, College Park, MD 20742, USA Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720, USA Center for Excellence in High Energy Physics and Astrophysics, SuranareeUniversity of Technology, Nakhon Ratchasima 30000, ThailandE-mail: [email protected]
E-mail: [email protected]
E-mail: [email protected] opological background discrimination in the PandaX-III experiment Abstract.
The PandaX-III experiment plans to search for neutrinoless double betadecay (0 νββ ) of
Xe in the China JinPing underground Laboratory (CJPL). Theexperiment will use a high pressure gaseous Time Projection Chamber (TPC) toregister both the energy and the electron track topology of an event. This article isdevoted to demonstrate our particular detector setup capabilities for the identificationof 0 νββ and the consequent background reduction.As software tool we use REST, a framework developed for the reconstruction andsimulation of TPC-based detector systems. We study the potential for backgroundreduction by introducing appropriate parameters based on the properties of 0 νββ events. We exploit for the first time not only the energy density of the electron track-ends, but also the electron scattering angles produced by an electron near the endof its trajectory. To implement this, we have added new algorithms for detectorsignal and track processing inside REST. Their assessment shows that backgroundcan be reduced by about 7 orders of magnitude while keeping 0 νββ efficiency above20% for the PandaX-III baseline readout scheme, a 2-dimensional 3 mm-pitch strippedreadout. More generally, we use the potential of REST to handle 2D/3D data to assessthe impact on signal-to-background significance at different detector granularities, andto validate the PandaX-III baseline choice. Finally, we demonstrate the additionalpotential to discriminate surface background events generated at the readout planein the absence of t o , by making use of event parameters related with the diffusion ofelectrons.
1. Introduction
The neutrino sector has been one of the most promising research areas for searching fornew physics beyond the Standard Model (SM). Neutrino oscillations and the inferrednon-zero neutrino mass offered a concrete evidence of new physics, as demonstratedby experiments including Super-Kamiokande [1], SNO [2], and etc. Early in 1937, thepossibility for an electrically neutral fermion to be the anti-particle of itself was raisedby Majorana [3], and neutrinos are the most promising candidates for the so-calledMajorana fermions. Soon after that, physicists started to use the neutrinoless doublebeta decay (0 νββ ) to search for the existence of Majorana neutrinos [4]. In a SM-allowed two-neutrino double beta decay process, two neutrons in a candidate nucleusdecay into two protons simultaneously and emit two electrons together with two electronantineutrinos. Such a process has been observed in a dozen or so isotopes, including Ge,
Te,
Xe, and etc (see, for example [5]). If neutrinos are Majorana fermions,no electron antineutrinos are released in the double beta decay process. It has also beenargued with the Black Box Theorem that an observation of 0 νββ directly indicatesthe Majorana nature of neutrinos [6]. The experimental observation of 0 νββ will alsodistinctly violate the conservation of the lepton number, and have far-reaching impactbeyond the neutrino sector [7]. After about 80 years of experimental effort, no firmevidence for 0 νββ has been obtained. Several major experiments are taking data orare under construction and many more smaller-scale efforts are in R&D phase. Currentstatus and expected sensitivity can be seen in reference [8] and references within. opological background discrimination in the PandaX-III experiment νββ of Xe using a high pressuregaseous Time Projection Chamber (TPC) [9]. The experiment will be located in thenewly excavated China JinPing underground Laboratory Phase II (CJPL-II) in SichuanProvince, China [10]. As a calorimeter, PandaX-III measures the energy of two electronsfrom 0 νββ and constructs an energy spectrum at the Region Of Interest (ROI) aroundthe Q ββ value of Xe, 2,457.83 keV [11]. The expected energy resolution is better than3% Full-Width-Half-Maximum (FWHM) at the Q ββ value [12, 13]. PandaX-III followsthe standard recipe of a low background experiment, including deep underground labenvironment, passive shielding, and careful screening of detector as well as electronicsmaterial to minimize the number of dubious background events in the ROI. Thedescendants of U and
Th, mainly
Bi and
Tl, contribute most significantlyto the background in the ROI. One of the gamma lines from
Bi at 2,448 keV, only10 keV below the 0 νββ
Q-value, poses a major challenge to event identification withenergy alone. The expected background level at the ROI including a realistic detectorresponse is on the order of 10 − keV − kg − y − when considering only the event energy.Additional background suppression can be realized with event tracking information,which is the main topic of this paper. Different from other detector technologies, agaseous TPC will record detailed trajectories of the two electrons from a potential0 νββ event. PandaX-III will exploit the electron tracking potential using fine-pitchedMicrobulk Micromegas [14] readout planes to reach millimeter level spatial resolution,in comparison with the typical 0 νββ track length of 10 cm scale at 10 bar. The signalidentification will exploit the features of the electron tracks topology produced by 0 νββ decays. The two electrons generated by a 0 νββ decay will produce two bright Braggpeaks, occurring on at least 95% of the decays [15]. On the other hand, gammabackground events in the ROI normally have only one Bragg peak. We will reviewthe details on the main characteristics of signal and background events, previouslyinvestigated in reference [15], and we will exploit them to perform a discriminationanalysis to demonstrate the ultimate background level achievable by the PandaX-IIIsetup.The work presented in this paper includes an accurate Monte Carlo demonstrationof the operation of the PandaX-III detector setup from the point of view of 0 νββ eventidentification. Previous work, published in reference [9], provided a rough estimation ofthe final background achievable. This paper provides a complete and detailed analysisfor PandaX-III including a realistic 2-dimensional detector readout.PandaX-III adopts the event-oriented software framework REST ‡ for simulationand data analysis, especially to facilitate the topological analysis. With REST andthe underlying Geant4 framework, we simulate 0 νββ events and background eventswith energy deposition and tracking information in the gas medium. Realistic detectorresponse, including the strip readout scheme, is then added to generate mock data, ‡ We include in Appendix A necessary technical details on the software used, and the description ofthe event data and event process routines used in our analysis. Any keyword starting by
TRest will doreference to REST and it will be detailed in one of the appendices of this document. opological background discrimination in the PandaX-III experiment
2. Background rejection on the PandaX-III baseline readout scheme
We present here the results obtained using a realistic detector readout descriptionbased on the existing PandaX-III baseline Microbulk Micromegas design [16]. Forrigourosity, we provide in Appendix B details on how we generate our Monte Carlo event data including any necessary details such as physics considerations and detaileddetector readout description for PandaX-III, based on a 2-dimensional charge readout,which represents a major milestone on the event reconstruction and data analysis ofthe experiment. In section 2.1, we define the parameters, extracted during the eventdata processing, that will be used for event pattern recognition, leading to our finalbackground discrimination results reported in section 2.2.
This section does not focus on the nature, or the source, of background events, butmostly on the type of background events that might mimic a 0 νββ in the ROI at the Q ββ energy of Xe. Such background events, producing a topological structure similarto a 0 νββ decay, can only be produced in the active detector volume by gammas withan energy equal to or above the Q ββ value. Some of those gammas end up producinga long electron track of characteristics similar to the 0 νββ signal. Still, a good choiceof parameters extracted from the physical track provides an excellent instrument todifferentiate between this kind of events and electron tracks produced by 0 νββ decays.Previous studies on 0 νββ pattern recognition [23–25] have already shown thepotential of certain parameters, such as the number of secondary tracks or end-trackenergies to differentiate background and signal events. We reach the same conclusions,and we obtain comparable results on their discrimination power. Furthermore, we willinvestigate the potential of novel parameters never used in previous studies, viz. as theend-track twist parameter and the track length . Below we discuss the respective meritsof both, previously mentioned and novel parameters. • Number of secondary tracks, or track energy ratio.
One of the mostpowerful discriminators is related to the number of independent tracks identified opological background discrimination in the PandaX-III experiment † . Background eventsare originated by high energy gammas, and many of those gammas interacting inthe detector will produce multi-track events due to Compton scattering combinedwith a photoelectric interaction absorbing the remaining gamma energy, thereforeproducing a main long energetic track. Additionally, the higher initial energy ofthe single electron background compared to the initial energy of each of the twoelectrons generated in the 0 νββ decay makes so that the probability of producingsecondary gamma radiation is higher for single electron background events.In practice, it is convenient to define the track energy ratio , θ , as the ratio betweenthe total energy of secondary tracks and the total energy of the event, E tot , expressedas, θ = 1 E tot N i X n i =1 E i,n (1)where E i,n is the energy of track number n from projection i , and n i =0 correspondsto the most energetic track of each projection. If the event does not containsecondary tracks, as it is frequently the case in 0 νββ events, the value of θ will bezero. Such a definition accommodates the 2D and 3D detector readouts in a singleobservable, and provides a probability density function (pdf) of the θ parameter thatcan be exploited for signal and background separation. It is important to remarkthat the definition of θ is done for convenience on the flexibility to tune the signal-to-background ratio by selecting an appropriate θ -value. We have compared ourselvesthis observable with other approaches used in other studies [23], obainning verysimilar results. It must be remarked, that using the θ parameter does not constrainthe number of tracks. However, typically low values of θ will accept mostly eventscontaining only one or two tracks, and rarely three. • End-track energies, or blobs charge.
