Pattern recognition of 136 Xe double beta decay events and background discrimination in a high pressure Xenon TPC
S Cebrian, T Dafni, H Gomez, D C Herrera, F J Iguaz, I G Irastorza, G Luzon, L Segui, A Tomas
aa r X i v : . [ phy s i c s . i n s - d e t ] O c t Pattern recognition of
Xe double beta decayevents and background discrimination in a highpressure Xenon TPC
S Cebri´an, T Dafni, H G´omez ‡ , D C Herrera, F J Iguaz,I G Irastorza, G Luz´on, L Segui § , A Tom´as k Laboratorio de F´ısica Nuclear y Astropart´ıculas, Departamento de F´ısica Te´orica,Universidad de Zaragoza, 50010 Zaragoza, Spain.E-mail: [email protected]
Abstract.
High pressure xenon gas Time Projection Chambers (TPC) for thedetection of the neutrinoless double beta decay of
Xe provide good energy resolutionand detailed topological information of events. The ionization topology of the doublebeta decay event of
Xe in gaseous xenon has a characteristic shape defined bythe two straggling electron tracks ending in two larger energy depositions. Witha properly pixelized readout, this topological information is invaluable to performpowerful background discrimination. In this study we carry out detailed simulationsof the signal topology, as well as of the competing topologies from gamma events thattypically compose the background at these energies. We define observables based ongraph theory concepts and develop automated discrimination algorithms which reducethe background level in the region of interest in around three orders of magnitude whilekeeping signal efficiency of 40%. This result supports the competitiveness of currentor future ββ experiments based on gas TPCs, like the Neutrino Xenon TPC (NEXT)currently under construction in the Laboratorio Subterr´aneo de Canfranc (LSC).PACS numbers: 14.60, 23.40, 29.40, 29.85 Keywords : Double beta decay, TPC detectors, pattern recognition
Submitted to:
J. Phys. G: Nucl. Phys. ‡ Present address: Laboratoire de l’Acc´el´erateur Lineaire (LAL). Centre Scientifique d’Orsay.Bˆatiment 200 - BP 34. 91898 Orsay Cedex, France. § Present address: Physics Department , University of Oxford, The Denys Wilkinson Building, KebleRoad, Oxford, OX1 3RH, UK. k Present address: Blackett Laboratory, Imperial College London, SW7 2AZ, UK. attern recognition of
Xe double beta decay events
1. Introduction
The observation of neutrino oscillations in atmospheric and solar neutrinos implies thatthey have mass and mix, but it has left open questions about their mass hierarchy modelsand their nature, Dirac or Majorana. This has given new motivation for the searchesof the neutrinoless double beta decay [1]–[6]. Double beta decay is a rare transitionbetween two nuclei with the same mass number, (
Z, A ) → ( Z + 2 , A ) + 2 e − + 2¯ ν ),implying the emission of two electrons and two neutrinos ( ββ ν ). This process has beenmeasured for several nuclei with lifetimes of the order of 10 –10 years. A hypotheticalprocess without neutrinos in the final state ( ββ ν ) violates lepton number and requires,in the simplest theoretical models, the virtual exchange of massive Majorana neutrinos.Though different experiments have explored the region of effective neutrino massabove 250 meV, this decay has never been observed. Current lifetime limits for thismass are around 10 –10 years depending on the isotope. The near–future aim isto be sensitive to neutrino masses down to 50-100 meV. To achieve this goal a newgeneration of experiments is being designed and built with a detection mass around100 kg, improved energy resolution, and lower background level. Several approacheshave been considered up to now: semiconductor detectors or bolometers with anexcellent energy resolution (GERDA [7] or CUORE [8]) using segmented detectors toreject multiple–hit events, tracking detectors with pattern recognition capabilities todiscriminate background events versus signal (SUPERNEMO [9]), liquid scintillatordetectors with a ββ decaying isotope disolved in their active volume (SNO+ [10]and KAMLAND [11]), or Xenon TPCs with improved resolution and high trackingcapabilities (NEXT [12]) or a possible ion product tagging (EXO [13]). See reference[6] for a review of present experiments and an overview of future programs. Moreover,it would be desirable that any of these designs be easily scalable to reach the inverted–hierarchy scale region (about several tons of isotope mass and extra handles to deal withbackground events).In this paper we will focus on the high pressure xenon gas option which offers severaladvantages. On one hand the isotope: xenon has a natural abundance of 8.9% in Xe( ββ emitter) and can be enriched by centrifugation at reasonable cost; it has also ahigh two–electron energy end point [14]( Q ββ = 2458 keV), and a large ββ ν lifetime( T ββ ν / ∼ . × years, as recently measured by EXO [15] and KamLAND [16])which minimizes the overlap of the populations of the two neutrinos and the neutrinolessmodes; it does not have other long–live radioactive isotopes and responds to the passageof particles by a prompt <
100 ns scintillation light, that can be used as start of the event.These features have motivated several experiments to use this double beta emitter asthe aforementioned EXO and KamLAND. On the other hand, the use of high pressurexenon gas improves the energy resolution in this medium [17] and provides new handlesto reduce background thanks to its extraordinary pattern recognition capabilities whichallow distinguishing the characteristic signature of a ββ event from other backgroundevents. Moreover, a xenon gas TPC offers scalability to large masses of ββ isotope. The attern recognition of Xe double beta decay events ∼
178 mm VUV primary scintillation light) and ionization electrons whichare drifted towards the TPC anode by an electric field entering in a region with amore intense electric field where further VUV photons are generated isotropically byelectroluminescence. The conceptual design proposes the measurement of the energy(electroluminiscent light) and the event start (primary scintillation) in a sparse plane ofPMTs (the energy plane) located behind the cathode. The tracking plane will be placedat the anode plane and consists of 1 mm Silicon Photomultipliers forming arrays of 1 cmpitch. The experiment was proposed to the Laboratorio Subterr´aneo de Canfranc (LSC),Spain, in 2009 [12], with a source mass of the order of 100 kg. Three years of intenseR&D have resulted in a Conceptual Design Report (CDR) [19] and a Technical DesignReport (TDR) [20].
Figure 1.
