Pulse shape discrimination for GERDA Phase I data
M. Agostini, M. Allardt, E. Andreotti, A.M. Bakalyarov, M. Balata, I. Barabanov, M. Barnabe Heider, N. Barros, L. Baudis, C. Bauer, N. Becerici-Schmidt, E. Bellotti, S. Belogurov, S.T. Belyaev, G. Benato, A. Bettini, L. Bezrukov, T. Bode, V. Brudanin, R. Brugnera, D. Budjáš, A. Caldwell, C. Cattadori, A. Chernogorov, F. Cossavella, E.V. Demidova, A. Domula, V. Egorov, R. Falkenstein, A. Ferella, K. Freund, N. Frodyma, A. Gangapshev, A. Garfagnini, C. Gotti, P. Grabmayr, V. Gurentsov, K. Gusev, K.K. Guthikonda, W. Hampel, A. Hegai, M. Heisel, S. Hemmer, G. Heusser, W. Hofmann, M. Hult, L.V. Inzhechik, L. Ioannucci, J. Janicskó Csáthy, J. Jochum, M. Junker, T. Kihm, I.V. Kirpichnikov, A. Kirsch, A. Klimenko, K.T. Knöpfle, O. Kochetov, V.N. Kornoukhov, V.V. Kuzminov, M. Laubenstein, A. Lazzaro, V.I. Lebedev, B. Lehnert, H.Y. Liao, M. Lindner, I. Lippi, X. Liu, A. Lubashevskiy, B. Lubsandorzhiev, G. Lutter, C. Macolino, A.A. Machado, B. Majorovits, W. Maneschg, M. Misiaszek, I. Nemchenok, S. Nisi, C. O'Shaughnessy, L. Pandola, K. Pelczar, G. Pessina, A. Pullia, S. Riboldi, N. Rumyantseva, C. Sada, M. Salathe, C. Schmitt, J. Schreiner, O. Schulz, B. Schwingenheuer, S. Schönert, E. Shevchik, M. Shirchenko, H. Simgen, A. Smolnikov, L. Stanco, H. Strecker, M. Tarka, C.A. Ur, A.A. Vasenko, et al. (14 additional authors not shown)
EEur. Phys. J. C manuscript No. (will be inserted by the editor)
Pulse shape discrimination for
Gerda
Phase I data
M. Agostini , M. Allardt , E. Andreotti , A.M. Bakalyarov , M. Balata ,I. Barabanov , M. Barnab´e Heider , N. Barros , L. Baudis ,C. Bauer , N. Becerici-Schmidt , E. Bellotti , S. Belogurov ,S.T. Belyaev , G. Benato , A. Bettini , L. Bezrukov , T. Bode ,V. Brudanin , R. Brugnera , D. Budj´aˇs , A. Caldwell , C. Cattadori ,A. Chernogorov , F. Cossavella , E.V. Demidova , A. Domula ,V. Egorov , R. Falkenstein , A. Ferella , K. Freund , N. Frodyma ,A. Gangapshev , A. Garfagnini , C. Gotti , P. Grabmayr ,V. Gurentsov , K. Gusev , K.K. Guthikonda , W. Hampel ,A. Hegai , M. Heisel , S. Hemmer , G. Heusser , W. Hofmann ,M. Hult , L.V. Inzhechik , L. Ioannucci , J. Janicsk´o Cs´athy ,J. Jochum , M. Junker , T. Kihm , I.V. Kirpichnikov , A. Kirsch ,A. Klimenko , K.T. Kn¨opfle , O. Kochetov , V.N. Kornoukhov ,V.V. Kuzminov , M. Laubenstein , A. Lazzaro , V.I. Lebedev ,B. Lehnert , H.Y. Liao , M. Lindner , I. Lippi , X. Liu ,A. Lubashevskiy , B. Lubsandorzhiev , G. Lutter , C. Macolino ,A.A. Machado , B. Majorovits , W. Maneschg , M. Misiaszek ,I. Nemchenok , S. Nisi , C. O’Shaughnessy , L. Pandola , K. Pelczar ,G. Pessina , A. Pullia , S. Riboldi , N. Rumyantseva , C. Sada ,M. Salathe , C. Schmitt , J. Schreiner , O. Schulz , B. Schwingenheuer ,S. Sch¨onert , E. Shevchik , M. Shirchenko , H. Simgen , A. Smolnikov ,L. Stanco , H. Strecker , M. Tarka , C.A. Ur , A.A. Vasenko ,O. Volynets , K. von Sturm , V. Wagner , M. Walter ,A. Wegmann , T. Wester , M. Wojcik , E. Yanovich , P. Zavarise ,I. Zhitnikov , S.V. Zhukov , D. Zinatulina , K. Zuber , G. Zuzel INFN Laboratori Nazionali del Gran Sasso, LNGS, Assergi, Italy Institute of Physics, Jagiellonian University, Cracow, Poland Institut f¨ur Kern- und Teilchenphysik, Technische Universit¨at Dresden, Dresden, Germany Joint Institute for Nuclear Research, Dubna, Russia Institute for Reference Materials and Measurements, Geel, Belgium Max-Planck-Institut f¨ur Kernphysik, Heidelberg, Germany Dipartimento di Fisica, Universit`a Milano Bicocca, Milano, Italy INFN Milano Bicocca, Milano, Italy Dipartimento di Fisica, Universit`a degli Studi di Milano e INFN Milano, Milano, Italy Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia Institute for Theoretical and Experimental Physics, Moscow, Russia National Research Centre “Kurchatov Institute”, Moscow, Russia Max-Planck-Institut f¨ur Physik, M¨unchen, Germany Physik Department and Excellence Cluster Universe, Technische Universit¨at M¨unchen, Germany Dipartimento di Fisica e Astronomia dell‘Universit`a di Padova, Padova, Italy INFN Padova, Padova, Italy Physikalisches Institut, Eberhard Karls Universit¨at T¨ubingen, T¨ubingen, Germany Physik Institut der Universit¨at Z¨urich, Z¨urich, SwitzerlandReceived: date / Accepted: date a Present Address:
CEGEP St-Hyacinthe,Qu´ebec, Canada b Present Address:
INFN LNGS, Assergi, Italy c also at: Universit`a di Firenze, Italy d also at: Moscow Inst. of Physics and Technology, Russia e also at: Int. Univ. for Nature, Society and Man “Dubna”,Russia f Present Address:
Shanghai Jiaotong University, Shanghai,China g Present Address:
University North Carolina, Chapel Hill,USA h Present Address:
University of L’Aquila, Dipartimento diFisica, L’Aquila, Italy a r X i v : . [ phy s i c s . i n s - d e t ] J u l Abstract
The
Gerda experiment located at the Lab-oratori Nazionali del Gran Sasso of INFN searches forneutrinoless double beta (0 νββ ) decay of Ge usinggermanium diodes as source and detector. In Phase I ofthe experiment eight semi-coaxial and five BEGe typedetectors have been deployed. The latter type is used inthis field of research for the first time. All detectors aremade from material with enriched Ge fraction. Theexperimental sensitivity can be improved by analyzingthe pulse shape of the detector signals with the aimto reject background events. This paper documents thealgorithms developed before the data of Phase I wereunblinded. The double escape peak (DEP) and Comp-ton edge events of 2.615 MeV γ rays from Tl decaysas well as two-neutrino double beta (2 νββ ) decays of Ge are used as proxies for 0 νββ decay.For BEGe detectors the chosen selection is based ona single pulse shape parameter. It accepts 0 . ± .