An electron traveling in a gas mediumwith energies above ∼ MeV experiences a constant energy loss, dE/dx , along itstrajectory in the medium. Once the electron loses most of its energy, at levelswell below 1 MeV, its dE/dx increases suddenly until it loses all of its kinematicenergy. This phenomenon produces a high density charge region at the electrontrack end, or Bragg peak, commonly called blob . Obviously, a 0 νββ track emittingtwo electrons with a common origin will be similar to a single track with two blobs at the track ends, while single electron background tracks will only produce oneBragg peak. The end of single electron tracks where no blob is found will be called tail .The energy, or charge, Q , in a certain blob is determined by summing up the energydeposited around a sphere of radius R o centered at each of the high density track endcoordinates ‡ . The following mathematical expression summarizes our blob charge † The number of tracks is found after using
TRestHitsToTrackProcess , described in Appendix A.2,while the conditions in which those are obtained is described in Appendix B.1 ‡ The blob coordinates are obtained by
TRestFindTrackBlobsProcess , detailed in Appendix B.3 opological background discrimination in the PandaX-III experiment Q j = X d = r j,n Another feature characterizing the behavior of the electrontrajectory near the blob is the erratic nature of its trajectory. This erratic behavior,due to higher electron scattering angles, does not manifest at the initial interactionvertex, or tail , at single electron background events. On the contrary, energeticelectrons, with initial energies of the order of the Q ββ value, will usually produce aclear straight tail .In order to quantify this effect we introduce the twist parameter that measures theangle between consecutive hits belonging to a top-level track § near the track ends.The twist parameter , ξ , is expressed as follows, ξ j = 1 N j N j X i =0 (1 − ˆ n i · ˆ n i +1 ) / , and ξ l = min( ξ , ξ ) (3)where ˆ n i represents the unit vector defined by the i th and i th + 1 nodes of areconstructed top-level track , and i = 0 can be identified with the first (or last)node of the physical track . The total number of hits, N j , considered in each end-track, j =1,2, is relative to the total number of hits, N tot , at the top-level track .In our analysis we have defined N j as the 25% of N tot , i.e. a track containing N tot =28 hits will average the 6 angles formed by the 7 hits closer to the end-tracks.The normalization factor 2 in the previous expression is introduced to assure ξ ismathematically contained in the range (0 , ξ =0 means that the nodes arefully aligned. As in the previous observable, we define ξ l as the lowest value betweenthe twist parameter obtained at each end-track, and obtain independent values foreach projection, ξ Xl and ξ Yl , for the 2-dimensional case. • Track length. We might also expect that two electron 0 νββ tracks will producea slightly shorter path due to the generation of two blobs, and therefore a § A top-level track in our analysis identifies with the physical track reconstructed, see also TRestTrackEvent definition at Appendix A, opological background discrimination in the PandaX-III experiment dE/dx in average. Although this observable is expected to have a weakdiscriminating power, we still assess its performance.The track length , L , is simply calculated as the total measured distance betweenthe track ends, following the ordered node sequence at the top-level track producedafter TRestTrackReconnectionProcess . Expressed as, L = N − X i =0 d i,i +1 (4)where N is the total number of hits, or nodes, in the top-level track , and d i,i +1 is thedistance between the hit i and i + 1, or connected hits . Again, for the 2-dimensionalcase we will obtain 2 independent length measurements for each projection, L X and L Y .In summary, these observables will allow us to discriminate background bydifferentiating the main background and signal properties. When identifying a 0 νββ signal event we search for a main energetic track, with almost negligible energydeposition on secondary tracks belonging to the event. Signal events will generallylack the presence of an end-track tail , and therefore, the combination of low end-trackvalues for blob charge , Q l and twist parameter , ξ l , will be decisive on the identification ofsuch a feature. These main characteristics can be easily recognized on the backgroundand signal events shown on Figure B3, at Appendix B.Finally, it is important to remark that these parameters serve also to describe in aquantitative way each event, i.e. they can be exploited to characterize the experimentaldata and support the construction of a Monte Carlo background model. The naturefrom different background contributions due to the different contamination sources andcomponents in the detector might be better understood by studying the behavior ofthese parameters on different populations of events, measured at different data takingconditions. Therefore, even if a parameter does not contribute finally on the signal-to-background significance, it may be valuable in other scenarios to help understandingthe nature of the data collected with the detector. We report in this section the results obtained on background reduction consideringthe topological features of signal and background events. We will take into accountthe forecasted PandaX-III data taking conditions, i.e. a vessel filled with 10 bar ofxenon+TMA 1% gas mixture, and a detailed detector response, carefully describedin Appendix B.The Monte Carlo 0 νββ signal events, used to define our signal efficiency have beenimported in RestG4 using a Decay0 [26] pre-generated event population. The initial4-momentum definition of each of the two electrons produced by the 0 νββ decay israndomly positioned at the active volume of the detector, or gas volume, for each event,and then tracked using Geant4 physics processes. opological background discrimination in the PandaX-III experiment U and Th decay chains at those detector components. For thecopper vessel we generate our events randomly on the bulk of the material, while for theMicromegas contamination we generate surface events at the readout plane location,behind 10 µ m of copper. In order to guarantee enough statistics at the end of ourtopological analysis we have generated near 10 decays of U and Th isotopes forthe vessel contribution, and 5 · decays for the Micromegas contributions. Our signalefficiency has been calculated over an initial population of 10 generated 0 νββ events.Signal and background events have been processed following the scheme describedon Appendix B.1. Figure 1 shows the parameter distributions obtained during the dataprocessing chain, and described previously on section 2.1. Except for the track energyratio , it must be noted that the other distributions follow similar patterns for differentsimulated background components.We apply our criteria to discriminate signal from background sequentially on theseparameters, following the order af the list provided in section 2.1. We combine theXZ- and YZ-projections into a single parameter by choosing the minimum value of eachprojection for the blob charge , Q min , and twist parameter , ξ min , i.e. for each event weonly consider the 2-dimensional projection where tail identification is more obvious.While we have chosen the maximum track length of each projection, L max , supportedby the argument that 0 νββ events are expected to be shorter. We have obtained ourthreshold values, or cuts, such that they maximize the signal-to-background significanceby maximizing the figure of merit, ǫ s / √ ǫ b , at each of the four topological criteria usedin our analysis, i.e. track energy ratio , blob charge , twist parameter and track length .Here, ǫ s and ǫ b correspond to the signal and background reduction factors at each ofthose steps. The following topological parameter conditions were obtained after suchoptimization, θ < . · − , Q minl > 176 keV ξ minl > . L max < . . The final selected event population, signal or background events, will necessarilysatisfy those conditions. We should mention that these values have been obtained byoptimizing the dataset corresponding to the U vessel generated events. However,it must be noted that such a choice is not critical in view of the similar behaviorof the different topological parameters produced by different background sources andcomponents, as it can be observed in Figure 1. As a consequence, the threshold values opological background discrimination in the PandaX-III experiment − − − ββν (a) (b) (c) (d) Figure 1. The distributions of topological parameters, normalized to unity, obtainedfrom the XZ-projection of 0 νββ event tracks (filled curve), compared to the equivalentdistributions of the four background datasets considered in our study (colored curves).The distributions are built using only the events contained in the ROI, i.e. in the energyrange (2395,2520) keV. On top of that, each distribution accumulates the sequentialtopological criteria we applied in the preceding parameter. (a) The track energy ratio,or θ parameter. Different physics processes contribute to create certain structures onthis distribution. Peaks found at low θ -values, θ . . 01, are related to the escape peaksof xenon, while hills appearing at higher values are related to bremsstrahlung gammaemission produced by high energy electron tracks, or Compton scattering processesthat end up on a photoelectric process producing a main electron energetic track. (b)The lower track energy blob, Q Xl . Events satisfying θ < · − . (c) The lower twistparameter , ξ Xl , satisfying θ < · − and Q Xl < 176 keV. (d) The track length, L X ,satisfying θ < · − , Q Xl < 176 keV and ξ Xl < opological background discrimination in the PandaX-III experiment C oun t s C oun t s after detector responseafter track cutafter blob cutafter twist cutafter length cut (a) (b) Figure 2. (a) The simulated energy spectrum response of 0 νββ events around the Q ββ value, and the resulting spectra after applying the different topological criteriasequentially, i.e. track energy ratio , blob charge , twist parameter and track length . Themain peak corresponds to 0 νββ events for which full decay energy was acquired byour detector, while the distribution left tail corresponds to 0 νββ events with partialenergy loss outside the detector readout plane boundaries, or partially contained in thedetector acquisition window, limited by the electronics. (b) The equivalent backgroundspectra resulting from U decays generated from the copper vessel. The peaksobserved correspond to two high energy gammas, 2,204 keV and 2448 keV, from thespectrum gamma emission of Bi present in the U decay chain. The 3% FWHMGaussian smearing introduced by the TRestHitsSmearingProcess can be recognized inboth figures. obtained are not strongly dependent on this choice. Anyhow, we must remark that themost sensitive threshold value corresponds to the track energy ratio parameter, as it canbe induced from the distribution presented in Figure 1(a). Anyhow, in our particularconditions, we observe that the low value of θ , resulting in our particular optimization,constrains our event selection practically to the population of events that contain onlyone single main track.Before applying the sequential topological criteria we filter the event population tothose events that are found in the ROI, defined as Q ββ ± σ , where σ =31 keV is givenby the assumed 3% FWHM energy resolution, introduced in TRestHitsSmearingProcess (see Appendix A.2).The energy definition considered