Two electrons energy spectrum for Xe ββ ν decay with end point Q ββ = 2458 keV; the ββ ν peak is shown (not to scale). In the upper right inset theregion around Q ββ is zoomed in, showing the overlap of both populations due to finitedetector energy resolution. Though the ββ ν signal can be well characterized as a peak at the end of the ββ ν spectrum (figure 1), its extremely low rate makes its detection a big experimentalchallenge: an effective neutrino mass of near m ββ = 100 meV implies just a few countsper year for an isotope mass of 100 kg; and around a 1 ton of isotope is needed toget a few counts per year assuming an effective neutrino mass of 50 meV. Due tofinite energy resolution, events from the ββ ν distribution tail may constitute anirreducible background for the detection of the ββ ν signal events. The need to keep attern recognition of Xe double beta decay events ∼ ∼ − c keV − kg − yr − at the Q ββ is required for a100 kg experiment to achieve sensitivity to m ββ ∼
100 meV in a few years data takingcampaign. For a detector of a few tons to explore the inverse hierarchy region abackground level down to ∼ − c keV − kg − yr − could be needed. In addition tostandard background reduction strategies, like operation underground, use of shieldingand selection of radiopure detector components through screening, pattern recognitiontechniques to discriminate signal from background events must be exploited at themaximum.Pattern recognition for ββ searches has been widely studied, e.g. for germaniumexperiments [21, 22], using the event pulse shape to distinguish single–site from multi-site events. In gaseous xenon, the Gothard group [23] pioneered the study and use ofevent topology, and introduced some key ideas like the presence/absence of two higherenergy depositions at the ends of the ββ electron tracks. They successfully demonstratedthe application of these concepts to real data (in a 5.3 kg gas Xe TPC), although thediscrimination was done through visual inspection. The aim of the work presentedin this paper is to supersede the topological recognition techniques initiated by theGothard group, introducing new ideas for reconstruction and analysis, including thefull simulation of the expected signals and background in a high pressure Xenon TPC,and elaborate automated discrimination algorithms with this topological information[24][25].In section 2, the predicted Xe ββ ν signal and other expected background eventsin the energy Range of Interest (RoI) are described stressing their main distinguishingtopological features. In section 3, the algorithms used to characterize the events aredescribed, and the selection criteria used to discriminate signals from background eventsdefined. Their rejection power factor is presented in section 4 together with the signalefficiency comparing both high and low diffusion media. Finally some conclusions andan outlook of possible improvements in the analysis are gathered.
2. Signal and background topological signature in detectors equipped withpixelized readouts
The neutrinoless double beta decay of
Xe entails the emission of two electrons froma common vertex, sharing a total energy of 2458 keV [14]. During their travel throughthe high pressure gas they typically produce a characteristic ionization pattern that,although with variations from event to event, allows to define a prototype topologyon which to base our identification criteria. The prototype topology for the signalevents is a continuous straggling ionization track of around 30 cm (for a gas pressureof 10 atm) and, at both ends of the track, high energy depositions (blobs) due to theBragg peak of the electrons. Obviously, also the ββ ν events have the same topology; attern recognition of Xe double beta decay events Q ββ energy will consist of one or more single–electron tracks,and their prototype topology will be that of a single ionization track with only one higherenergy blob at one of the track’s ends. These two conceptual topologies offer a cleardistinction between signal and background events and are the basis for the design ofthe discrimination criteria. However, the distinction is in practice limited by additionalphysical interactions (secondary radiation, multi-site interactions,...) or detector effects(diffusion in the gas and readout digitization). Whether the discrimination criteria canbe designed to be inmune to these effects, and to which extent, is the main goal of ourstudy.In the following the signal and background events able to deposit their energy ina energy RoI around Q ββ will be simulated and studied in detail. All our results areexpressed as fractions of the events inside this RoI that are rejected or accepted bythe different criteria. The width of this RoI should include most signal events andtherefore it is linked to the energy resolution of the experiment. Due to the fact thatthe background population is either flat in energy around Q ββ , or, in the case of Bi, in apeak too close to the ββ ν peak to be resolved by energy resolution, our results are, infirst approximation, independent on the choice of the RoI. For this work we have takenthe practical choice of 2400-2500 keV for the RoI, which corresponds to a ±
2% around Q ββ and should generously encompass the ββ ν peak for the target energy resolutionof modern Xe gas TPCs: NEXT-100 targets a resolution of 0.5% FWHM, while someof its prototypes are already showing an energy resolution below the 1% FWHM [20] ¶ .Another choice in our analysis is the gas pressure, assumed to be 10 bar. This is areasonable design choice (followed by the NEXT TPC) out of a compromise betweendetector compactness and quality of the topological information. However a detailedstudy of the topological figure of merit versus gas pressure is still pending. Any emission of particles with energies above the Q ββ constitutes potentially a sourceof background for the experiment. We are concerned in particular with those able toleave single ionization tracks of energies in the RoI (electrons or gammas) in the fiducialvolume of the detector, as they may end up mimicking the two–blob signal topology bymeans of secondary photon emission or straggling. In the following points we discussthe different background populations to identify the relevant ones and focus our studyon them:(i) Radioactive contamination of laboratory walls. ¶ Other experiments using xenon show a more modest energy resolution, as KAMLAND-Zen, wherethe
Xe isotope has been disolved in liquid scintillator, with a 9.9% FWHM resolution at the Q ββ of Xe [16], or EXO-200, based on a liquid Xe TPC, which achieves currently an energy resolution of4% FWHM [15] (an energy resolution as low as 3.3% FWHM could be reached [26]). attern recognition of
Xe double beta decay events γ cm − [27] produces a background level around10 c keV − kg − yr − in the RoI in absence of shielding. This value is several ordersof magnitude higher than the total internal contribution but it can be reduced toless than 10 − c keV − kg − yr − with a lead shielding of at least 25 cm thickness[20]. Also airborne Rn, which decays into
Bi, can increase the backgroundlevel since it can reach the detector vessel. A continuous flushing of liquid nitrogeninside a sealed plastic bag surrounding the detector prevents the radon intrusion.Thus only internal contaminations will be included in our analysis.(ii)
Radioactive contamination of shielding and detector materials.
The materials used in the detector setup and shielding contain impurities ofradioactive elements, mainly the natural decay chains of
Th and
U. Theydecay emitting alpha or beta particles, as well as photons due to subsequent decaysto ground levels. Both alpha particles and electrons are quickly absorbed in mediaand only those emitted near surfaces facing the sensitive volume are detected,but easily rejected by fiducialization. Then, only a few energetic enough gammaemissions are relevant: the 2614.5 keV photon emitted in the 99% of the Tl β decays; and the 2447.8 keV (1.57% of intensity) gamma line following a low energy Bi β decay. Also, for this last isotope, some energetic β emissions with Q βmax of3272 keV (18.2%), 1894.3 keV (7.43%) or 2662.7 keV (1.7%) produce electrons insidethe RoI. Other contaminants, like Co, can be neglected, according to preliminarysimulations, since its two gamma emission (1173 keV and 1332 keV), when bothgammas are interacting in the gas, deposits up to 2505 keV (slightly above theRoI) and produces at least two well separated energy depositions in the gas evenin the case of high diffusion media. The rejection factor in that case is 2 orders ofmagnitude higher than that of the
Bi (limited by simulation statistics).