02 ofsignal-like events while about 80 % of the backgroundevents at Q ββ = 2039 keV are rejected.For semi-coaxial detectors three analyses are devel-oped. The one based on an artificial neural networkis used for the search of 0 νββ decay. It retains 90 %of DEP events and rejects about half of the eventsaround Q ββ . The 2 νββ events have an efficiency of0 . ± .
02 and the one for 0 νββ decays is estimatedto be 0 . +0 . − . . A second analysis uses a likelihood ap-proach trained on Compton edge events. The third ap-proach uses two pulse shape parameters. The latter twomethods confirm the classification of the neural networksince about 90 % of the data events rejected by the neu-ral network are also removed by both of them. In gen-eral, the selection efficiency extracted from DEP eventsagrees well with those determined from Compton edgeevents or from 2 νββ decays. Keywords neutrinoless double beta decay · ger-manium detectors · enriched Ge · pulse shapeanalysis PACS β decay; double β decay; electron andmuon capture · ≤ A ≤ · γ -ray spectroscopy · The
Gerda (GERmanium Detector Array) experimentsearches for neutrinoless double beta decay (0 νββ de-cay) of Ge. Diodes made from germanium with anenriched Ge isotope fraction serve as source and de-tector of the decay. The sensitivity to detect a signal,i.e. a peak at the decay’s Q value of 2039 keV, depends i Correspondence , email: [email protected] on the background level. Large efforts went thereforeinto the selection of radio pure materials surroundingthe detectors. The latter are mounted in low mass hold-ers made from screened copper and PTFE and are op-erated in liquid argon which serves as cooling mediumand as a shield against external backgrounds. The argoncryostat is immersed in ultra pure water which providesadditional shielding and vetoing of muons by the detec-tion of ˇCerenkov radiation with photomultipliers. Thebackground level achieved with this setup is discussedin Ref. [1]. Details of the apparatus which is located atthe Laboratori Nazionali del Gran Sasso of INFN canbe found in Ref. [2].It is known from past experiments that the time de-pendence of the detector current pulse can be used toidentify background events [3,4,5,6,7,8]. Signal eventsfrom 0 νββ decays deposit energy within a small vol-ume if the electrons lose little energy by bremsstrahlung(single site event, SSE). On the contrary, in backgroundevents from, e.g., photons interacting via multiple Comp-ton scattering, energy is often deposited at several loca-tions well separated by a few cm in the detector (multisite events, MSE). The pulse shapes will in general bedifferent for the two event classes and can thus be usedto improve the sensitivity of the experiment. Energydepositions from α or β decays near or at the detectorsurface lead to peculiar pulse shapes as well that allowstheir identification. Gerda proceeds in two phases. In Phase I, fivesemi-coaxial diodes from the former Heidelberg-Moscow(
HdM ) experiment (named ANG 1 - ANG 5) [9] andthree from the
Igex experiment (named RG 1 - RG 3) [10]are deployed. For Phase II, 30 new detectors of BEGetype [11] have been produced of which five have alreadybeen deployed for part of Phase I (GD32B, GD32C,GD32D, GD35B and GD35C). The characteristics ofall detectors are given in Refs. [1,2].Each detector is connected to a charge sensitive am-plifier and the output is digitized with Flash ADCs with100 MHz sampling frequency. The deposited energy andthe parameters needed for pulse shape analysis are re-constructed offline [12,13] from the recorded pulse.The effect of the PSD selection on the physics datais typically always compared in the energy interval 1930- 2190 keV which is used for the 0 νββ analysis [1]. Theblinded energy window 2034 - 2044 keV and two inter-vals 2099 - 2109 keV (SEP of
Tl line) and 2114 -2124 keV (
Bi line) are removed. The remaining en-ergy range is referred to as the “230 keV window” inthe following.Events with an energy deposition in the window Q ββ ± Q ββ ± Fig. 1
Cross section of a semi-coaxial detector (top) anda BEGe detector (bottom). The p+ electrode is drawn ingrey and the n+ electrode in black (thickness not to scale).The electrodes are separated by an insulating groove. Colorprofiles of the weighting potential [14] are overlayed on thedetector drawings. Also sketched for the BEGe is the readoutwith a charge sensitive amplifier. selections and calibrations had been finalized. This arti-cle presents the pulse shape analysis for Gerda
Phase Ideveloped in advance of the data unblinding.