is the value extracted from TRestTriggerAnaly-sisProcess (see Appendix B.3) which contains all the effects introduced by the detectorreadout response. The resulting energy spectrum for 0 νββ , together with one of thebackground components studied is shown on Figure 2, including the accumulated effectof sequential cuts on signal efficiency and background reduction.Table 1 shows the percentage of accepted signal events and background reduction opological background discrimination in the PandaX-III experiment Xe [%] U Th U Th Geant4 × − × − × − × − Response × − × − × − × − Track × − × − × − × − Blob × − × − × − × − Twist × − × − × − × − Length × − × − × − × − Table 1. Percentage of accepted Xe signal events, or signal efficiency, together withthe absolute background reduction factors at the ROI for the PandaX-III CDR baselinereadout, after applying the detector response and sequential topological cuts describedin the text. Each row includes the accumulative reduction of all previous cuts. Forthe sake of simplicity we avoid to express statistical errors in this table, although wewill propagate them in Table 2, where final background rates are given. Systematicerrors related to the Geant4 generator were studied previously in reference [9] usingtwo independent Monte Carlo generators and geometry implementations. Any othersource of uncertainty will be discussed in our conclusions. factors, i.e. the final number of events surviving after each cut per simulated one.The first row, Geant4 , is the calorimetric response where we consider all the energydepositions in our active volume, here we only integrate events inside our ROI; thesecond row, Response , corresponds to the population of events that remain in the ROIafter applying the detector response, i.e. after applying readout fiducialization andboundaries imposed by the electronics acquisition window. We should remark, thatwhen considering background events with energies above the ROI, they may finally getinside the ROI definition due to the partial event energy registered by our detector.The subsequent rows in the table show the accumulative effect of the topological cutsapplied there after. The resulting topological selection contains only contributions fromthe Tl isotope decay produced inside the Th decay chain, and Bi produced insidethe U chain.We discover looking into Table 1 that the topological background reduction is abouta factor 100, and it is comparable for all the background components except for the UMicromegas dataset, which is worse by about a factor 2. This result is explained mainlydue to the failure of our topological cuts to discriminate surface events, as revealedby Figure 3(a). The surface background contamination originated from the Micromegasreadout is related to Bi decays producing β -tracks emanating from the readout plane.The Bi decay is the only isotope, inside the U decay chain, producing a β -decaywith Q β end-point energy above our ROI. The surface contamination coming from the Th Micromegas decays is also present, but as it is observed in Figure 3(b), thereis also an important volume component which is due to a 2,614 keV gamma which isproduced at practically each Tl decay in the Th chain. The volume component dueto Bi in the Micromegas is negligible, compared to its surface contribution, related opological background discrimination in the PandaX-III experiment − − C oun t s after detector responseafter track cutafter blob cutafter twist cutafter length cut − − − − − − − 10 1 C oun t s ββν (a) (b) Figure 3. (a) The distribution of the average z -position for tracks from Thgenerated events originated from the Micromegas readout plane, placed at z =1000 mm,after different steps of the topological cuts. (b) The distribution of the average z -position for signal and the four background contributions studied, after all thetopological cuts have been applied. Lateral vessel Micromegas Units U Th U Th6 ± ± < < 223 10 − cpy0.365 ± ± < < − keV − kg − y − Table 2. Final background contribution after applying all the topological cuts, i.e.renormalizing the results of the last row presented on Table 1 using the expected Thand U isotope contamination for the different detector components. The results arepresented in the usual units, counts per year (top row) and keV − kg − y − (bottomrow). Measurements of Microbulk Micromegas surface contamination provide resultswithin the sensitivity limit of the measuring device, and therefore, our result for thiscomponent is given as an upper limit of the final background contribution to theexperiment. to the fact that only about 1.5% of the decays produce a 2,447 keV gamma.Table 2 shows the final background contribution of the detector componentsstudied, after renormalization with the corresponding material activities of Uand Th for Micromegas and vessel components. We use the same values asreported in reference [9]. The surface contamination upper limit of Micromegas being < 45 nBq/cm and < 14 nBq/cm , and the radiopure copper vessel bulk contaminationbeing 0.75 µ Bq/kg and 0.2 µ Bq/kg [27], for U and Th, respectively.We conclude that the vessel contamination contribution is negligible comparedto the contribution of the Micromegas readout plane, being its estimated overall opological background discrimination in the PandaX-III experiment Xe U Th Xe U Th Xe U Th Track Blob Twist Total Xe U Th Xe U Th Track Blob Twist Total Table 3. Relative signal efficiency and background reduction factors, in percentage,after each topological criterion, at different pitch values (1 mm, 2 mm, 3 mm, 4 mmand 6 mm) for the 2-dimensional stripped readout. The initial population of eventsconsidered at each step are the events in the ROI surviving from the previous criteria. contribution at the level of 1 cpy. Of course, the final value will ultimately dependon the real surface contamination present at the Micromegas readout. Considering thatthe contamination levels used in our Monte Carlo are limits obtained experimentallywe may still remain optimistic about this contribution. In section 4 we will show howwe can achieve an additional reduction on the surface contamination near the readoutplanes by exploiting the effect of electron diffusion on the time signals registered byour TPC [13]. Finally, we must also consider our result as conservative from the pointof view that there will be probably room for improvement by enhancing the existingparameter correlations, e.g. exploiting more sophisticated multivariate methods.We reserve any discussion on the discrimination potential of the topologicalparameters used in our analysis for section 3, where we will also argue on the benefitof introducing the twist parameter for our particular readout granularity, and we willassess the appropriateness of the 2-dimensional 3mm-pitch detector choice as a baselinefor the PandaX-III experiment. 3. Readout topology and granularity studies This section extends our study on background discrimination to different readouttopologies and granularities. We will evaluate our new event reconstruction algorithms-detailed in Appendix A- using two different readout layouts, a 2-dimensional strippedlayout and a 3-dimensional pixel layout, to assess the potential gain on signal efficiencyand/or background reduction. The results presented in this section will provide insight opological background discrimination in the PandaX-III experiment Xe U Th Xe U Th Xe U Th Track Blob Twist Total Xe U Th Xe U Th Track Blob Twist - - - - - - Total Table 4. Relative signal efficiency and background reduction factors, in percentage,after each topological criterion, at different pitch values (2 mm, 4 mm, 6 mm, 8 mm and10 mm) for the 3-dimensional pixel readout. The initial population of events consideredat each step are the events in the ROI surviving from the previous criteria. on the optimum readout scheme to be used in the PandaX-III data taking conditions,i.e. a vessel filled with 10 bar of xenon+TMA 1% gas mixture. We will discuss then theappropriateness of the PandaX-III baseline readout choice -detailed in Appendix B.2-considering the advantages and disadvantages of 2-dimensional versus 3-dimensionalevent reconstruction, for different sizes of the readout channels, or detector granularity.We have re-processed the same datasets analyzed in section 2. However, this timewe focus only on the U and Th background contributions originated in the vessel.The same processing chain -as described in Appendix B.1- has been applied, being thereadout used for event reconstruction the only modified element. We have systematicallyproduced different readout structures in 2D and 3D at different pitch values. For the , the 3 mm pitch PandaX-III baseline readout module design hasbeen generalized to allow the definition of readout channels of any pitch value. Whendefining a different pitch value we keep the size of the module unchanged, e.g. when wedefine a 1 mm pitch readout we increase the number of readout channels from 64 to 192.For the we have simply designed a readout module using squaredpixels, and for practical reasons we adapt the number of pixels to keep constant the sizeof the readout module as a function of the pixel size. We must remark anyhow thatminor adjustments are required at the processing chain when dealing with different pitchsizes, e.g. the cluster distance used to identify tracks (see TRestHitsToTrackProcess description at Appendix A.2) was set to 2.5 × the pitch size, and the radius of the blobcharge definition was fine tuned, being as low as R =1 cm for 1 mm pitch, and as highas R =2 cm for 1 cm pitch. opological background discrimination in the PandaX-III experiment k , so that theevent reconstruction limits are just bound by the field cage wall defined in the Geant4 geometry.Tables 3 and 4 show the effects of topological criteria, similar to those applied onsection 2, for the simulated signal and background populations with different readoutlayouts and granularities. For each criterion ( track energy ratio , blob charge and twist parameter ) we provide the relative reduction, in percentage, with respect to thesurviving event population from the previous criterion, or cut. We maximize our signalsignificance at each step by maximizing the quantity, ǫ s / √ ǫ b . We observe that thereduction potential of the track energy ratio criterion is slightly better compared to theversion where we included the fiducial detector response in section 2, i.e. by comparingthe 3mm-pitch stripped readout results shown in Table 3 with the values that can bededuced from Table 1. This difference is mostly due to the fact that multi-track eventshave left the ROI after applying the detector response, and a subset of the backgroundevent population loses its multi-track features when we apply the detector response.One interesting finding is that the newly introduced twist parameter starts to beefficient below 6 mm pitch, for both, the 2-dimensional and the 3-dimensional readoutversions. As observed in Table 3, the 8 mm and 10 mm pitch pixel readouts studieddid not improve the significance of the signal when using the twist parameter criterion.Figure 4 shows the evolution of the twist parameter and it confirms the advantageto differentiate signal and background distributions as the pitch value is reduced.Furthermore, we have added to this figure a third dataset where we generate singleelectrons with energy equal to the Q ββ of Xe, demonstrating a small dependency onthe quality of the topological observables related to the nature of the background source.The twist parameter provides the less powerful topological criterion (as it is deducedfrom Tables 3 and 