Rn emanated by materials inside the vessel can also constitute a relevantbackground source. It can diffuse in the detector gas and reach the sensitivevolume. Its α decay is harmless as it produces a very distinctive almost point–like signal (less than 5 mm of range in xenon at 10 atm) of energy much above theRoI, but the resulting positively charged Po ions can drift and deposit on surfaces(especially on the TPC cathode). Among the following progeny is
Bi. Therefore,for the purpose of this study, this background source is equivalent to a surface
Bicontamination.(iii)
High energy photons due to underground muon interactions.
Cosmic muons passing through matter produce high energy photons which resultfrom muon bremsstrahlung, direct pair production by muons and muon–nuclearinteraction. At Canfranc Laboratory underground muons present a mean energyof 290 GeV and a flux intensity of around 5 × − cm − s − sr − . Preliminarysimulations show that their contribution to background is low (of the order of attern recognition of Xe double beta decay events − c keV − kg − yr − ). Moreover the use of active veto detectors around theexperiment would veto not only muons but also any event induced by muons inshielding and detector materials. Therefore, this contribution will be neglected inthe following.(iv) Neutron activation.
There are no worrisome cosmogenic isotopes to be activatedin the gas and in the detector materials by sea level neutrons. Even cosmoisotopesas Co, very disturbing for some of the ββ experiments, can be neglected in ourcase. Once materials and gases are stored underground, the radioactive capture by Xe of medium energy neutrons may produce
Xe, which decays with a half lifeof 3.8 min, 67% of the times as a beta decay with Q β = 4173 keV and a 30% as abeta decay with Q β = 3717 . − kg − ,and makes this contribution irrelevant.Summarizing the analysis of the different sources, only Tl and
Bi, are relevant aspossible background contributions in the experiment. For this reason, the studies whichfollow will be focused on these isotopes.
The aim of this work is to study generic properties of event topologies and discriminationcriteria, as independent as possible from the specific detector design choices. As some ofthe aspects of the work may depend on geometrical issues (e.g., the origin of the
Bi or
Tl contaminations or the size of the fiducial volume), to understand to some extentthese dependencies, we have implemented a simplified generic geometry of a gaseousTPC in our simulations, that is shown in figure 2. We want to stress that the aim ofthis work is not to elaborate a background model, for which a more detailed geometryand a complete material account would be needed.The main element of the simulated geometry is a cylindrical vessel, closed by twosemispherical end caps, as shown in figure 2. The vessel walls are made of copper of3 cm thickness. The chosen dimensions of the cylinder are a length of 1.5 m and adiameter of 1.6 m. Inside the TPC, there is a field cage made of teflon, with copperrings embedded on it, to shape the drift field along the z –direction. At both sides ofthe field cage there are two surfaces representing the cathode and the pixelized readout(1 × area) placed at the anode. All the space between the walls and the field cage isfilled with xenon gas at 10 bar. The sensitive volume, where the interactions of particlesare recorded, is the cylindrical volume inside the field cage, whose dimensions are 1.5m of drift length and a diameter of 1.38 m. This volume of gas corresponds to a totalmass of 124 kg of xenon at 10 bar.The simulation and analysis can be divided into three logical blocks: 1) theinteraction of ionizing particles with the gas; 2) the simulation of the detector response;3) the analysis of 3D events. Figure 3 illustrates the implementation diagram of theselogical blocks in the software. attern recognition of Xe double beta decay events Pixelized readout
Field cage Cathode
Fiducial volume
PVessel and end-caps
Figure 2.
A view of the geometry simulated in GEANT4, explained in detailed inthe text. The different volumes of the TPC can be observed: the fiducial volume, thefield cage, the cylindrical TPC with its two endcaps, the cathode and the readout.
Geometry Initial particles Interactions 3D event Charge creation Gas diffusion
Readout’s pixelization
Part 1:
Monte Carlo Part 2: TPC features Part 3: Discrimination algorithms
Analysis results Event topology
Fiducial volume Physics
Track analysis
Figure 3.
Data flow of the simulation and analysis organized into three logical blocks.
The first block consists of a Monte Carlo simulation, including all the physicalprocesses involved in the passage of particles through matter. It provides the interaction attern recognition of
Xe double beta decay events ββ signal anddistinguish it from the different background events, is described in detail in section 3.Each of the two kind of contaminations studied ( Tl and
Bi) are separatelysimulated from different representative volumes of the geometry, in order to analysethe possible dependence of the algorithm on the origin of the contamination. Foursuch volumes are considered: the lateral part of the vessel (a volume far from the gasactive volume), the field cage (volume facing the gas), the cathode (surface on top ofthe gas) and the readout (surface at the bottom). Signal events have been simulatedhomogeneously in the gas volume. The number of events simulated is fixed differentlyfor each of the simulations so that the initial number of events falling in the RoI is 10 ,so enough statistics on which to apply the discrimination criteria is gathered.An important aspect affecting the topology is the diffusion of the electrons driftingin the TPC. It is known that diffusion in pure Xe is relatively large, e.g., the longitudinaland transversal diffusion coefficients respectively are ∼
300 and 1000 µ m / √ cm for a driftfield 1 kV cm − bar − . An additional low diffusion scenario will be studied, to assess theimpact of diffusion in the discrimination capabilities. The use of a small quantity ofadditives to the Xe, like CF or trimethylamine (TMA), might reduce the diffusioncoefficients down to ∼ µ m / √ cm in the same conditions of drift field and pressure. attern recognition of Xe double beta decay events X ( mm ) -80 -60 -40 -20 0 20 40 Y ( mm ) -520-500-480-460-440-420-400-380 Z ( mm ) (a) Y ( mm ) -200-150-100-50050 X ( m m ) Z ( mm ) (b) X-axis (mm)-80 -60 -40 -20 0 20 40 Y - a x i s ( mm ) -520-500-480-460-440-420-400-380 010002000300040005000600070008000 View X-Y (c)
X-axis (mm)-200 -150 -100 -50 0 50 Y - a x i s ( mm ) View X-Y (d)
Figure 4.