Semi-coaxial and BEGe detectors have different geome-tries and hence different electric field distributions. Fig. 1shows a cross section of a semi-coaxial and a BEGe de-tector with the corresponding weighting potential pro-files. The latter determine the induced signal on thereadout electrode for drifting charges at a given posi-tion in the diode [14]. For both detectors, the bulk is p type, the high voltage is applied to the n+ electrodeand the readout is connected to the p+ electrode. Theelectrodes are separated by an insulating groove. 2.1 BEGe detectorsThe induced current pulse is largest when charges driftthrough the volume of a large weighting potential gra-dient. For BEGe detectors this is the case when holesreach the readout electrode. Electrons do not contributemuch since they drift through a volume of low fieldstrength. The electric field profile in BEGes causes holesto approach the p+ electrode along very similar tra-jectories, irrespective where the energy deposition oc-curred [15]. For a localized deposition consequently, themaximum of the current pulse is nearly always directlyproportional to the energy. Only depositions in a smallvolume of 3-6 % close to the p+ electrode exhibit largercurrent pulse maxima since electrons also contribute inthis case [15,16]. This behavior motivates the use of theratio A/E for pulse shape discrimination (PSD) with A being the maximum of the current pulse and E beingthe energy. The current pulses are extracted from therecorded charge pulses by differentiation.For double beta decay events (0 νββ or two-neutrinodouble beta decay, 2 νββ ), the energy is mostly de-posited at one location in the detector (SSE). Fig. 2(top left) shows an example of a possible SSE chargeand current trace from the data. For SSE in the bulkdetector volume one expects a nearly Gaussian distri-bution of A/E with a width dominated by the noise inthe readout electronics.For MSE, e.g. from multiple Compton scattered γ rays, the current pulses of the charges from the differentlocations will have – in general – different drift timesand hence two or more time-separated current pulsesare visible. For the same total energy E , the maximumcurrent amplitude A will be smaller in this case. Sucha case is shown in the top right plot of Fig. 2.For surface events near the p+ electrode the currentamplitude, and consequently A/E , is larger and peaksearlier in time than for a standard SSE. This featureallows these signals to be recognized efficiently [17]. Atypical event is shown in the bottom left trace of Fig. 2.The n+ electrode is formed by infusion of lithium,which diffuses inwards resulting in a fast falling con-centration profile starting from saturation at the sur-face. The p-n junction is below the n+ electrode sur-face. Going from the junction towards the outer surface,the electric field decreases. The point when it reacheszero corresponds to the edge of the conventional n+ electrode dead layer, that is 0.8 - 1 mm thick (1.5 -2.3 mm) for the BEGe (semi-coaxial) detectors. How-ever, charges (holes) from particle interactions can stillbe transferred from the dead layer into the active vol-ume via diffusion (see e.g. Ref. [18]) up to the pointnear the outer surface where the Li concentration be- t [ns]81200 81400 81600 81800 82000 a . u . ChargeCurrentSSE t [ns]81200 81400 81600 81800 82000 a . u . MSE t [ns]81200 81400 81600 81800 82000 a . u . + p t [ns]81200 81400 81600 81800 82000 a . u . + n GERDA 13-06
Fig. 2
Candidate pulse traces taken from BEGe data for a SSE (top left), MSE (top right), p+ electrode event (bottom left)and n+ surface event (bottom right). The maximal charge pulse amplitudes are set equal to one for normalization and currentpulses have equal integrals. The current pulses are interpolated. comes high enough to result in a significant recombina-tion probability. Due to the slow nature of the diffusioncompared to the charge carrier drift in the active vol-ume, the rise time of signals from interactions in thisregion is increased. This causes a ballistic deficit lossin the energy reconstruction. The latter might be fur-ther reduced by recombination of free charges near theouter surface. The pulse integration time for A is ∼ A/E ratio. This is utilized to identify β particles penetrat-ing through the n+ layer [19]. The bottom right traceof Fig. 2 shows a candidate event.A pulse shape discrimination based on A/E hasbeen developed in preparation for Phase II. It is appliedhere and has been tested extensively before through ex-perimental measurements both with detectors operatedin vacuum cryostats [16] and in liquid argon [20,21,22]as well as through pulse-shape simulations [15].For double beta decay events, bremsstrahlung ofelectrons can reduce A and and results in a low sidetail of the A/E distribution while events close to the p+ electrode cause a tail on the high side. Thus thePSD survival probability of double beta decay is < p+ contact but the gradient is lower and hencea larger part of the volume is relevant for the current signal. Fig. 3 shows examples of current pulses from lo-calized energy depositions. These simulations have beenperformed using the software described in Refs. [15,23].For energy depositions close to the n+ surface (at ra-dius 38 mm in Fig. 3) only holes contribute to the signaland the current peaks at the end. In contrast, for sur-face p+ events close to the bore hole (at radius 6 mm)the current peaks earlier in time. This behavior is com-mon to BEGe detectors. Pulses in the bulk volume showa variety of different shapes since electrons and holescontribute. Consequently, A/E by itself is not a usefulvariable for coaxial detectors. Instead three significantlydifferent methods have been investigated. The main oneuses an artificial neural network to identify single siteevents; the second one relies on a likelihood method todiscriminate between SSE like events and backgroundevents; the third is based on the correlation between
A/E and the pulse asymmetry visible in Fig 3.2.3 Pulse shape calibrationCommon to all methods and for both detector typesis the use of calibration data, taken once per week, totest the performance and – in case of pattern recog-nition programs – to train the algorithm. The
Thcalibration spectrum contains a peak at 2614.5 keVfrom the
Tl decay. The double escape peak (DEP, at1592.5 keV) of this line is used as proxy for SSE whilefull energy peaks (FEP, e.g. at 1620.7 keV) or the singleescape peak (SEP, at 2103.5 keV) are dominantly MSE.The disadvantage of the DEP is that the distribution time [s] c u rr en t [ a . u .] radius 6 mm8 mm 14 mm20 mm26 mm 32 mm 38 mm G E RDA - Fig. 3
Simulated pulse shapes for SSE in a semi-coaxialdetector. The locations vary from the outer n+ surface (ra-dius 38 mm) towards the bore hole (radius 6 mm) along aradial line at the midplane in the longitudinal direction. Theintegrals of all pulses are the same. The pulses are shaped tomimic the limited bandwidth of the readout electronics. of the events is not homogeneous inside the detectoras it is for 0 νββ decays. Since two 511 keV photonsescape, DEP events are dominantly located at the cor-ners. Events due to Compton scattering of γ rays spana wide energy range and also contain a large fraction ofSSE. Therefore they are also used for characterizing thePSD methods, especially their energy dependencies.The 2 νββ decay is homogeneously distributed andthus allows a cross check of the signal detection effi-ciency of the PSD methods. BEGe detectors from Canberra [11] feature not only asmall detector capacitance and hence very good energyresolution but also allow a superior pulse shape discrim-ination of background events compared to semi-coaxialdetectors. The PSD method and its performance is dis-cussed in this section. The full period of BEGe datataking during Phase I (July 2012 - May 2013) with anexposure of 2.4 kg · yr is used in this analysis. One ofthe five detectors (GD35C) was unstable and is not in-cluded in the data set.3.1 PSD calibrationCompton continuum and DEP events from Th cal-ibration and the events in the 2 νββ energy range inphysics data feature
A/E distributions with a Gaus-sian part from SSE and a low side tail from MSE as
A/E 0.92 0.94 0.96 0.98 1.00 1.02 1.04 c oun t s GERDA 13-06
Fig. 4
A/E distribution for Compton continuum data fittedwith function (1). The dashed blue curve is the Gaussian com-ponent and the green curve is the component approximatingthe MSE contribution. shown in Fig. 4. It can be fitted by the function: f ( x = A/E ) = nσ A/E · √ π · e − ( x − µA/E )22 σ A/E + m · e f · ( x − l ) + de ( x − l ) /t + l (1)where the Gaussian term is defined by its mean µ A/E ,standard deviation σ A/E and integral n . The MSE termis parameterized empirically by the parameters m , d , f , l and t . σ A/E is dominated by the resolution σ A of A which is independent of the energy, i.e. for low energies σ A/E ∝ σ A /E ∝ /E .There are a few effects which are corrected in theorder they are discussed below. To judge their rele-vance, already here it is stated that events in the in- date Jul-12 Aug-12 Oct-12 Dec-12 Mar-13 May-13 A / E m D . exp(-p2 . f(t) = p0 + p1correction for discrete jumpsGD32BGD32C GD32DGD35B GERDA 13-06
Fig. 5
Gaussian mean µ A/E for DEP events for individual
Th calibrations. The data points in the period before theoccurrence of jumps are fitted with an exponential function asspecified. Each
A/E distribution is normalized such that theconstant of the fit ( p
0) is one. Separate constant correctionsare determined as averages over the periods corresponding tothe discrete jumps. terval 0 . < A/E < .