4). However, we should take into account that this criterion operatesafter the event selection of track energy ratio and blob charge criteria. It is remarkablethen that the twist parameter criterion is still capable to improve the signal significance,meaning that the twist parameter definition is an additional track feature that can beexplored, exploited, and optimized in a future multivariate analysis that combines thetrack observables more efficiently.We summarize our results in Figure 5, where we present the total signal significance,measured as ǫ s / √ ǫ b , obtained with our topological criteria for different readouts. Thisfigure allows us to assess now the gain on experimental sensitivity when reducing thedetector granularity, and quantify the impact of using a 2-dimensional readout compared k Instead of using the 41-modules readout plane scheme described in Appendix B.2, we extend thereadout definition limits by adding readout modules as needed to cover the full active area. opo l o g i c a l b a ckg r o u n dd i s c r i m i n a t i o n i n t h e P a n da X - III ex p e r i m e n t Xe136vessel_Ra228vessel_Th234gasElectron_2458keVStrip 2D - 1mm Strip 2D - 3mm Strip 2D - 4mm Strip 2D - 6mm (a) (b) (c) (d) Pixel 3D - 2mm Pixel 3D - 4mm Pixel 3D - 8mm Pixel 3D - 10mm (e) (f) (g) (h) Figure 4. The distribution of the twist balance, ξ b , parameter, a variant of the twist parameter calculated as ξ b = ( ξ h − ξ l ) / ( ξ h + ξ l ), being ξ h the higher end-track twist parameter value, and ξ l the lower end-track twist parameter value. The different plots show the evolution ofthis parameter for different detector granularities, and different readout topologies, 2D strips (top figures), and 3D pixels (bottom figures).The distribution from 0 νββ signal events (filled curve) is compared to the background distribution of different contaminations as describedin the text. For the 2D strips distributions only one of the projections is represented. opological background discrimination in the PandaX-III experiment S i gn i f i c an c e Pitch [mm] This work [Strips 2D Th232]This work [Strips 2D U238]This work [Pixels 3D Th232]This work [Pixels 3D U238]S. Cebrian et al. [Pixels 3D Th232]S. Cebrian et al. [Pixels 3D U238]J.Renner et al. [Pixels 3D Th232]J.Renner et al. [Pixels 3D U238]J.Renner et al. [Pixels 3D Th232]J.Renner et al. [Pixels 3D U238] Figure 5. Total significance of topological criteria for the different detectorgranularities and topologies studied. The lines interconnecting data points show ourresults for the two different contaminations studied ( Th and U), and the twodifferent readout topologies (Strips 2D and Pixels 3D). We add to this figure thesignificances obtained in previous studies, calculated from the background and signalefficiencies reported at references [23, 25], and discussed in the text. Moreover, we use Figure 5 to compare our results to previously published studies- where they use similar conventional discrimination techniques. As it is observed, wefind remarkably good agreement with reference [23] on the final significance at 1 cm 3Dpixel readout, for both vessel contaminations. While, for reference [25], although wefind reasonably compatible results for the U contamination chain (or Bi), we findtheir result on Th (or Tl) surprisingly high when compared to our data, beingthe origin of the main discrepancy at the level of the track energy ratio criterion. Thedifference between our results and those reported in reference [25] are even larger whenwe consider that their 1 cm results correspond to pure xenon, and it was claimed inreference [23] that background reduction due to blob identification is worse by a factor3 due to the higher electron diffusion in pure xenon, and that finally implies almost afactor 2 worse on significance. The source of this discrepancy might be related to thenon-independent treatment of electron diffusion and detector granularity in [25], and the opological background discrimination in the PandaX-III experiment 4. Fiducial background rejection in charge based TPC readouts. The results obtained in section 2 unveiled the weakness of our topological cuts todiscriminate surface contamination events originated from the Micromegas readoutplanes, as revealed by Figure 3(a). Our setup lacks an absolute reference time, t o ,from the interactions taking place in the detector volume. Without such a reference wecannot directly determine the event absolute z-position, making it hard to discriminatesurface events originated on the readout planes, or the cathode.In this section we develop a basic technique to demonstrate the remainingpotential for further background reduction by attenuating the negative impact of surfacecontamination, even in the absence of t o . For that we take advantage of the readoutsignal dependence on the diffusion of ionized electrons drifting towards the readoutplanes. The time signals induced on the Micromegas readout, due to a particular energydeposition on the TPC volume, will be broader when the electron cloud has drifted alonger distance towards the readout plane. However, the resulting primary electronsfrom β -tracks generated near the readout plane will drift a very short distance, andtherefore the original charge distribution will be almost unaffected by the electron drift.We have re-processed the 0 νββ signal and Micromegas background datasetsanalyzed in previous sections using the same data chain parameters as defined insection 2. However, now we need to include few additional effects in order to extracta parameter, σ w , that correlates to the diffusion of electrons in the gas. The obtentionof this parameter is performed under realistic conditions including the signal shapingintroduced by electronics and a typical electronic noise level (further details on theextraction of this parameter are given in Appendix C). In Figure 6 we observe the desireddependence of σ w with the z-position of the simulated 0 νββ event, together with the σ w distribution produced by the two Micromegas background components compared to the0 νββ signal one. We observe clearly how background surface events peak at low valuesof σ w .Therefore, we exploit the properties of σ w to introduce an additional selectioncriterion in our data by accepting only the population of events that are above a certaindiffusion threshold, as quantified by σ w . Table 5 presents the results on event acceptanceafter applying cuts for different threshold values, where we observe that we manageto reduce by an additional factor 0.15 the contribution from the U chain, due to Bi decays, while keeping our signal efficiency near 75%. We must remember that the opological background discrimination in the PandaX-III experiment [ s a m p l e s ] w σ w σ Xe136micromegas Th232micromegas U238 (a) (b) Figure 6. (a) A contour plot produced using the 0 νββ signal event population, andshowing the diffusion parameter, σ w , as a function of the event position. Only one halfof the symmetric TPC is shown here. Lower σ w values correspond to events takingplace near the readout plane, at z=1000 mm, and larger values correspond to eventstaking place near the cathode, at z=0 mm. (b) The distribution of the σ w parameterfor 0 νββ signal events (filled curve), and the two background Micromegas componentsstudied. σ w > σ w > σ w > Th 93.3 53.7 44.4 U 80.9 20.1 15.1 Xe 99.4 83.0 74.5 Table 5. Overall background reduction, in percentage, for events generated from theMicromegas readout plane, Th and U contaminations, and the correspondingsignal efficiency, after applying different cuts on the diffusion parameter, σ w . Micromegas contribution of U was a dominant component in Table 2. The backgroundreduction on the U chain is more significant than in the Th chain, due to the factthat the 2,614 keV gamma from Tl is produced in almost any decay, generating finallya higher ratio of volume to surface events compared to the Bi contribution, whichproduces a β decay with high energy gamma emmission only at 1.5% of the decays.We should remark that the values presented on Table 5 have been obtained withoutapplying topological cuts. Still, these results are independent on previous topologicalcuts, since we do not observe any dependence on the z-distribution after cuts, as itwould have been revealed by the 0 νββ population in Figure 3(b), after the topologicalanalysis performed in section 2.Finally, in Figure 7 we show the background distribution as a function of the event opological background discrimination in the PandaX-III experiment − − No cuts > 9 w σ > 10 w σ > 10.5 w σ − − (a) (b) Figure 7. Distribution of the average z-position for events produced by Th (a), inlinear scale, and U (b), in logarithmic scale, generated from the Micromegas readoutplane, placed at z=1000 mm. Different curves represent the background reductionafter applying different threshold values on the diffusion parameter, σ w . The initialpopulation of events, tagged as ”No cuts”, are the events found in our ROI definition. position, for each of the two Micromegas isotope contaminations, after applying different σ w threshold values. In these figures we observe how all the events from surface naturehave been completely removed already for σ w > 10, and how the remaining backgroundevent population on Table 5, i.e. 20.1% for U and 53.7% for Th, are only due tovolume events that can only be removed by exploiting topological event features. 5. Conclusions In this work, we have presented results on topological background discriminationconsidering a realistic detector response for the PandaX-III TPC baseline design.The realistic response includes an accurate description of the existing Micromegasdetector layout used for the reconstruction of events in a similar way as it is done withexperimental data. However, the most important element on the detector response relieson an appropriate definition of the energy of each event by considering the electronicacquisition window and the readout plane boundaries of the PandaX-III design.We observe a negative effect on our topological background discrimination whenwe apply the detector response to the Monte Carlo event data, hence the importanceto include those effects in our study. The results obtained show that a promising finalbackground level is achievable. Using topological arguments, we find that for a signalreduction of ∼ opological background discrimination in the PandaX-III experiment t o , and remove a considerable amount of surfacebackground events that cannot be eliminated by other means. By exploiting thistechnique we are able to reduce the Micromegas background contribution to levels wellbelow 1 count per year, preserving 80% of the 0 νββ signal.We have also addressed the question relative to the impact of a 2-dimensionalreadout on the pattern recognition of 0 νββ . It is obvious that the lack of a full3-dimensional event reconstruction leads to a reduced discrimination power. In the2-dimensional case, our event identification and classification must be based on 2projections of the event, and necessarily some of those event projections hide informationthat can only be revealed by a 3-dimensional reconstruction. Occasionally, a secondarytrack will be hidden by the projection and counted as energy of the main track,affecting the track energy ratio criterion, while in other events, the integration ofthe charge of an electron moving orthogonally to the projection may mimic a blob ,reducing the rejection power of the blob charge and the twist parameter criteria. Wehave systematically studied the significance of our topological criteria for differentdetector granularities at 