Three–dimensional representation (top) and two–dimensional projection(bottom) of Xe ββ ν events simulated in a 10 bar Xenon TPC. On the left: twoelectrons of similar energy has been emitted from a vertex (black mark) and show bigenergy depositions at the end of their tracks (yellow marks). On the right, a smallertrack far from the main one can also be seen. A substantial fraction of signal events may differ from the prototype single–track–with–two–blob pattern described before for the Xe ββ signal (see figure 4). More than 80%of ββ ν events in the RoI have secondary photon emission (x-rays or bremsstrahlungphotons). Although most of them do not have enough energy to travel far from the mainelectron track, in some cases they may leave the sensitive volume (reducing the signalefficiency) or cause the event to show more than one disconnected track. In overall, forthe geometry considered, only about 60% of the signal events are classified as singletrack events. An effective way to protect the algorithm from this feature is to consideras acceptable signal topologies those with a second short track (i.e. with energy lowerthan 100 keV) disconnected from the main one, as will be seen in subsection 3.1. When attern recognition of Xe double beta decay events X ( m m ) -540 -520 -500 -480 -460 -440 -420 Y ( mm ) -180-160-140-120-100-80-60-40-200 Z ( mm ) (a) X ( mm ) -400 -350 -300 -250 -200 Y ( mm ) Z ( mm ) (b) X-axis (mm)-540 -520 -500 -480 -460 -440 -420 Y - a x i s ( mm ) -180-160-140-120-100-80-60-40-200 0200040006000800010000 View X-Y (c)
X-axis (mm)-400 -350 -300 -250 -200 Y - a x i s ( mm ) View X-Y (d)
Figure 5.
Three–dimensional representation (top) and two–dimensional projection(bottom) of simulated background events in a 10 bar Xenon TPC. On the left, a
Bielectron coming out from the lateral wall leaves a continuous track and shows a higherdeposition at the end. On the right, an event caused by a
Tl 2614.5 keV photonpresents several tracks. this is done, the signal acceptance is increased by 20% while the impact on the rejectionof background events, normally showing more than two long tracks, is minimal.As already mentioned, most background events (coming from beta and gammaemissions from
Tl and
Bi contaminants) will produce multitrack topologies in thegas (see figure 5) and will be easily rejected. Beta decays from surface contaminationscan also be rejected by fiducialization. The most dangerous cases are when single tracksare produced in the fiducial volume. This can happen after photoelectric absorption ofthe
Bi 2447.9 keV photon emission, which falls right in the middle of the RoI (seefigure 6). The 2614.5 keV gamma emission of
Tl can also produce single track ofenergy in the RoI if part of the event energy escapes the sensitive volume, either viaCompton scattering or bremsstrahlung radiation.The population of background events leaving a single track in the fiducial volume attern recognition of
Xe double beta decay events X ( m m )
40 60 80 100 120 140 160 Y ( mm ) -480-460-440-420-400-380-360-340 Z ( mm ) (a) Y ( mm ) -400-380-360-340-320-300-280 X ( mm )
240 260 280 300 320 340 360 380 400 Z ( mm ) (b) X-axis (mm)40 60 80 100 120 140 160 Y - a x i s ( mm ) -480-460-440-420-400-380-360-340 0200040006000800010000 View X-Y (c)
X-axis (mm)-400 -380 -360 -340 -320 -300 -280 Y - a x i s ( mm ) View X-Y (d)
Figure 6.
Three–dimensional representation (top) and two–dimensional projection(bottom) of a background (
Bi ) event misidentified as signal event (left) and a ββ ν signal event misidentified as background event (right). On the left a Bi2448 keV photon has produced a secondary photon due to Compton interaction whichhas deposited its energy too close to the main track and originated a second blob. Onthe right, 3 low energy bremsstrahlung photons and 2 x-rays have interacted close tothe track and originated extra energy depositions increasing the charge of one of thetrack’s end. can be further constrained by looking for the characteristic two–blob feature of signalevents. However, background events can still show higher energy depositions that mimicthose from the Bragg peak in signal events, caused by secondary low energy radiation(x-rays or δ -rays) or excessive straggling of the main track. These effects are alsopresent in signal events and can affect their correct identification (and, therefore, theefficiency of the discrimination). Finally, the diffusion of the electronic cloud and readoutdigitization will affect in general the quality of the topological information, as only asomewhat blurry version of the physical track is available for analysis.All the considerations here exposed constitute the rationale of the discriminationcriteria. In the next section we describe quantitatively such criteria and the algorithmthat implements them. attern recognition of Xe double beta decay events
3. The discrimination algorithms
In the following we describe in detail the algorithm developed on the basis of theconsiderations discussed in the previous sections. It depends on a number of parameters,that will be introduced along the explanations of the algorithm below (they are allcompiled in tables 1, 2 and 3). The values for each of them have been chosen followingdiverse considerations (described in the following) to improve the discrimination ofbackground and signal events, and so the performance of the algorithm. However,an overall optimization procedure of the whole set of parameters is still pending andremains for future work.The algorithm is divided in three parts. The track method described in subsection3.1 identifies the number and charge of the tracks of the event and applies criteria onthem. The blob method explained in subsection 3.2 identifies the number and charge ofthe blobs of the main track and applies criteria on them. Finally, the fiducial methodof subsection 3.3 applies a fiducial criterion.
The algorithm identifies a track as a set of 3D-pixels linked by a relation of proximity.This proximity relation can be defined as being adjacent or, in a more general way, asbeing closer than a given distance. A distance of d p = 10 mm around the pixel center hasbeen chosen in this case to take into account adjacent pixels. The track identificationis then based on a general mathematical graph algorithm described in [34, 35]: eachpixel of an event corresponds to a vertex of a mathematical graph and its relations tosegments. An initial point is then chosen and all vertices linked to it by one or successivesegments are found. The process is repeated and all the connected points form a track.Only pixels with a charge higher than a threshold q i > q th are considered due to twomain reasons: a) in real life each pixel in the readout will have a threshold imposed by,e.g., a level of noise; and b) to reduce diffusion effects and have a better identificationof separated clusters. To remain immune to the presence of pixels accidentally with nocharge (due e.g. to straggling or to technical problems in real data) a new charge Q t i isassociated to each pixel in this method and defined as Q t i = X j q j , (1)where j runs over all pixels closer than r t = 1 cm to pixel i (i.e. adjacent pixels). Onlypixels with a Q t i ≥ Q tth are finally taken into account, where we have taken Q tth to be 45electrons (around 1 keV). Table 1 summarizes the parameters defined for the method.As shown in figure 7 (left), most of the background events have more than twotracks. However, only around a 60% of signal events are single track, due to the emissionof xenon x-rays (energies around 30 keV) or bremsstrahlung photons (in more of the80% of the events) with typical energies below 100 keV. These two effects produce asubstantial reduction of signal efficiency if only single track events are selected. As attern recognition of Xe double beta decay events Table 1.
Parameters used in the track method and selected values. q th is the thresholdfor the charge of a single pixel, d p is the distance between two pixels to be consideredas joined, r t is the radius around a pixel to compute its charge in this method, Q tth is the threshold in this charge for the pixel to be taken into account and E tth is thethreshold energy for short tracks.Parameter q th d p r t Q tth E tth Value 45 e −
10 mm 10 mm 45 e −
100 keV
Number of tracks P e r c en t age o f e v en t s ( % ) Total number of tracks
Number of tracks with E>100 keV P e r c en t age o f e v en t s ( % ) Number of tracks with E<100 keV P e r c en t age o f e v en t s ( % ) Number of short tracks
Figure 7.