07 are accepted as signal (seeSect. 3.2).1. After the deployment in July 2012, µ A/E driftedwith a time scale of about one month for all detec-tors (see Fig. 5). The total change was 1 to 5 % de-pending on the detector. The behavior is fitted withan exponential function which is then used to cor-rect
A/E of calibration and physics data as a func-tion of time. Additionally, jumps occurred e.g. aftera power failure. These are also corrected.2. µ A/E increases by up to 1 % during calibration runswhich last typically one hour (Fig. 6). During physicsdata taking, µ A/E returns to the value from beforethe calibration on a time scale of less than 24 hours,which is short compared to the one week interval be-tween calibrations. This causes µ A/E in calibrationsto be shifted to slightly higher values compared tophysics data taking. This effect is largely removedby applying a linear correction in time (fit shownin Fig. 6) to calibration data. Afterwards, µ A/E ofphysics data in the interval 1.0 - 1.3 MeV agrees ap-proximately with Compton events from calibrationdata in the same energy region (see Fig. 7).3.
A/E shows a small energy dependence (Fig. 8). It ismeasured by determining the Gaussian mean µ A/E at different energies in the
Tl Compton contin-uum between 600 and 2300 keV. The size is about0.5 to 1 % per MeV. This approach is documentedand validated in Refs. [16,24]. The correction is ap-plied to both calibration and physics data.The corrections discussed above are empirical andresult in energy and time independent
A/E distribu-tions. The origin of the time drifts might be due toelectric charges collected from LAr on the surface ofthe insulating groove. This is a known phenomenon [25]and pulse shape simulations show that
A/E changes of time since start of calibration [min] 10 20 30 40 50 60 A / E m A/E for Compton events
GERDA 13-06
Fig. 6
Gaussian mean µ A/E of the
A/E distribution forCompton events as a function of the time since the start of acalibration run. The data from all calibrations are combinedafter the correction according to Fig. 5 has been applied.
A/E 0.96 0.98 1.00 1.02 1.04 no r m a li z ed c oun t s bbn GD32B
GERDA 13-06
Fig. 7
A/E distribution of GD32B from physics data eventsbetween 1.0 and 1.3 MeV (blue, dominantly 2 νββ decays),Compton continuum in the same energy range (red) and DEPevents (black). The latter two are taken from the sum of allcalibrations. All corrections are applied. The tail on the leftside of the Gaussian is larger in the Compton events due to ahigher fraction of MSE compared to the physics data in thisenergy range. the observed size are conceivable. The small observedenergy dependence of
A/E (item 3) is thought to be anartefact of data acquisition and/or signal processing.Since
A/E has arbitrary units, it is convenient torescale the distribution at the end such that the meanof the Gaussian is unity after all corrections. This easesthe combination of all detectors.The compatibility of calibration data with physicsdata after the application of all corrections is verifiedin Fig. 7. The
A/E
Gaussian parameters are quanti-
Fig. 8
A/E energy dependence shown with
Th calibra-tion data (blue density plot) and events from physics datataking (predominantly 2 νββ , yellow points). The distribu-tions of µ A/E for the different energy bins are fitted witha linear function (green line). The 2 νββ continuum is fittedwith the same function, leaving only the constant of the fitfree (red line). The data from GD32D are shown.
Table 1
Comparison of
A/E
Gaussian mean µ A/E and width σ A/E from physics data (events between 1.0 MeV and 1.3 MeV,dominantly 2 νββ decays) and calibration data (Compton continuum in the region 1.0 MeV - 1.3 MeV and DEP at 1592.5 keV)after applying all corrections.detector µ A/E (2 νββ ) - µ A/E (DEP) µ A/E (2 νββ ) - µ A/E (Compton) σ A/E (2 νββ ) σ A/E (Compton)GD32B − . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . . ± . − . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . tatively compared in Table 1. The agreement of µ A/E for DEP and 2 νββ events validates also the energy de-pendence correction (item 3). Small differences remaindue to imperfections of the applied corrections. Theywill be taken into account as a systematic uncertaintyin the determination of the 0 νββ efficiency in Sect. 3.3.In contrast to the SSE Gaussian, the MSE part ofthe
A/E distribution and the part from p+ electrodeevents is only negligibly affected by the A/E resolu-tion and its change with energy. This motivates the useof an
A/E cut that is constant at all energies: If thecut position is many σ A/E of the Gaussian resolutionaway from one, the survival fraction is practically in-dependent of the energy. Only at low energies this isno longer the case. At about 1 MeV, the cut position
A/E > .
965 corresponds to a separation from one by2.6 σ A/E corresponding to the 99 % quantile of a Gaus-sian (see Fig. 9). For lower energies the efficiency lossof the Gaussian peak becomes relevant. Therefore theefficiency determination is restricted to energies above1 MeV. energy [keV]
800 1000 1200 1400 1600 1800 2000 2200 A / E s Th Compton data in A/E s + p1 p0 / E(E) = A/E s ) A/E s Gaussian 99% quantile (2.6 PSD cut level with uncertainty
GERDA 13-06
Fig. 9
Width σ A/E of the
A/E
Gaussian versus energy(points with error bars) for GD35B with a fit (black dashedline). The blue full line shows the 99 % quantile of the Gaus-sian (2.6 σ A/E ). The red horizontal line corresponds to thelow side PSD cut distance from the nominal µ A/E = 1. Theuncertainty band is given by the maximal deviation of the
A/E scale as determined in Table 1.