3-dimensional pixel and 2-dimensional stripped readout designs,concluding that the negative impact on 2-dimensional readout pattern recognition iscounterbalanced by a reduced detector granularity, i.e. a 1 cm pixel readout reaches anevent topological rejection power comparable to a 3 mm stripped readout. Consequently,the 3 mm pitch stripped baseline readout choice for PandaX-III detector is much moreconvenient, not only in terms of detector design complexity due to the reduced number ofchannels required, but also minimizing the impact of typically non-radiopure electronicsequipment near the detector readout planes.We have introduced novel track parameters, as the end-track twist and the tracklength , never exploited before on the pattern recognition of 0 νββ using conventionaltechniques. We have assessed their discrimination potential, and observed how the end-track twist feature is still contributing to the signal-to-background significance, evenafter filtering the event population previously with other topological criteria, as the trackenergy ratio and the blob charge . Furthermore, we have found that this parameter isrelevant for pattern recognition when the detector granularity is below 6 mm, concludingthat such granularity or better is necessary to reveal the aforementioned track features.We believe our results are conservative, and that there exists room for improvementand optimization through multivariate methods that better exploit the differentparameter correlations. Additionally, exploring the use of novel track parameters,or improving the existing ones, can push the conventional background discrimination opological background discrimination in the PandaX-III experiment dE/dx along the track, previously studied atreference [29], and its peculiarities at the end-tracks could allow to improve these resultsby properly combining them with the parameters studied in this work.Recently, we have seen how machine learning methods provide enhanced capabilitiesfor pattern recognition, as reported in references [22, 25, 28]. These techniques, whichprovide excellent signal-to-background discrimination ratios, could never replace aconventional analysis. In a conventional analysis the different topological parametersserve as a mechanism to control the goodness of the Monte Carlo event reconstruction.In other words, we will be able to validate the different event parameters obtainedby comparing with the experimental data, allowing us to be confident on our eventreconstruction and the effectiveness of our topological criteria. The use of machinelearning techniques, without further or complementary analysis, will not be sufficientby itself to prove the background of the detector.The present work served to demonstrate the existing software infrastructureimplemented in REST for event reconstruction, and the flexibility to add a detaileddetector response at different levels, as necessary. REST has been conceived to providea high degree of modularity allowing to connect or disconnect different event processes atany place of the event data processing chain. We have designed dedicated event processes and metadata structures to construct the PandaX-III Monte Carlo processing chain.Still, additional details can be included in future studies, that may implement evenmore realistic event reconstruction. A future Monte Carlo event processing may considerfurther details ignored in this work, as e.g. the gap inter-distance between neighbour readout modules , or the necessary unconvolution of the electronic signal shaping.Finally, when comparing to real experimental conditions we will need to considerdifferent systematic effects due to different parameters that may fluctuate, or change,during the data taking periods of the experiment, such as the electronic noise, thedrift field intensity or irregularities, the concentration of TMA and its effect on thegas properties, the gain inhomogenities on each detector module, the effect of readoutmodule gaps on the event reconstruction, possible dead channels in the detectors, etc.All those studies must be addressed in the near future in order to have full control onthe detector performance. The present work represents a necessary step towards thosestudies. Appendix A. REST as a data analysis framework. RESTSoft (Rare Event Searches with TPCs Software) is a collaborative software effortproviding a common framework for acquisition, simulation, and data analysis for gaseousTime Projection Chambers (TPCs) [30]. REST is composed of a set of libraries writtenin C++ and is fully integrated in ROOT [31], i.e. all REST classes inherit from TObjectand can be read/accessed/written using the ROOT I/O interface. The only structuraldependence is related to ROOT libraries, while other packages, as Geant4 [32] or Garfield++ [19], can be optionally integrated and used within the REST framework opological background discrimination in the PandaX-III experiment metadata and event data are storedtogether in a unique file. We understand by metadata any information required to givemeaning to the data registered in the event data , as it can be the initial run data takingconditions, the geometry of the detector, the gas properties, or the detector readouttopology. Additionally, any input or output parameters, required during the processingor transformation of event data , using event processes , will be stored as metadata . Anyprevious existing metadata structures inside the REST input file will be transferred toany future output, assuring full traceability, as well as reproducibility of results obtainedwith a particular dataset.An ambitious feature of REST is its capability to analyze Monte Carlo andexperimental data using common event processes . This is possible by using existingREST event processes to condition the input data generated, for example, by a Geant4 Monte Carlo simulation. After an appropriate event data conditioning, our MonteCarlo generated event will reproduce the rawdata of the detector (as it is shownin Appendix C). Once we are at that stage, we can benefit from using the same eventprocesses to analyze Monte Carlo and real experimental data. A realistic Monte Carlo rawdata reconstruction will allow us to assess, validate and optimize the processes thatwill be involved in the real event reconstruction and analysis even before the start ofthe physics run of the experiment.In the following subsections, we recall the definitions of the different componentsof REST, viz. event types , event processes , and analysis tree . These definitions willserve as a reference for the article. Note that we do this having in mind the case wherethe physics variables of interest are local energy deposits, called hits, and the signal isdigitized by a sampling ADC. The REST software is versatile enough, though, to handlemany other cases. We include here only those components of REST that are relevantto our study. Appendix A.1. Event types REST defines basic event types , or data structures, commonly used to store event data generated during the data acquisition, production and/or event data processing. Thedefinition of a reduced set of basic event types allows for better inter-process connectivity.The following data structures defined in REST are used in our study. • TRestHitsEvent: This structure contains an arbitrary number of elements or hitsused to store a physical variable, φ i , defined in a 3-dimensional coordinate system( x i , y i , z i ). In our study, we use this event type to describe the energy depositionson the volume of the detector. • TRestG4Event: It is a natural extension of TRestHitsEvent containing additionalinformation gathered during the Geant4 simulation, such as the physical interaction opological background discrimination in the PandaX-III experiment • TRestTrackEvent: A more sophisticated structure where hits are grouped intotracks, following e.g., a proximity criterion. Tracks can, in turn, be grouped intohigher level structures. An identification number and a parent number are assignedto each object and allow to keep the record of its genealogy. A track that is notassociated to a parent track will be denominated as an origin track , while a trackwith no daughter tracks will be denominated as a top-level track . Therefore, inthis scheme we may distinguish different track levels related to the number of trackgenerations. • TRestRawSignalEvent: Stores the digitized signal samples, in the shape of fixedsize arrays. Each array corresponds to one front-end electronics channel, and isassigned a logical signalId . The set of signalId ’s is mapped to the geometry of thedetection with help of a readout metadata table, typically known as decoding . Thearrays generally describe the time evolution of the signal. • TRestTimeSignalEvent: It contains an arbitrary number of non-fixed size arraysthat define a physical quantity, φ i , at arbitrary times, t i , expressed in physical timeunits. Each array dataset may contain a different number of data points. Thiskind of event type can be exploited, e.g. for experimental data reduction or storageof timed signals produced in Monte Carlo generated data. As in the case of a TRestRawSignalEvent , each array is also identified using a signalId associated tothe electronic channels described inside the readout metadata description.We stress again that the event types defined in REST aspire to be as generic andabstract as possible. It is the role of processes , and other metadata information usedduring the data processing, to provide a physical meaning, or final interpretation, tothe information that is contained in our event type . In the scenario where certainspecialization is required, as it is the case of a TRestG4Event , an existing REST eventprocess will be capable to transform this specialized, or dedicated, event type into anexisting and more basic one, as it is a TRestHitsEvent .The event types described are not only containers to store event data in REST, butthey implement methods associated to the nature of each data structure, as e.g. spatialrotation or translation of coordinates in a TRestHitsEvent or time signal processingmethods in a TRestRawSignalEvent , as e.g. differentiation, smoothing or Fast FourierTransform (FFT) methods, together with prototyped methods, i.e. common to all the event types , for visualizing and printing the contents of a particular stored event. Appendix A.2. Event processes REST offers a large variety of event processes operating on the basic event types inorder to manipulate the event data , transform it and extract relevant information inthe intermediate steps taking place during a particular event data processing chain. An opological background discrimination in the PandaX-III experiment event process in REST is modular, and it can be integrated in REST by fixing onlyits input and output event types . In other words, any event process that participatesin a data processing chain must satisfy that its input event type corresponds with theoutput event type of the previous event process , although there are exceptions as will bedescribed in Appendix A.3.Therefore, event processes can be classified as processes that transform an eventtype into another, i.e. conversion processes , and those which operate in a particular event type , i.e. hit , raw signal or track processes , in which the output event type remainsunchanged (although its content - the event data - will usually be transformed). In thefollowing sub-sections we provide a description of the different processes involved in ourdata processing. A full, detailed and up-to-date list of documented processes will beavailable at [34] for further