Left: Number of identified tracks of any energy for events in the RoIgenerated by ββ ν (red squares), Tl (up blue triangles) and
Bi (down purpletriangle). As an example, the contaminations are chosen to emit from the field cage.Center: Number of long (energies greater than 100 keV) tracks. Right: Number of short tracks (energies below 100 keV). observed in the plot at the centre of figure 7, if only the number of long tracks (trackswith energies above E tth = 100 keV) were taken into account to reject an event, as donealso in [23], we could recover almost a 30% of signal acceptance. However, the numberof background events surviving this discrimination criterion would also increase. Forthis reason, the number of short tracks has also been considered (figure 7, right). Afterstudying the effectiveness of the method for several possibilities, only those events withone long track and up to one short track will be selected as allowed signal topologies. This stage of the algorithm is only applied to the track of the highest energy in theevent, identified in the previous stage. Its purpose is to locate the two blobs as well asthe longest track–line (set of connected pixels of the track) that joins them both. Thenseveral criteria are applied on the number and charge of the blobs found. This algorithmworks in the following steps that are also graphically illustrated in figure 8. attern recognition of
Xe double beta decay events (a) (b)(c) (d) Figure 8.
A dummy 2D event used to describe in the text the selection of the blobpixels. It consists of two real blobs (red squares), a fake one (orange square), normalpixels (magenta squares) and pixels with little charge (blue squares). From top left tobottom right: event pixels are identified with graph vertices and adjacent ones linkedby segments; pixels with very low charge are removed to avoid twists; vertexes withthe greatest charge (marked by arrows) are considered blob candidates; two track–linesare drawn between the two blob candidates (pink line) or starting at one of the blobcandidates and ending at some point with a charge accumulation (green line). As thefirst track–line is a 30% longer than the second one, the first one is selected. (i) For each pixel i of the track a new charge Q b i is defined as the sum of the chargesof all the pixels placed at a certain distance to it, r b , greater than the r t distanceused in the track method. Q b i = X j q j , (2)where j runs over all the pixels placed at a distance d ij < r b . The distance r b hasbeen chosen to be 18 mm.(ii) Blobs are defined as pixels with a charge higher than a certain threshold Q bth =130 keV (almost 6000 electrons) Q b i ⋆ > Q bcth . (3)They are ordered according to their energy and the first N C = 6 of them labeled as blob candidates . attern recognition of Xe double beta decay events Q b i > Q bth ) are taken into account. The threshold Q bth has beenconsidered to be 150 electrons in the case of high diffusion and 75 electrons in lowdiffusion mixtures. This condition cleans part of diffusion effects.(iv) As the electron energy loss dE/dx is higher at the end of its path, one–electrontrack should be longer than a two–electron track. Thus, the longest track–linebetween two blob candidate and the longest track–line starting at a blob candidate and ending at any other point are compared. If the second track–line is a R tl = 30%longer than the first one, the second track–line is chosen, otherwise, the first oneis considered. In such a way, track–lines where one of the ends is placed at themiddle of the track are avoided. Finally, the two ends of the selected track–lineare identified with the final two blobs the algorithm was looking for. Notice that insome cases one of the ends may have not been labeled previously as blob candidate .(v) At this stage, a track–line and its two end–points have been identified. Charges Q and Q are computed as the sum of the charges of all pixels inside of spheresof radius r blob centered at both ends and assigned to the large blob and to the smallblob respectively. Only those events with similar charges at both ends and above athreshold energy ( Q blobth = 440 keV) will be selected. Q > Q > Q blobth , (4) Q blob2 Q blob1 ≤ R blobs , (5)with R blobs =2 in this work.(vi) For a small fraction of events, the final two blobs identified by the algorithm donot correspond to the real ones. In those cases, the track–line found out by thealgorithm follows only part of the real topology, leaving the other part outside. Toveto these cases, an additional variable labeled track coverage has been defined asthe ratio between the charge contained in a given lego –tube around the calculatedtrack–line (a r lt = 30 mm radial distance for the tube has been chosen, see figure9) and the total charge of the track. Then, it is required that more of the R cv ofthe charge be inside this tube ( R cv = 95% for pure xenon and R cv = 98% in thecase of low diffusion Xe gas mixture). It can be seen how the use of a low diffusionmixture improves the pattern recognition.The first parameters of the method ( r b , Q bth , Q bcth , N C and R tl , summarized in table2) have been chosen to optimize the effectiveness of the method to find the real blobsof the event. For most cases, the distance between the real and the reproduced blobposition is less than 2 times the pixel length. attern recognition of Xe double beta decay events (a) h1Entries 5699Mean 0.9108RMS 0.08407 Charge ratio0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 N u m b e r o f eve n t s ( % ) h1Entries 5699Mean 0.9108RMS 0.08407 (b) h1Entries 537Mean 0.8561RMS 0.1157 Charge ratio0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 N u m b e r o f eve n t s ( % ) h1Entries 537Mean 0.8561RMS 0.1157 (c) h1Entries 5565Mean 0.9527RMS 0.07409 Charge ratio0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 N u m b e r o f eve n t s ( % ) h1Entries 5565Mean 0.9527RMS 0.07409 (d) h1Entries 374Mean 0.8564RMS 0.1151 Charge ratio0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 N u m b e r o f eve n t s ( % ) h1Entries 374Mean 0.8564RMS 0.1151 Figure 9.
Figure shows the track coverage in the case of xenon (plots on the left) andin the case of background events (plots on the right). Upper plots correspond to purexenon gas detector and lower ones to the use of a low diffusion mixture. On each plotthe ratios for different values of the radius r lt of the lego tube are shown: solid line for30 mm (chosen value), dashed line for 15 mm, long dashed line for 18 mm and dottedline for 36 mm. As can be seen, most of the signal events have a charge ratio around1, accentuated in the case of a low diffusion mixture. Values above 1 mean that extracharges from pixels below the threshold q th used to separate tracks or from smallertracks have been enclosed inside the lego tube . Table 3 summarizes the second part of parameters used in the blob method ( r blobs , Q blobsth , R blobs , r lt , R cv ). To select the parameter values, it has been looked for rangesof these parameters which maximizes the figure of merit ∼ ǫ √ F , where ǫ is the signalefficiency and F is the rejection factor due to a specific discrimination criterion. Amongvalues given equal figure of merit, we have favored the highest signal acceptance. As anexample, once the radius r lt has been fixed to 30 mm, ranges of Q blobth from 440 keV to572 keV and R cv from 95% to 98% are maximize the figure of merit in the case of purexenon, but 440 keV for Q blobth and 95% for R cv present the highest signal acceptance. Asalready mentioned, an optimization of the whole set is foreseen in future work. attern recognition of Xe double beta decay events Table 2.