The energy dependence of µ A/E is determined be-tween 600 keV and 2300 keV. Since the dependence isweak, even beyond these limits the cut determinationis accurate to within a few percent. This is acceptablefor example to determine the fraction of α events at the p+ electrode passing the SSE selection cut.3.2 Application of PSD to dataFig. 10 shows A/E plotted versus energy for physicsdata in a wide energy range together with the accep-tance range. The data of all detectors have been addedafter all applicable corrections and the normalization ofthe Gaussian mean to one. The cut rejects events with
A/E < .
965 (“low
A/E cut”) or
A/E > .
07 (“high
A/E cut”). The high side cut interval was chosen twicewider due to the much lower occurrence and better sep-aration of p+ electrode events. The cut levels result in ahigh probability to observe no background event in thefinal Q ββ analysis window for the Phase I BEGe dataset, while maintaining a large efficiency with small un-certainties. As can be seen from Fig. 9, at Q ββ the cutis ≥ . σ A/E apart from one.Fig. 11 shows the combined energy spectrum of theBEGe detectors before and after the PSD cut. In thephysics data set with 2.4 kg · yr exposure, seven out of40 events in the 400 keV wide region around Q ββ (ex- energy [keV] A / E A/E cutdatablinded region
GERDA 13-06
Fig. 10
A/E versus energy in a wide energy range for thecombined BEGe data set. The acceptance region boundariesare marked by the red lines. The blinded region is indicatedby the green band.
Table 2
Removed fractions by the low
A/E cut and high
A/E cut and total surviving fractions applying both cuts in severalenergy regions in physics data and
Th calibration data (combined data sets of all detectors). In the physics data set, the1839 keV - 2239 keV region excludes the blinded 8 keV window around Q ββ . Peak regions have the underlying Comptoncontinuum subtracted. Uncertainties are statistical only.region low A/E cut high
A/E cut surviving fraction
A/E < . A/E > .
07 0 . < A/E < . Th calibrationDEP 1592.5 keV 0 . ± .
003 0 . ± .
001 0 . ± . . ± .
008 0 . ± .
002 0 . ± . . ± .
005 0 . ± .
001 0 . ± . . ± .
05 0 . ± .
015 0 . ± . . ± .
011 0 . ± .
004 0 . ± . /
40 3 /
40 7 / > α at p+ ) 1 /
35 33 /
35 1 / cluding an 8 keV blinding window) are kept and hencethe background for BEGe detectors is reduced from(0.042 ± +0 . − . ) cts/(keV · kg · yr). In thesmaller 230 keV region three out of 23 events remain.Table 2 shows the surviving fractions for several in-teresting energy regions in the physics data and Thcalibration data. The suppression of the K γ line at1525 keV in physics data is consistent with the one ofthe Bi line at 1621 keV. The rejection of α events atthe p+ electrode is consistent with measurements withan α source in a dedicated setup [17].The energy spectrum of the physics data can be usedto identify the background components at Q ββ as de-scribed in Ref. [1]. About half of the events are from Kdecays on the n+ electrode surface which are rejectedby the low side A/E cut with large efficiency [19]. Aboutone third of the background at Q ββ is due to Biand
Tl. Their survival probability can be determinedfrom the calibration data (52 % for
Tl) or extrap-olated from previous studies [21,22] (36 % for
Bi).The remaining backgrounds e.g. from Ga inside the energy [keV] c oun t s / ( k e V ) before A/E cutafter A/E cutblinded region energy [keV] c oun t s / ( k e V ) G E RDA - Fig. 11
Energy spectrum of the combined BEGe data set:grey (blue) before (after) the PSD cut. The inset shows azoom at the region Q ββ ±
200 keV with the 8 keV blindedregion in green. detectors and from the p+ surface are suppressed ef-ficiently [15,17]. The rejection of 80 % of the physicsevents at Q ββ is hence consistent with expectation.In Fig. 12, the A/E distribution of physics data inthe Q ββ ±
200 keV region is compared with the distri-butions from different background sources. The peak at0.94 can be attributed to n+ surface events. The A/E distribution of the other events is compatible withinstatistical uncertainty with the ones expected from thedifferent background sources.3.3 Evaluation of 0 νββ cut survival fraction for BEGesThe PSD survival fraction of DEP events can vary fromthe one for 0 νββ events because of the difference ofthe event locations in a detector (see Sect. 2.3) and
A/E 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 c t s ( a . u . ) ph ys i cs da t a c t s A/E cutK n+ surface events, simulation Co, simulation Compton 1.8 - 2.2 MeV, calibrationFEP @ 1.6 MeV, calibration 200 keV, physics data – bb Q G E RDA - Fig. 12
A/E histogram of the physics data within 200 keVof Q ββ (red) compared to Compton continuum events (greendot-dot-dashed) and 1621 keV FEP events (black) from cal-ibration data. Also shown are simulations of K decays atthe n+ electrode surface (blue dashed) and Co (black dot-dashed) [15]. The scalings of the histograms are arbitrary.Three physics data events have large
A/E values ( p+ elec-trode events) and are out of scale. The accepted interval isshown in grey. due to the different energy release and the resultingbremsstrahlung emission.The influence of these effects was studied by simula-tions. The first effect was irrelevant in past publicationssince only a low A/E cut was studied and p+ electrodeevents have higher A/E . In the present analysis, we re-quired also
A/E < .
07. Therefore we use a pulse shapesimulation of 0 νββ events [15] to determine the rejectedfraction of signal events by the high
A/E cut.The second effect can influence the low
A/E cutsurvival. To estimate its size, we compare the pulseshape simulation result [15] with a Monte Carlo simu-lation [16] which selects events according to the brems-strahlung energy. The latter is approximately equiva-lent to a cut on the spatial extent of the interactionsince higher energy bremsstrahlung γ rays interact far-ther from the main interaction site (electron-positronpair creation vertex for DEP or 0 νββ decay vertex).The fraction of DEP events with a Compton scatter-ing before the pair creation was taken into account.The determined fraction of MSE in DEP and 0 νββ events was the same within uncertainties. In contrast,the pulse shape simulation removes 1.8 % events morefor A/E < . νββ compared toDEP or due to simulation artefacts [15]. Here we followthe result of the Monte Carlo simulation, i.e. use theDEP survival fraction for the low A/E cut, and takethe difference to the pulse shape simulation as system-atic error.Thus, the survival fraction (cid:15) νββ of the 0 νββ signalis estimated as follows: – the rejected fraction for the low side cut of 0.054 isdetermined from DEP events (Table 2). This valuevaries from 0.042 ± ± – the rejected fraction by the high A/E cut of 0.025is determined from the 0 νββ pulse-shape simula-tion [15].Finally, the efficiency is (cid:15) νββ = 0 . ± .