reference. Appendix A.2.1. Conversion processes • TRestG4ToHitsProcess: A simple process to transform a TRestG4Event into a TRestHitsEvent , visualized in Figure A1(a). Any specific hits information relatedto Geant4 will be lost after this step. Then, the only way in REST to have thisinformation available at the end of the data processing chain will be through the analysis tree , described in Appendix A.3. • TRestHitsToSignalProcess: This process produces a time projection of the primaryelectron positions in the TPC volume into the readout plane of the detector,producing the result shown in Figure A1(c). The coordinates of hits ( x i , y i , z i )stored in a TRestHitsEvent are transformed into a TRestTimeSignalEvent .This process uses the REST readout metadata structure (described in detailon Appendix B.2) to associate each hit coordinates ( x i , y i ) with a detector readoutchannel † , and perform a spatial to time conversion of the z i coordinate using thereadout plane position and the drift velocity of electrons in the gas. The gasproperties can be introduced directly as an input metadata parameter, or extractedfrom a specific metadata class, named TRestGas , that interfaces with Garfield++ to obtain the properties of any gas mixture as calculated by Magboltz . A samplingtime, δt , can be provided optionally to discretize the resulting time values at theoutput TRestTimeSignalEvent . • TRestSignalToHitsProcess: The inverse process of a TRestHitsToSignalProcess ,producing the result shown in Figure A1(d). We recover, or reconstruct, thehit coordinates using the time information inside a TRestTimeSignalEvent andthe gas properties. The reconstructed coordinates are obtained using the readoutmetadata description and the corresponding readout channel number, associated toeach signalId . † As an argument to support this description we assume here that the field drifting the electrons isdefined along the z -axis, although the readout plane can be placed in any arbitrary orientation. opological background discrimination in the PandaX-III experiment 520 530 540 550 560 570 580 590X-axis (mm)520540560580600620 Z - a x i s ( mm ) 520 530 540 550 560 570 580 590X-axis (mm)520540560580600620 Z - a x i s ( mm ) (a) (b) 200 210 220 230 240 250 s] µ Drift time [024681012141618 E ne r g y [ k e V ] 520 530 540 550 560 570 580X-axis (mm)520540560580600620 Z - a x i s ( mm ) (c) (d) Figure A1. Representation of different event type outputs after different eventprocesses on the simulation of a Xe 0 νββ event. (a) Top-left panel visualizes a TRestG4Event type, and represents the XZ-plane projection of the charge densityof the 3-dimensional event. (b) Top-right panel shows a TRestHitsEvent event typeafter applying the TRestElectronDiffusionProcess where we can appreciate the effectof electron diffusion in a xenon + 1%TMA gas mixture at 10 bar, the readout planeis placed at z = 990 mm. (c) Bottom-left panel shows a TRestTimeSignalEvent typeafter the conversion by a TRestHitsToSignalProcess . (d) Bottom-right panel showsa TRestHitsEvent type after the reconstruction using TRestSignalToHitsProcess . Ascatter plot is used in this case to emphasize the effect introduced by the 3mm-pitchdetector readout that can be observed along the x-axis, and the 200 ns sampling rateof the electronics on the z-axis. At this stage the TRestHitsEvent is not anymore a3-dimensional event, since we used here the PandaX-III stripped readout describedon Appendix B.2. opological background discrimination in the PandaX-III experiment E ne r g y w i ndo w [ k e V ] Drift time [ms] Figure A2. A figure illustrating the trigger definition using the threshold methodimplemented in TRestSignalToRawSignalProcess for a Xe 0 νββ event. The filledcurve, in red, represents the charge distribution (in arbitrary units not representedon this plot) as a function of the electron drift time. The blue curve is constructedwith the integral of the charges (with magnitude represented on the y-axis of thisplot) in a fixed time width, here of about ∼ µ s, and corresponding to the half sizeof the acquisition window of the electronics, of about ∼ µ s. When the integrationexceeds a certain threshold E th , in this case equal to Q ββ / Xe, the center of theacquisition window is fixed. The resulting acquisition window is represented by t Start and t End . An additional offset is introduced on the definition of t Start to assure fewtime bins will be available for baseline definition during the raw signal event processing. • TRestSignalToRawSignalProcess: This process takes as input a TRestTimeSig-nalEvent type and samples its contents into a fixed data array compatible withthe TRestRawSignalEvent output type, i.e. fixing the number of data points andsampling time, δt , which are provided as an input parameter to this process. Areference time, or trigger definition , is used to define the physical time correspond-ing to the first sample of the resulting data array. Figure A2 describes one of thetrigger methods available on this process which we use later in this study. • TRestHitsToTrackProcess: This process takes as input a TRestHitsEvent type andtransforms it into a TRestTrackEvent . The hit inter-distances inside the input eventare evaluated, and those which fall within a certain distance will be assigned to thesame identifiable track . This distance is introduced as a metadata input parameterto the process, named cluster distance . The algorithm starts creating a first trackby adding an arbitrary and unassociated hit ‡ . The track definition will only endwhen no more unassociated hits are found to satisfy the inter-distance relation with- and this is important - any of the hits already added to the track , i.e. the inter-distances are evaluated recursively. If after ending the definition of the first trackthere are still unassociated hits, the process continues to define a second track, andsuccessively. The process ends when no more unassociated hits are found inside the ‡ A hit that does not belong yet to any track opological background discrimination in the PandaX-III experiment TRestHitsEvent . Appendix A.2.2. Hit processes • TRestElectronDiffusionProcess: This process uses the longitudinal and transversecoefficients of a particular gas mixture to emulate the relative deviation ofelectrons from their original positions in TRestHitsEvent , presumably produced byprimary ionization. The energy of each hit found inside the input TRestHitsEvent is converted to the corresponding number of primary electrons that would beproduced in the ionization process. Each electron will be a new hit in theoutput TRestHitsEvent structure, and their coordinates will be randomly deviatedfollowing a Gaussian distribution related to the gas parameters, longitudinal andtransverse diffusion coefficients, and the distance to the readout plane, whichis given as metadata input. The result of applying this process is shown inFigure A1(b). This process may optionally add the possibility to include the effectof electron attachment. • TRestHitsSmearingProcess: This process smears the energy of the input TRestHitsEvent according to a Gaussian distribution described by parameters givenas metadata input. Appendix A.2.3. Track processes for νββ topology • TRestTrackReductionProcess: This process reduces the number of hits in each of thetracks stored in a TRestTrackEvent , as seen in Figure A3(a). An input metadataparameter, N max , specifies the maximum number of hits on each of the reducedtracks at the output TRestTrackEvent . The closest hits are merged iteratively tillthe N max condition is satisfied. When two hits are merged, the resulting hit positionis calculated weighting the energy of each merged hit. The input parent tracks arealso stored in the output TRestTrackEvent , together with the reduced tracks whichacquire a relation of inheritance. • TRestTrackPathMinimizationProcess: This process operates only on each of the top-level tracks found in TRestTrackEvent and - using graph theory - finds theshortest path that connects all the hits within each track, as seen in Figure A3(b).We have integrated in this process a heldkarp algorithm [35] optimized for problemsthat contain between 25 and 35 nodes. This algorithm was extracted from the concorde Travel Sales Problem (TSP) libraries [36, 37]. It is important to noticethat the minimization is performed in a closed loop, i.e. the extremes of the physicaltrack are not properly identified at the end of this process. From now on, we willdenominate two consecutive hits as connected hits . • TRestTrackReconnectionProcess: This process will be commonly used incombination with TRestTrackPathMinimizationProcess . This process will detectunphysical path connections between the hits, or nodes. We understand byunphysical connection a distance between nodes that is larger than the average opological background discrimination in the PandaX-III experiment 520 540 560 580X-axis (mm)520540560580600620 Z - a x i s ( mm ) 520 540 560 580X-axis (mm)520540560580600620 Z - a x i s ( mm ) 520 540 560 580X-axis (mm)520540560580600620 Z - a x i s ( mm ) (a) (b) (c) Figure A3. A TRestTrackEvent representation of a Xe 0 νββ event after thedifferent track processes used for physical track identification. This event correspondsto the same event used in Figure A1. (a) An image of the hit reduction produced by TRestTrackReductionProcess . The red circles represent the final position of reducedhits, which size corresponds with their energy value. The small grey circles on thebackground represent the hits of the parent track used as input. (b) A polylineis added to this representation to visualize the hits inter-connectivity after the TRestTrackPathMinimizationProcess . If path minimization works on the whole, itproduces at times obviously unphysical connections, as our example illustrates. (c) Theunphysical connections are corrected using TRestTrackReconnectionProcess . by a certain number of sigmas, or where no hits from the origin track are found inbetween, as seen in Figure A3(c). The track is split at those unphysical connectionsand reconnected with the closest hit. Using this technique, the extremes of thephysical track are found naturally. Although it was not used in our analysis, thisprocess allows to identify secondary track branches of complex event tracks whenreconnection is not possible. Appendix A.2.4. Raw signal processes • TRestRawSignalShapingProcess: This process realizes the simulation of theacquisition electronics signal shaper in a TRestRawSignalEvent . It implements theconvolution of an analytical response function with the input TRestRawSignalEvent ,presumably containing the original charge distribution produced in the detector.The analytical response function requires a single parameter, which is the shapingtime . However, this process offers the possibility to introduce any arbitrarywavefunction as response function, adding realism to the generated output. • TRestRawSignalAddNoiseProcess: It is used to include the effect of electronic noiseand emulate the fluctuations on the acquired time signal. A value is introduced asinput metadata to define the amplitude of the noise. We use a basic noise methodimplemented in this process that assigns an independent random value, Gaussiandistributed, to each of the bins inside a TRestRawSignalEvent . opological background discrimination in the PandaX-III experiment Appendix A.3. The analysis tree The different event processes can be combined in sequence to build a more complexprocessing chain. In REST, only the event data produced in the last event process will be saved to the output file § . There are two main reasons why it is not desirableto stock intermediate event data into a single data file k . First, we risk to pile-up, orreplicate unnecessarily, data that might require to allocate a non negligible amount ofdisk space. Second, the traceability of changes introduced in the data might be lost bystoring data at different levels of processing inside a unique file. This possibility wouldadd an undesirable degree of complexity to the future tracking of the data processing,if for example, we decide to continue processing data using a previously processed filewith event data at different processing levels but we start our event data processing atan intermediate state.However, the inconvenience of this scheme resides on the fact that, during theprocessing, the event data is transformed in a way that information might be lost, aswhen we transform a TRestGeant4Event into a TRestHitsEvent . Therefore, it will benot available at the end of the event data processing. The analysis tree is a RESTcomponent that emerges to solve this problem. It is based on a ROOT TTree structure,and it is accessible at any stage of the event data processing by any event process .Any process in REST is allowed to create a new entry, or variable, inside the analysistree which will be always available in any REST file. Future processing may add newvariables to the analysis tree preserving the existing ones from previous processing levels.Therefore, the analysis tree is used to gather relevant information along the processingchain that might not be anymore available at the event data output of the last process.In this context, and just for classification purposes, we can distinguish two newtypes of event processes , the analysis processes and the pure analysis processes . Bothtype of processes have in common that they do not modify or transform the input event data , and are just dedicated to add new entries to the analysis tree . Furthermore,the pure analysis processes will not even require access to the event data , being theseprocesses the only ones that can be connected at any place of the processing chainwithout input/output event type restrictions. For example, a pure analysis process might be a process that reads a variable (or branch) in the analysis tree to perform amulti-peak fit, and write the results of the fit in a metadata structure. Appendix B. PandaX-III Monte Carlo event simulation in REST The first step of Monte Carlo simulation is to consider PandaX-III as a simplecalorimeter and simulate the energy deposition of particles interacting in the gaseous § However, other metadata information used in the processing chain, e.g. process parameters,simulation conditions, readout definition, or gas properties, will be stored without exception, includingprevious historical metadata information k Although no restrictions apply to produce intermediate files with a snapshot of the event data at aparticular step of the processing chain. opological background discrimination in the PandaX-III experiment Geant4 -basedsimulation packages BambooMC and RestG4 . In Geant4 , detailed tracks of the ionizingparticles in the TPC active volume are generated. As a particle travels in the gasmedium, it deposits energy along the trajectory via multiple scattering and otherphysical processes. Geant4 tracks the trajectory in pre-defined steps. In each step,information such as timestamp, particle type, momentum, energy deposition, position,and physical process involved in the interaction are registered.In our study, we use the RestG4 package as an interface to define the simulationconditions through a REST metadata structure named TRestG4Metadata , and to storeall event information in a TRestG4Event type that can be further processed insideREST, i.e., RestG4 serves to generate a first event dataset. Event tracks can bereconstructed using this original dataset, and we call those MC-true tracks . The MC-true tracks have been generated in Geant4 with a spatial precision of 0.2 mm, implyingthat every step of the simulation of the movement of a particle is no more than 0.2 mm,with particle information being recorded after each step. The G4EmLivermorePhysics physics list - describing the electromagnetic processes in Geant4 - was used in the eventgeneration.The main features of the PandaX-III TPC are faithfully represented in our detectorgeometry. The cylindrical TPC is 1.5 m in diameter and 2 m in length. The cathode inthe middle divides the TPC into two symmetrical drift volumes, in which electrons aredrifted away from the cathode and collected by the charge readout planes located atboth ends. When running at 10 bar pressure the TPC can hold 200 kg xenon gas. Theactive volume is contained by a 3 cm thick copper vessel, and placed in a water shieldingtank in the laboratory. The geometry description, written in GDML [17], is the same asthe one used at reference [9]. Therefore, we refer to that publication for further detailson the different detector components implemented, materials used, and drawings. Appendix B.1. Data processing chain for PandaX-III. The generated MC-true tracks are introduced in the REST processing scheme to achievea realistic detector response, including electron drift diffusion, energy resolution, chargereadout segmentation, and signal sampling.Figure B1 shows the complete data chain, or event data flow, used to process Geant4 Monte Carlo generated data, and includes different effects related to the detectorresponse. Obvious event type conversion processes detailed on Appendix A.2.1, andanalysis processes described later on in this chapter, have been omitted in this drawingin order to facilitate focusing on the key aspects of the chain. In our data chain wecan differentiate up to three different phases, or stages. In the first phase the eventdata is conditioned to take into account the physical response of the electrons driftingin the gas medium, in the second phase the readout topology and electronics sampling opological background discrimination in the PandaX-III experiment Figure B1. Data processing chain used to manipulate the Monte Carlo eventsas described in the text. This figure gives an overview of the data flow throughthe successive event types (red ovals). Few event processes (blue rectangles) havebeen omitted, for simplicity’s sake. The chain starts with Geant4 generateddata (yellow rectangle at top-left). The flow is from left to right. We candistinguish two rows of event processes . The top row ( TRestElectronDiffusionProcess , TRestHitsToSignalProcess , etc) represent processes used to include the detectorresponse (or first phase ) and event reconstruction (or second phase ), while the bottomrow represents the track processes used for physical track reconstruction (or thirdphase ). Just in this figure, the TRest prefix and Process termination has been removedfrom the REST process and event names. is considered, and finally in the third phase a physical track ¶ reconstruction takes placeto condition the data and make it suitable for a topological track study. The descriptionof event processes required for a full understanding of the processing chain is detailedin Appendix A.2.The first phase of the processing takes place exclusively at the TRestHitsEvent level. The input generated by RestG4 , encapsulated inside a TRestG4Event type, is transformed into a TRestHitsEvent type using TRestG4ToHitsProcess .Two processes are responsible to include the physical detector response, we use TRestElectronDiffusionProcess to emulate the electron diffusion in the gaseousmedium, and TRestHitsSmearingProcess to include the stochastic effect of thedetector energy resolution on each independent event. The gas properties usedin TRestElectronDiffusionProcess were obtained from Magboltz [18] through the Garfield++ [19] interface integrated in TRestGas . In our study we used a gas mixtureof xenon+1%TMA at 10 bar pressure, setting the TPC drift field to 1 kV/cm leads toan electron drift velocity of 1.86 mm/ µ s, and 1.46 × − cm / and 1.01 × − cm / , forthe longitudinal and transverse electron diffusion coefficients, respectively. The number ¶ We will use the term physical track to refer to the final state of the event reconstruction, where thereconstructed track has physical meaning. opological background discrimination in the PandaX-III experiment W -value, i.e. the energy required to extract anelectron from an atom. We use a W -value of 21.9 eV [20] for our gas mixture. Thedetector energy resolution introduced in TRestHitsSmearingProcess was defined as 3%-FWHM at Q ββ = 2457 . 83 keV.During the second phase the conversion processes TRestHitsToSignalProcess and TRestSignalToHitsProcess are responsible to introduce the detector granularity andelectronics sampling of the time signal induced on the detector readout. These processesare strongly dependent on the TRestReadout definition, detailed in Appendix B.2. Fornow, it is enough to mention that TRestHitsToSignalProcess discretizes our event data into time signals in steps of 200 ns, using a 2-dimensional readout of 3 mm pitch. At thisstage, other details related to time signal conditioning could be added, despite the factthat it is not the aim of this work to include those effects, and any future improvementwill be later discussed in our final conclusions. Then, TRestSignalToHitsProcess reconstructs the event recovering the TRestHitsEvent structure including the effectsintroduced by the previous process, as it is shown in Figure A1(d).In the final third phase , the reconstructed TRestHitsEvent is classified into tracksthrough the TRestHitsToTrackProcess using a cluster distance value of 7.5 mm, i.e. twotracks are considered to be independent if the closest hits distance from one track toanother is above 7.5 mm. In this phase the processes described in Appendix A.2.3 areused to determine the physical track , evaluating the hit distances and connectivity.Figure A3 shows the result of the three track processes implemented in this phaseof the processing chain; TRestTrackReductionProcess (where we use N max =35), TRestTrackPathMinimizationProcess and TRestTrackReconnectionProcess . At the endof this processing chain we end up with a reconstructed physical track where track endscan be recognized naturally. It is the responsibility of the analysis processes to extractinformation, or observables, along the data processing chain, to be used in a final patternrecognition analysis.It is important to remark that the event data processing chain discussed here isfully compatible with 2 and 3-dimensional event representation, i.e., a TRestHitsEvent structure is able to identify if it contains 2D or 3D hits, and the hit and track processes will act on the event data accordingly, e.g. TRestTrackPathMinimizationProcess willindependently minimize the paths of different projections and tracks produced by a2-dimensional readout. Ultimately, it is the sole responsibility of the TRestReadout metadata structure to define the topological nature of the event data . Appendix B.2. PandaX-III readout metadata description For charge readout, PandaX-III baseline design relies on Microbulk Micromegastechnology due to its good intrinsic radiopurity levels, good energy resolution andcapability to operate at high pressure [12, 13]. A modular design has been conceived tobuild each detector readout plane in the PandaX-III TPC design due to the Microbulk opological background discrimination in the PandaX-III experiment Figure B2. (a) The PandaX-III readout plane description in REST, built using 41Micromegas modules of size 192 mm × 192 mm. The circle of size R=75 cm defines theinner