Parameters used in the blob method and their selected values to find thelongest track–line. r b is the radius around a pixel to compute its charge in this method, Q bth is the threshold in charge for a pixel to be joined to other by segments, Q bcth , thethreshold in the charge to be considered as a blob candidate , N C is the number of blobscandidates, R tl , the maximum ratio between the longest track–line with two blobs andjust one to choose the second one. In brackets values for low diffusion mixtures in casethey are different from those of pure xenon.Parameter r b Q bth Q bcth N C R tl Value 18 mm 150 e −
130 keV 6 30%(75 e − ) Table 3.
Parameters used in the blob method and their selected values to discriminatebetween one–blob and two–blobs track–lines. Q blobth is the threshold energy for any ofthe two end blobs of selected track–line which have been calculated in a radius r blob , R blobs , the maximum ratio between both end blobs, r lt , the radius around the track–line to estimate the charge inside, and, finally R cv is the minimum charge ratio whichhas to be included inside this radius versus the total charge. In brackets values for lowdiffusion mixtures in case they are different from those of pure xenon.Parameter r blobs Q blobsth R blobs r lt R cv Value 30 mm 440 keV 2 30 mm 95%(98%)
Among all the background sources, we need to deal with gammas, but also with betaparticles produced on surfaces close to the gas sensitive volume. To exclude these eventsthe outermost part of the active volume ( r veto = 1 cm width) is treated as an active veto,i.e., events depositing energy in this region are rejected. Experimentally it is easy toidentify events close to the field cage walls: pixels in the border of the tracking planewill contain charge in this case. Events produced close to the cathode or the anodecan be identified using the t of the event. The same situation occurs for those eventsnear the anode. This criterion has been applied after the previous ones to study its realimpact on background rejection and signal efficiency since part of these surface eventswill have already been rejected, mainly after the one track method.
4. Background rejection factor and signal efficiency after discriminationcriteria
In this section the results of the application of the discrimination algorithms describedin section 3 on background and signal simulated events will be presented. Backgroundrejection factors have been computed separately for both
Tl and
Bi contaminations,as well as for each of the four representative volumes defined in section 2.2: cathode, attern recognition of
Xe double beta decay events Table 4.
Number of signal events (in %) in the RoI around the Q ββ (first column)and final efficiency after all the discrimination algorithms have been applied in the caseof pure xenon (second column) and a low diffusion xenon mixture (last column).RoI events Final eff.(HD) Final eff.(LD) Xe ββ ν ± ± ± readout plane, field cage and lateral part of the vessel.Our results are summarized in several tables in this section for both, backgroundrejection factor and signal efficiency, in the case of pure xenon, high diffusion (HD), anda low diffusion (LD) Xe mixture. Two sets of tables are presented for each of the cases:a) the net reduction in both gases, to be commented below; and b) the relative effect ofeach selection criteria applied subsequently to be detailed in subsections 4.1 and 4.2;Focusing our discussion on efficiencies (table 4), it can be appreciated that onlyaround a 70% of the ββ ν events are fully contained in the detector and deposit theirenergy in the chosen RoI. That is just detector geometry dependent and, therefore, thesame for both gases. In the Gothard experiment, a much smaller TPC, this value wasaround 30% [23] for a RoI between 2 and 3 MeV.The last two columns of the table 4 give information about final efficiencies. Theyshow similar numbers for both gases: over the 40%. That makes almost a 60% ofefficiency if just RoI events are taken into account, a bit below the value of 74%given by Gothard experiment, but where the inefficiency was estimated as only due toevents where one of the electrons had not enough energy to produce a blob. However,considering also the geometrical factor, Gothard had estimated a 22% of overall efficiencyto be compared to the 40% estimated in the present work.In table 5, background reduction factors (i.e. number of events surviving the cutsper simulated one) are shown. Values for events in the RoI and for events after all thecuts are given.The first column of table 5 reveals that only a small fraction of the simulated eventsdeposit their energy in the chosen RoI: 10 − for events originated close to the gas andsmaller fractions for events coming from farther volumes due to attenuation and smallersolid angles; then, the farther volume, the lower fraction will pass. The reason why theRoI event fraction is larger for the Bi contamination on surfaces facing the sensitivevolume is due to the fact that additional beta electrons can reach the active volume anddeposit part of their energy the RoI.The second and third columns of table 5 exhibit an additional reduction of atleast three orders of magnitude due to the use of topological discrimination, a factor 3better in the case of a mixture with a lower diffusion since pattern recognition improves(discussed in subsection 4.2). This reduction is slightly worse for events coming fromthe cathode because the distance to the readout plane plays also an important role indiffusion. For events in the RoI, the background reduction factors depend very much attern recognition of
Xe double beta decay events Table 5.
Background reduction factors for the different background sources in a RoIaround the Q ββ (first column), and after the application of all selection criteria in thecase of pure xenon (second column) and in the case of a low diffusion xenon mixture(last column).Origin Isotope RoI events Final ev. (HD) Final ev. (LD)( × − ) ( × − ) ( × − )Lateral Tl 0.4 7.0 ± ± Bi 0.03 1.5 ± ± Tl 2.0 13.4 ± ± Bi 0.2 4.1 ± ± Tl 2.7 5.4 ± ± Bi 1.4 0.9 ± ± Tl 2.2 7.4 ± ± Bi 1.0 1.1 ± ± Table 6.
Surviving events(in %) of the different sources of background simulatedafter the successive application of the selection criteria in the RoI for a 1 cm–lengthpixelized detector in a xenon at 10 bar. Each column shows the effect of a given cuton the event population selected by the previous one. Fiducial methodOrigin Isotope Track method Blob method Lateral Bottom TopLateral
Tl 7.0 ± ± ± ± ± Bi 14.1 ± ± ± ± ± Tl 4.8 ± ± ± ± ± Bi 41.9 ± ± ± ± ± Tl 3.2 ± ± ± ± ± Bi 51.6 ± ± ± ± ± Tl 3.8 ± ± ± ± ± Bi 65.7 ± ± ± ± ± on the origin of the contamination being much more effective for surface contaminants(cathode and readout cases) due mainly to the presence of electrons (more relevant inthe case of the Bi), than for a volume contamination (case of the vessel). In this lastcase, however, it is easier to reject
Tl events than those caused by
Bi due mainlydue mainly to the multi–track topology of
Tl events, as discussed later.