02. Theuncertainty is the quadratic sum of the following com-ponents: – statistical uncertainty of the DEP survival fraction:0.003 – uncertainty from the A/E energy dependence (item 3in Sect. 3.1): 7.5 · − – uncertainty due to the residual differences betweencalibration and physics data (change of the cut bythe largest difference between µ A/E for 2 νββ andCompton events in Table 1): 0.004 – systematic uncertainty due to the difference betweenthe survival fraction of 0 νββ from the pulse shapesimulation [15] and the one measured with DEPevents: 0.018.The 0 νββ survival fraction can be cross checkedwith the one determined for 2 νββ decays. The energyregion is chosen between 1. and 1.45 MeV to excludethe γ lines at 1461 keV from K and 1525 keV from K. The spectral decomposition of the BEGe data [1]yields a fraction of f νββ = 0 . ± .
03 of 2 νββ decays.The parts f i of the remaining components are listed inTable 3 together with the PSD survival fractions (cid:15) i . Thebackground origins mostly from Compton scattered γ quanta. The fractions (cid:15) i were extrapolated from severalstudies involving experimental measurements as well assimulations. For Th, (cid:15) i is determined from presentcalibration data.The PSD survival fraction for 2 νββ decays (cid:15) νββ is then related to the overall PSD survival fraction forevents in the interval (cid:15) data = 0.748 ± (cid:15) data = f νββ · (cid:15) νββ + (cid:88) i f i · (cid:15) i (2)The resulting survival fraction of 2 νββ events is (cid:15) νββ = 0.90 ± n+ transition layer. The longpulse rise time for these events (see Sect. 2.1) leads toa ballistic deficit in the reconstructed energy, i.e. 0 νββ events do not reconstruct at the peak position. Thisloss is already accounted for in the definition of thedead layer thickness. For 2 νββ events the energy spec-trum is continuous, i.e. the effective dead volume issmaller. But A/E is reduced as well and a fraction ofabout 0.015 ± νββ PSD survivalfraction, this correction should be added such that fi-
Table 3
Decomposition of events in the region between1 MeV and 1.45 MeV. Listed are the estimated fraction f i [1] and the total efficiency (cid:15) i for each component i .component f i (cid:15) i K 0 . ± .
009 0 . ± . K in LAr 0 . ± .
022 0 . ± . K at n+ surface 0 . ± .
017 0 . ± . Co 0 . ± .
013 0 . ± . Co intrinsic 0 . ± .
001 0 . ± . Ga intrinsic 0 . ± .
007 0 . ± . Bi 0 . ± .
014 0 . ± . Th 0 . ± .
002 0 . ± . p+ events 0 . ± .
002 0 . ± . . ± .
024 0 . ± . nally a fraction of 0.91 ± (cid:15) νββ = 0.92 ± p+ contact BEGe detectors of-fer a powerful pulse shape discrimination between Ge0 νββ signal events of localized energy deposition andbackground events from multiple interactions in the de-tector or energy deposition on the surface.The parameter
A/E constitutes a simple discrimi-nation variable with a clear physical interpretation al-lowing a robust PSD analysis. The characteristics ofthis quantity have been studied for several years andare applied for the first time in a 0 νββ analysis.
Thdata taken once per week are used to calibrate the per-formance of
A/E and to correct for the observed timedrifts and small energy dependencies. The whole proce-dure of the PSD analysis was verified using 2 νββ eventsfrom Ge recorded during physics data taking.The chosen cut accepts a fraction of 0.92 ± νββ events and rejects 33 out of 40 events in a400 keV wide region around Q ββ (excluding the cen-tral 8 keV blinded window). The latter is compatiblewith the expectation given our background compositionand PSD rejection. The background index is reduced to(0.007 +0 . − . ) cts/(keV · kg · yr).Applying the PSD cut to 2 νββ events results in anestimated 0 νββ signal survival fraction of 0.91 ± In the current Phase I analysis, three independent pulseshape selections have been performed for the semi-coaxialdetectors. They use very different techniques but it turnsout that they identify a very similar set of events asbackground. The neural network analysis will be usedfor the 0 νββ analysis while the other two (likelihoodclassification and PSD selection based on the pulse asym-metry) serve as cross checks.All methods optimize the event selection for everydetector individually. They divide the data into differ-ent periods according to the noise performance. Twodetectors (ANG 1 and RG 3) had high leakage currentsoon after the deployment. The analyses discussed hereconsider therefore only the other six coaxial detectors. 4.1 Pulse shape selection with a neural networkThe entire current pulse or - to be more precise - therising part of the charge pulse is used in the neuralnetwork analysis. The following steps are performed tocalculate the input parameters: – baseline subtraction using the recorded pulse infor-mation in the 80 µ s before the trigger. If there isa slope in the baseline due to pile up, the event isrejected. This selection effects practically only cali-bration data, – smoothing of the pulse with a moving window aver-aging of 80 ns integration time, – normalization of the maximum pulse height to oneto remove the energy dependence, – determination of the times when the pulse reaches1, 3, 5, ..., 99 % of the full height. The time whenthe pulse height reaches A = 50 % serves as refer-ence. Due to the 100 MHz sampling frequency, a(linear) interpolation is required between two timebins to determine the corresponding time points (seeFig. 13).The resulting 50 timing informations of each chargepulse are used as input to an artificial neutral networkanalyses. The TMVA toolkit implemented in ROOT [26]offers an interface for easy processing and evaluation.The selected algorithm TMlpANN [27] is based on mul-tilayer perceptions. Two hidden layers with 51 and 50neurons are used. The method is based on the so called“supervised learning” algorithm.Calibration data are used for training. DEP eventsin the interval 1593 keV ± · FWHM serve as proxy forSSE while events of the full energy line of
Bi inthe equivalent interval around 1621 keV are dominantlyMSE and are taken as background sample. Fig. 14 showsas an example of the separation power the distributionof the time of 5 % and 81 % pulse height for the twoevent classes. Note that both event classes are not pure time c ha r ge t r a c e [ a . u .] single site event SSEmulti site event MSE A A ) (A MSE t ) (A MSE t) (A SSE t ) (A SSE t GERDA 13-06
Fig. 13
Example physics data pulses for SSE and MSEcandidate events. The determination of the input parametersfor the TMVA algorithms is shown for pulse heights A and A .1 time i n t en t i t y [ a . u .] full energy peak FEPdouble escape peak DEP @ A = 0.81 @ A = 0.05 GERDA 13-06
Fig. 14