radius where the Xe gas is contained. The active detector area is formed bythe region of the modules found inside that circle. Small corners inside this circularregion are not covered by any readout module, and therefore, they will translate intoa signal efficiency loss in our final detector response. (b) The detail of a Micromegasreadout module region as implemented in REST, red lines define the limits of readoutpixels . Two readout channels on the X-axis and one readout channel on the Y-axisare drawn (black dots) using REST readout validation routines, which allow to select,or activate, a group of readout channels and - after generating a number of randomcoordinates - paint only those generated coordinates that are found inside the activechannels. The small embedded image is the corresponding area extracted from theoriginal Gerber [21] design used for fabrication. The Gerber representation has beenmodified to identify the two X-axis (blue pixels) and one Y-axis (orange pixels) readoutchannels active for the readout validation. size limitation imposed by its fabrication process + . In order to cover the full active areaof the detector, each readout plane consists of 41 independent Micromegas modules,as shown in Figure B2(a). The total number of acquisition channels is limited to amanageable level ∗ by physically interconnecting pixels along the horizontal or verticalaxis orientations and they are read out as a single readout channel , or strip, as shown inFigure B2(b). Each Micromegas module contains 64 X -strips and 64 Y -strips of 3 mmpitch.The integration of a realistic complex readout scheme in REST is done throughthe TRestReadout metadata structure. TRestReadout is a sophisticated structure that + Mainly due to the existing equipment used for production. ∗ Readout channel reduction plays an important role to simplify the design, reduce costs and minimizethe impact of typically non-clean electronics from the radiopurity point of view, on a detector componentthat must be placed as close as possible to the readout plane to minimize electronic noise induction onthe readout signal. opological background discrimination in the PandaX-III experiment readout planes , containing itself any number of readoutmodules composed of readout channels that are identified with the data acquisition(DAQ) channels registered by the electronics. A readout channel itself is built of one ormore readout pixels . A readout pixel is the most elementary component of the readoutdescription in REST, and it defines its position relative to the module coordinates, itssize, orientation, and shape. The combination of readout pixels with different sizes,orientations, and shapes at different positions allows to construct any desired readouttopology in REST.Different methods are available at TRestReadout and related classes to access thereadout description, and determine for a given hit coordinates which is the corresponding readout channel in an efficient way. These methods are accessed by related eventprocesses and they are exploited to translate a given TRestHitsEvent coordinatesinto TRestTimeSignalEvent channels, and vice versa. The TRestReadout definitionis a crucial element in the construction of the data processing chain and its genericimplementation provides versatility to study a common dataset with different detectorreadout topologies and granularities, as it is done in section 3.In particular, the 2-dimensional stripped baseline readout for PandaX-III cannotperform a univocal 3-dimensional reconstruction of the original event topology (seediscussion at reference [22]). In our design, a drifted electron that reaches aMicromegas module will induce a signal on either a X-strip or a Y-strip. Therefore,the TRestHitsEvent reconstruction after TRestSignalToHitsProcess is necessarily acombination of 2-projections, a projection formed by XZ-hits (i.e. hits with valid X and Z coordinates and undefined Y coordinate) derived from signals correspondingto the X-strips, and a projection formed by YZ-hits resulting from the signals foundat Y-strips. Figure B3 shows the resulting projections for a signal and a backgroundevent. End-track identification using the analysis processes described in the followingsubsection have been also represented in this figure. The main characteristics of signaland background events is discussed in section 2.1. Appendix B.3. Analysis event processes Additional event processes are used during the data processing chain in order to extractrequired event information in our posterior analysis. The analysis processes used, theplace of the processing chain where those processes are used, the particular informationextracted and/or other parameters required are detailed in the following list. • TRestFindG4BlobProcess: It is used at the beginning of the first phase of the dataprocessing chain. It operates in a TRestG4Event and it is used to extract the MC-true track coordinates of each electron track end in a 0 νββ event. These values areused to assess the goodness of our algorithms to identify the track ends after thephysical event reconstruction. • TRestG4AnalysisProcess: It is also used at the beginning of the data chain, afterthe previous process. This process is used to add different observables related with opological background discrimination in the PandaX-III experiment − − − − − X-axis (mm) Z - a x i s ( mm ) − − − − − Y-axis (mm) Z - a x i s ( mm ) (a) − − − − − − X-axis (mm) − − − − − − − Z - a x i s ( mm ) 500 520 540 560 580 600 620 Y-axis (mm) − − − − − − − Z - a x i s ( mm ) (b) Figure B3. A TRestTrackEvent representation of the 2-dimensional projectedelectron tracks for a 0 νββ (a) and a background event produced in the Udecay chain (b) at the end of the data processing chain. The colored filled circlescorrespond to the top-level track of a TRestTrackEvent , while the grey scatteredpoints in the background - where the 3 mm pitch granularity can be discerned -represent the hits in the origin track . The size of the circle in the top-level tracks is proportional to the hit energy, and different colors serve to identify independenttracks classified after the TRestHitsToTrackProcess . A black polyline shows the top-level track hits interconnectivity resulting after the TRestTrackReconnectionProcess ,and helps to visualize the physical track . Large blue circles correspond with our blobcharge definition (R=12 mm) obtained from TRestFindTrackBlobsProcess , describedin Appendix B.3. The starred black markers found in the 0 νββ event correspond withthe positions obtained from the TRestFindG4BlobProcess representing the last electronenergy deposition for each of the primary simulated electron tracks. opological background discrimination in the PandaX-III experiment TRestG4Event to the analysis tree , as e.g. the interaction types involved, orthe number and type of particles involved in the event. In our particular case weuse this process to extract the total energy deposited in the active volume of thedetector, without any fiducialization. • TRestTriggerAnalysisProcess: It is used at the second phase of the processing chain,at the TRestTimeSignalEvent level. This process uses the same trigger definitionimplemented in TRestSignalToRawSignalProcess shown previously in Figure A2.We apply a sampling rate of 5 MHz with a total number of 512 sampled points,as fixed by the PandaX-III electronics system, and a trigger energy threshold, E th ,of 1229 keV corresponding to Q ββ / 2. This process generates a new observable inthe analysis tree , defining the energy contained in the virtual acquisition windowdefined. It must be noted that this process, as any other analysis process , does notmodify the event data . • TRestTrackAnalysisProcess: It is used at the end of the third phase of the processingchain. It extracts parameters used for pattern recognition of 0 νββ events, such asthe number of tracks, the track energy ratio, or the twist parameter described insection 2.1. • TRestFindTrackBlobsProcess: It is also used at the end of the processing chain. Thetracks ends have been naturally identified after the TRestTrackReconnectionProcess ,and this process registers the coordinates or positions of the end-tracks in the analysis tree . This process searches for the highest density region within a 20% ofthe track length at the track end, in order to allow an additional degree of freedomidentifying the final blob position. This process is used to generate the observablesrelated to the blobs charge parameter, described in section 2.1. Appendix C. Full Monte Carlo detector response In order to test the detector´s capability to distinguish surface events we need to extract anew parameter connected with the diffusion of electrons, from the event data processingchain presented on Appendix B.1. We could extract such a parameter at differentstages in that chain, however, a straightforward parameter characterizing the spreadof the charge is the width of the pulses as recorded by the readout electronics. Werequire then additional event processing to accommodate our Monte Carlo generatedevents to a time signal similar to the recorded with the detector acquisition. Figure C1shows the additional event processes , detailed also in Appendix A.2, that we haveintroduced after TRestHitsToSignalProcess , at the second phase of the data chaindescribed in Appendix B.1.In this extension of the processing chain we transform our event data into a TRestRawSignalEvent where we introduce different effects on the detector response,as a semi-Gaussian electronic signal shaper with 1 µ s peaking time and a Gaussian noiselevel, at each channel. In order to adjust the noise level we have simulated a smallenergetic deposition, produced by a 10 keV electron, and we have chosen the noise level opological background discrimination in the PandaX-III experiment Figure C1. Extension of the event data chain to include appropriate detector readoutsignal conditioning, trigger definition , electronics shaping and electronic noise . Thefirst process TRestHitsToSignalProcess - inside the first grey box - corresponds tothe process shown previously in Figure B1. The event processing ends with the TRestRawSignalAnalysisProcess after we extract the parameters of interest for thefiducial analysis carried out in section 4. The TRest prefix and Process termination hasbeen removed from the REST process and event names, keeping the same nomenclatureas in Figure B1. that approximately reproduces our signal-to-noise values when taking data in normallaboratory conditions. The unit values at this stage are completely arbitrary. Figure C2shows the aspect of the final processed event after including all these effects.These additional effects are included at the TRestRawSignalEvent level togain realism, but at the same time to exploit the REST analysis process, TRestRawSignalAnalysisProcess , which is also used to analyze the real data of thedetector. This analysis process is used right after TRestRawSignalAddNoiseProcess toextract the diffusion parameter that we are interested in. In order to define our diffusionparameter, σ w , we pre-select those channels exceeding a certain energy thresholdmeasured in signal amplitude at the TRestRawSignalEvent . The threshold value isdefined as the 10% of the maximum amplitude found inside the TRestRawSignalEvent .Then, we obtain the FWHM of the maximum peak at each channel, and average the9 channels which produce the lowest FWHM values ♯ . The value of σ w is measured insamples, or bins, of 200 ns width which is the sampling value we used in the detectorresponse. 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