Table 6 summarizes the relative background reduction factors for each of the backgroundsources. Only events inside the RoI will are taken into account here. As alreadymentioned, each discrimination method is applied to events which have passed previouscuts. After the first selection, based on track method, the number of events surviving attern recognition of
Xe double beta decay events
Tl and from 14% up to 66% for the
Bi, depending on theirorigin. Three points to are to remark here: a) the systematically better rejection factorof the track method observed for
Tl events is due to the fact that they produce multi–track topologies (due to Compton or bremstrahlung) more often than
Bi events; b) inthe case of surface contaminations (cathode, readout) low energy electrons, emitted incoincidence with photons, reach the active volume and produce multi–track events, but,on the contrary, electrons from high energy β decays of Bi increases the number ofsingle–track events;and c)in the case of
Tl, the track method is slightly less effectivefor events originated far from the gas since they may have suffered Compton interactionsin materials resulting in one–track events in the detector.The effect of the topological recognition is quite similar for all contributions ofbackground independently of origin and isotope, as expected since it is applied on themain track. The surviving events after the application of this method with respect tothe previous one is of the order of 40%. The slight differences may be attributed to tworeasons: a) events due to β emissions ( Bi on surfaces) have less secondary tracks, sothey have passed the track criterion, but most of them show clearly one blob at the endfar from the surface and no extra charge at the end close to the surface, so they tendto be better rejected by the blob method; and b) diffusion joining tracks affects moreto events produced at longer drift distances and makes more difficult the topologicalrecognition for events from the cathode. That is commented later in next subsection(4.1) when reporting on a low diffusion Xe mixture data.The fiducial rejection criteria has a different effect depending on the origin of thebackground, playing a more important role for surface contamination, as pointed outin subsection 3.3, while for volumes far from the gas, its reduction is purely statistical.It has been applied separately in the three directions: first in the laterals and then inthe bottom and top. As shown in table 6 the rejection of events firing the outermostreadout pixels (lateral cut) has the most important impact, of the order of a 20%, sinceit is the largest surface. It has to be noted, however, that in the case of volumes close tothe gas (field cage) or surface contaminations (cathode and readout planes) the effectof the corresponding discrimination criterion is higher since beta emission can reach thegas and be rejected. They accompany the gamma emission in the case of
Tl and arepart of the high energy beta spectrum for
Bi. Here the rejection factor is higher than99%. It is interesting to note that apart from these surface beta emissions the effectof the fiducial cut is otherwise rather modest. This result is particularly interesting inorder to consider operation without t determination, something useful in the contextof certain gas mixtures with quenched scintillation.A more detailed analysis of surviving events shows that most of them have beenidentified as signal due to the presence of high energy ( >
100 keV) secondary photonsinteracting too close to the main track and producing a second blob. Roughly, halfof them are due to a Compton interaction, another fraction (around a 10%) to highbremsstrahlung emissions, and the remaining to low radiation and x-rays photons,straggling, or failures of the recognition algorithms. attern recognition of
Xe double beta decay events Table 7.
Relative efficiency of the simulated ββ ν events after the successiveapplication of selection criteria on events depositing energy in the RoI. Each columnshows the percentage of surviving events after a cut on events which have passed theprevious one. Considered a 1 cm—length pixelized detector in pure xenon gas at 10 bar.Eff. Fiducial vetoesOrigin Isotope Eff. Track Eff. Topology Lateral Bottom TopTarget Xe 77.5 ± ± ± ± ± Regarding signal events, table 7 shows the impact of cuts on ββ ν signal onceevents in the RoI have been selected. The most important reduction in efficiency is dueto the selection of events with just a long track and up to one short track. The topologyrecognition selection criteria will eliminate those events in which one of the electrons hastoo low energy to produce a blob, around a 5%. The remaining signal events rejected bythe blob method are the ones for which the algorithm fails to reproduce the real physicaltrack ( track coverage conditions explained in subsection 3.2), due to excessive stragglingof the track. Finally, the fiducial cut will reject those events which statistically depositpart of their energy close to surfaces.Electron diffusion along the drift makes the tracking more complicated since itwidens the final electron cloud and reduces the charge per pixel. Moreover, it is aneffect that depends on the distance of the event to the readout. A critical consequenceof diffusion is that different tracks produced closely may merge and fake a two–electron–single–track topology. The blob identification is also hindered by the presence ofdiffusion. Although our algorithm is able to partially compensate these effects byproperly adjusting its parameters (e.g. by means of the different pixel charge thresholdsdefined), the diffusion will affect the available topological information and the finaldiscrimination capabilities. In an attempt to quantify this effect, a low diffusion scenariois studied in the next section. In this subsection a low diffusion xenon mixture example is analyzed in order to studywhether it could imply an improvement on the topological recognition of the events. Arepresentative value of ∼ µ m / √ cm for both transversal and longitudinal diffusioncoefficients has been chosen in order to study the impact of this parameter in patternrecognition algorithms.As in the pure xenon case, each selection criterion is applied to a population whichhas passed previous cuts. Table 8 shows the relative background reduction factors (in%) for different background sources, and table 9 the relative ββ ν signal efficiencies ofeach selection criterion.A comparison between tables 8 and 6 shows that the low diffusion hardly changes attern recognition of Xe double beta decay events Table 8.
Percentage of the surviving events of the different sources of backgroundsimulated after the successive application of the selection criteria in the RoI for a 1 cm–length pixelized detector in a low diffusion xenon mixture at 10 bar. The percentageof events showed is with respect to the population passing previous cuts.Fiducial methodOrigin Isotope Track meth. Blob meth. Lateral Bottom TopLateral
Tl 7.1 ± ± ± ± ± Bi 16.0 ± ± ± ± ± Tl 4.4 ± ± ± ± ± Bi 42.1 ± ± ± ± ± Tl 2.4 ± ± ± ± ± Bi 37.2 ± ± ± ± ± Tl 4.8 ± ± ± ± ± Bi 57.4 ± ± ± ± ± Table 9.