Time distribution for crossing the 5 % (left) and81 % (right) pulse height for
Th calibration events withenergy close to the DEP (red) and close to the 1621 keVFEP (blue). samples but a mixture of SSE and MSE because of theCompton events under the peaks.The calibrations are grouped in three intervals. Thefirst period spans from the start of data taking to July2012 when the detector configuration and some elec-tronics was changed (p1). The second period (p2) laststhe first four weeks afterwards and the third period (p3)the rest of Phase I. For RG 2, the second period spansuntil November 2012 when its operating voltage was re-duced. For each period at least 5000 events are availableper detector and event class for training.The output of the neural network is a qualifier, i.e. anumber between ≈ ≈ Th calibration spectrum with andwithout PSD selection. For the analysis, the survivalfraction of MSE is studied. The survival is defined asthe fraction of the peak content remaining after the cut,i.e. the Compton events under the peak are subtractedby scaling linearly the event counts from energies belowand above the peak. The fractions are listed in Table 4for the different periods. The last column lists the num-ber of events in the 230 keV window around Q ββ before energy [MeV] A NN r e s pon s e RG1 G E RDA - Fig. 15
TMlpANN response versus energy for
Th cali-bration events. Shown is the distribution for RG 1. The lineat ∼ and after the cut. About 45 % of the events are classifiedas background.Fig. 18 shows the ANN response for DEP and SEPevents. Shown are also the qualifier distributions fordifferent samples from physics data taking: from theinterval 1.0 - 1.4 MeV (dominantly 2 νββ events, MSE ANN response r e l a t i v e i n t en s i t y RG2
GERDA 13-06
Fig. 16
TMlpANN response for Compton events for RG 2 atdifferent energies. The energy dependence for RG 2 is abouttwice bigger than for any other detector.2 energy [MeV] c t s / ( k e V ) ANG3 without PSDwith PSD energy [MeV] 1.570 1.605 1.640 c t s / ( k e V ) DEP G E RDA - Fig. 17
Th calibration spectrum without and with TMl-pANN pulse shape discrimination for ANG 3. The PSD cutis fixed to retain 90 % of DEP events (see inset). part subtracted), from the 1525 keV K γ line (domi-nantly MSE) and the qualifier for events in the 230 keVwindow. The events from the 1525 keV gamma peakare predominantly MSE and the shape agrees with theSEP distribution. The events in the 1.0 - 1.4 MeV re-gion are dominantly SSE and their distribution agreesquite well with the one for DEP events. The red curve Table 4
Survival fractions of the neural network PSD fordifferent event classes and different detectors. Numbers aregiven for calibration (cal.) or physics data from the peri-ods p1, p2 and p3. The statistics of physics data for p2 aresmall and hence not always listed. “2 νββ ” stands for the 1.0- 1.4 MeV interval which consists dominantly of 2 νββ decays. K signifies the 1525 keV full energy peak. ROI is here the230 keV window around Q ββ . The errors are typically 0.01for SEP and ROI for calibration, 0.02 for the 2 νββ data in-terval and 0.06 for the K γ peak. The last column list theevent count after/before the PSD cut.det. period SEP ROI 2 νββ K ROIcal. cal. data data dataANG 2 p1 0.33 0.58 0.74 0.30 2/4ANG 2 p2 0.50 0.65 0.65 0/1ANG 2 p3 0.47 0.63 0.73 0.40 6/8ANG 3 p1 0.32 0.56 0.79 0.43 6/9ANG 3 p2 0.34 0.56 0.75 2/3ANG 3 p3 0.40 0.63 0.82 0.44 4/6ANG 4 p1 0.29 0.54 0.78 0.45 1/1ANG 4 p2 0.28 0.53 0.63 0/1ANG 4 p3 0.33 0.58 0.83 0.44 2/4ANG 5 p1 0.26 0.55 0.79 0.41 2/11ANG 5 p2 0.21 0.45 0.57 0/2ANG 5 p3 0.33 0.59 0.80 0.30 6/16RG 1 p1 0.45 0.63 0.80 0.52 2/6RG 1 p2 0.43 0.60 0.77 2/3RG 1 p3 0.41 0.62 0.81 0.48 3/4RG 2 p1 0.30 0.53 0.82 0.49 10/12RG 2 p2 0.37 0.60 0.81 0.48 3/3RG 2 p3 0.45 0.61 0.76 0.56 2/2
ANN response r e l a t i v e i n t en s i t y physics datacalibration DEPcalibration SEP spectrum bbn
2 peak g K
90% efficiency f r a c t i on @ D EP [ % ] ANG3 G E RDA - Fig. 18
ANN response for
Th calibration events forDEP (green, long dashes) and SEP (dark blue) for ANG 3in the first period. The distributions from Compton events atthese energies are subtracted statistically using events in en-ergy side bands. Also shown in black are the qualifier valuesof events from physics data taking from a 230 keV windowaround Q ββ . The grey vertical line marks the cut position.Physics data events from the 1525 keV FEP of K are shownin magenta and the ones from the interval 1.0 - 1.4 MeV bybrown dashes (dominantly 2 νββ , MSE part subtracted). shows the DEP survival fraction versus the cut position(right scale).The training was performed for the periods individ-ually by combining all calibration data. The rules canthen be applied to every single calibration to look fordrifts in time. Fig. 19 shows the DEP survival fraction(blue triangles) for the entire Phase I from November2011 to May 2013 for all detectors. The plots show astable performance. Also shown are the equivalent en-tries (red circles) for events with energy around the SEPposition. For several detectors the rejection of MSE isnot stable. Especially visible is the deterioration start-ing in July 2012. This is related to different conditionsof high frequency noise.The distribution of the qualifier for all events in the230 keV window around Q ββ is shown in Fig. 20. Eventsrejected by the neural network are marked in red. Cir-cles mark events rejected by the likelihood method anddiamonds those rejected by the method based on thecurrent pulse asymmetry. Both methods are discussedbelow. In the shown energy interval, all events removedby the neural network are also removed by at least oneother method and for about 90 % of the cases, all threemethods discard the events. In a larger energy range s u r v i v a l f r a c t i on [ % ] s u r v i v a l f r a c t i on [ % ] ANG5
DEP SEP
GERDA 13-06
RG1 date of calibration
RG2
Fig. 19
DEP (blue) and SEP (red) survival fraction for individual calibrations for the entire Phase I. energy [keV] 1950 2000 2050 2100 2150 A NN r e s pon s e accepted by ANNrejected by ANNrange of ANN cuts rejected by likelihoodrejected by asymmetryblinding window G E RDA - Fig. 20
Neural network qualifier for events with energy closeto Q ββ . Events marked by a red dot are rejected. Circles anddiamonds mark events which are rejected by the likelihoodanalysis and the method based on the pulse asymmetry, re-spectively. about 3 % of the rejected events are only identified bythe neural network. energy [keV] c oun t s / ( k e V ) Without PSDWith PSD G E RDA - Fig. 21
Energy spectrum of semi-coaxial detectors with andwithout neural network PSD selection.