Efficiency of the simulated ββ ν events after the successive application ofthe selection criteria. Connection is applied over the events detected in the RoI andthen number of surviving events showed is calculated with respect the previous one.The events are simulated for a 1 cm–length pixelized detector in a low diffusion xenonmixture at 10 bar. Eff. Fiducial vetoesOrigin Isotope Eff. Track Eff. Topology Lateral Bottom TopTarget Xe 76.1 ± ± ± ± ± the rejection due to the track method since pixels with too little charge had been removedalso in the case of a high diffusion. Only in the case of the readout contamination,somewhat improved factors are achieved due to the fact that low diffusion is especiallyrelevant at low drift distances. However, it is in the topological recognition of blobswhere almost an additional factor 3 of improvement in rejection is obtained, mainly dueto the better recognition of secondary photons interactions near the main track: theimprovement is more important in the case of events caused by photons (case of Tlcontaminations) than in those which include also primary electrons (as those from betaspectrum of
Bi on surfaces). The fiducial rejection it is slightly worse than in thecase of pure Xe due to the fact that events are now less extended.Regarding signal (table 9), the use of a quencher to decrease the diffusion allowsa better determination of two separated tracks and some small extra depositions arenow distinguished apart from the main track. The track–line is also sharper (see figure9) for both, signal and background events, and, therefore track coverage parameter R cv (table 3) needs to be chosen more stringent to reject background. For this reason, theefficiency after the track and blob method is lower than in the case of pure Xe, but it is attern recognition of Xe double beta decay events
As already mentioned, the aim of this work is not to determine final backgroundlevels, for which a detailed background model including final detector geometryand components with their corresponding contaminations would need to be built.However, it is interesting to address the issue of whether the performance of thealgorithm developed could be generically sufficient to reach competitive backgroundlevels in the RoI that, as explained in the introduction, must be of the order of10 − c keV − kg − year − or below. To answer this question we do the following exercise.We have normalized the populations of simulated events in the different volumesof the simulated geometry with the following assumed volumetric contaminations:1 µ Bq/kg for
Tl and 10 µ Bq/kg for
Bi for copper (vessel, field cage wires andcathode), and 10 µ Bq/kg for
Tl and 5 µ Bq/kg for
Bi for teflon (field cagebody). These values are conservative upper limits of
Tl and
Bi contaminationstypically obtained for copper and teflon samples in the literature [36, 37]. Thebackground level in the RoI derived from these numbers amounts to (2 . ± . × − c keV − kg − year − in the case of pure xenon, while it is considerably lower,(0 . ± . × − c keV − kg − year − for the low diffusion scenario. In both cases muchbelow the specified 10 − c keV − kg − year − .Most probably, in a real TPC the background will be dominated by other internalcomponents linked to more specific detector features like adhesives, soldering, electroniccomponents, or other elements of the sensors, readout, connectors or feedthroughs. Ofthese, the ones closer to the gas volume will be the most critical. Rn emanation, asexplained before, may add up as an additional surface contamination of
Bi. Keepingthe generality of our work, we have proceeded now reversely to calculate which levelof surface contamination of the readout plane translates into a background level of10 − c keV − kg − year − after discrimination. The resulting values are of ∼ . µ Bq/cm for Tl and ∼ µ Bq/cm for Bi, for the case of pure xenon. In the low diffusionscenario this contamination could be 3 times higher. This calculation gives us an ideaof the level of internal contamination (simplistically expressed as an internal surfacecontamination of the readout) tolerated in view of the discrimination capabilities ofour algorithm. The obtained values, although stringent, are within the typical goals ofscreening campaigns carried out by current low background experiments.To conclude, together with state of the art radiopurity, the topologicaldiscrimination of a Xe gas TPC as implemented in our algorithm is capable of bringingthe levels of background of such a TPC to the required levels of the next generationexperiment. attern recognition of
Xe double beta decay events
5. Conclusions and outlook
In this paper, we have done a detailed simulation of the topology of ββ Xe events, aswell as of typical background events in the range of interest of the ββ ν decay mode,in a high pressure Xe TPC with pixelised readout. A pattern recognition algorithmhas been developed and applied to the simulated topologies to discriminate signal andbackground, and determine efficiency and rejection factors.The background events considered come from decays of Tl or
Bi in differentinternal components of the detector. The simulation includes the particle transport andinteraction with the detector (Geant4) as well as the drift and diffusion of the ionizationcloud in the TPC and the digitization of the signal in a pixelized readout of 1 × pixel size. The simulations are carried out within a generic TPC geometry includingabout ∼
100 kg of gas Xe at 10 bar pressure.The rationale of the discrimination criteria relies on the following features of signalevents: the absence of energy deposits close to the walls (fiducial cut), the presence ofonly one long track and the identification of two larger energy depositions (blobs) at thetwo ends of the track. The presence of a second track or secondary energy depositionsare also dealt with by the algorithm. These basic ideas are implemented in a patternrecognition algorithm based on graph theory concepts.The rejection factor for each of the background components studied has beendetermined, as well as the breakdown of this factor into each of the independent criteriaseparately. In overall, the algorithm is able to reduce the events falling in the energyRoI by about 3 orders of magnitude. The efficiency of the algorithm on signal events ismaintained at a 40%.Our result is comparable to the one previously achieved by visual inspection in[23] even with the relatively large diffusion of pure Xe, and it is now implemented in aautomated algorithm.The use of our algorithm with a lower diffusion gas has been tested and animprovement of an extra factor 3 in the rejection factor is easily achieved, while keepingthe same signal efficiency. This improvement is mostly concentrated on the criterion ofidentifying the two blobs. We consider this result conservative as it is probably limitedby the pixel size used, of 1 × , not optimized for the low diffusion case. We plannow to continue studying this case with smaller pixel sizes.In general the nature of the events surviving the discrimination criteria has beenbriefly discussed to understand the limitation of the algorithm. Extra energy deposition(by, e.g., x-ray emission or low energy photon radiation) close to the main track orexcessive straggling of the electron track are sometimes cause of bad reconstruction ofthe events. Several ideas are put forward to correctly reconstruct those events, and thereare prospects to further improvement of the algorithm. Future work will be focused ona deeper study of misidentified events to achieve a better blob identification. Positiveresults may open the possibility of increasing the gas pressure, resulting in a morecompact design, less electronic channels or the ability of working with larger volume attern recognition of Xe double beta decay events
Acknowledgements
We are grateful to our colleagues of the groups of the University of Zaragoza,CEA/Saclay and our colleagues from the NEXT and RD-51 collaborations for helpfuldiscussions and encouragement. We especially thank D. Gonz´alez-D´ıaz for carefulreading of the manuscript and giving useful comments. We acknowledge supportfrom the European Commission under the European Research Council T-REX StartingGrant ref. ERC-2009-StG-240054 of the IDEAS program of the 7th EU FrameworkProgram. We also acknowledge support from the Spanish Ministry of Economy andCompetitiveness (MINECO), under contracts ref. FPA2008-03456 and FPA2011-24058,as well as under the CUP project ref. CSD2008-00037 and the CPAN project ref.CSD2007- 00042 from the Consolider-Ingenio 2010 program of the MICINN. Part ofthese grants are funded by the European Regional Development Fund (ERDF/FEDER).F.I. acknowledges the support from the Eurotalents program and D.C.H. of the Univ.Zaragoza, under the program PIF-UZ-2009-CIE-03.
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