Fig. 21 shows the energy spectrum of all semi-coaxialdetectors added up before and after the PSD selection. νββ events.The distribution of DEP events in a detector is nothomogeneous since the probability for the two 511 keVphotons to escape is larger in the corners. It is thereforeconceivable that the ANN - instead of selecting SSE -is mainly finding events at the outer surface. The DEPsurvival fraction would in this case not represent theefficiency for 0 νββ decay which are distributed homo-geneously in the detector.2 νββ events are also SSE and homogeneously dis-tributed inside the detector. Hence a comparison of itspulse shape identification efficiency with the preset 0.90value for DEP events is a powerful test.Another SSE rich sample are events at the Comp-ton edge of the 2614.5 keV γ line. The energy rangeconsidered is 2.3 - 2.4 MeV, i.e. higher than Q ββ . Thecomparison to the DEP survival fraction allows alsoto check for an energy dependence. The distribution ofCompton edge events in detector volume is similar toDEP. νββ for neural network PSD The energy range between 1.0 and 1.3 MeV (positionof the Compton edge of the 1525 keV line) is suited forthe comparison of the SSE efficiency. At lower energiesthe electronic noise will deteriorate the discriminationbetween SSE and MSE. In this interval, the data setconsists to a fraction f νββ = 0 . ± .
01 of 2 νββ decaysaccording to the
Gerda background model [1]. Theremaining 24 % are Compton events predominantly ofthe 1525 keV line from K decays, of the 1460 keVline from K decays and from
Bi decays. Hence it isa good approximation to use the pulse shape survivalfraction (cid:15)
Compton from the calibration data to estimatethe suppression of the events not coming from 2 νββ decays. Typical values for (cid:15)
Compton are between 0.6 and0.7 for the different detectors, i.e. higher than the valuesquoted in Table 4 due to a small energy dependence (seeFig. 17).Fig. 22 shows the physics data (red) overlayed withthe background model (blue, taken from Ref. [1]) andthe same distributions after the PSD cut (in magentafor the data and in light blue for the model). For themodel, the 2 νββ fraction is scaled by the DEP survivalrate while the remaining fraction is scaled according to (cid:15)
Compton taken from the
Th calibration data for eachdetector. Both pairs of histograms agree roughly in therange 1.0 - 1.3 MeV. This is qualitatively confirmed energy [MeV] c t s / ( k e V ) datacut with ANNbackground model (BM)predicted ANN cut on BM [ % ] bbn f r a c t i on @ G E RDA - Fig. 22
Effect of the PSD selection on the data (in red andmagenta) and the expected effect on the background model(dark blue dotted and light blue dashed). Overlayed is alsothe extracted PSD efficiency (green filled histogram) for 2 νββ events (right side scale). if the 2 νββ
PSD efficiency is calculated using (2). Itsdistribution is also shown as the green filled histogramin Fig. 22. The average efficiency for the range 1.0 -1.3 MeV is (cid:15) νββ = 0 . ± .
02 where the error is dom-inated by the systematic uncertainty of (cid:15)
Compton . Thelatter is estimated by a variation of the central value by10 % which is the typical variation of (cid:15)
Compton between1 MeV and 2 MeV.The obtained efficiency (cid:15) νββ is close to the DEPsurvival fraction of (cid:15) DEP = 0 . νββ events inthe detectors. Calibration events at the Compton edge of the 2615 keV γ line, i.e. in the region close to 2.38 MeV, are enhancedin SSE and distributed similar to DEP events in the de-tector. The qualifier distribution for these events can beapproximated as a linear combination of the DEP dis-tribution and the one from multiple Compton scattered γ ray events (MCS). Events with energy larger than theCompton edge (e.g. in the interval 2420 - 2460 keV)consists almost exclusively of MCS. The total counts inthe qualifier interval 0 to 0.2 for Compton edge events and MCS are used for normalization and the MCS dis-tribution is then subtracted.The “MCS subtracted” Compton edge distribution(red curve in Fig. 23) shows an acceptable agreementwith the DEP distribution (green dotted curve). Thesurvival fraction is defined as the part above the se-lection cut. Its value varies for the 3 periods and the6 detectors between 0.85 and 0.94. No systematic shiftrelative to the DEP value e.g. due to an energy depen-dence of the efficiency is visible. If SEP events are usedto model the multi site event contribution, consistentvalues are obtained. The cross checks of the PSD efficiency address a pos-sible energy dependence and a volume effect due tothe different distributions of DEP and 0 νββ events. Allstudies performed are based on calibration or physicsdata and are hence independent of simulations.The possible deviations from 0.90 seen are com-bined quadratically and scaled up to allow for addi-tional sources of systematic uncertainties. The 0 νββ efficiency is (cid:15)
ANN = 0 . +0 . − . .4.3 Alternative PSD methodsTwo more PSD methods have been developed. They areused here to cross check the event selection of the neural ANN response r e l a t i v e i n t en s i t y compton edge (CE)multi site region (MCS)calibration DEPSSE part of CE90% efficiency ANG5 G E RDA - Fig. 23
Qualifier distribution for events at the Comptonedge (magenta) as a linear combination of MCS (blue) andDEP (green dotted) distributions. The Compton edge distri-bution after the subtraction of the SEP part is shown in red. network method (see Fig. 20). No systematic errors forthe signal efficiency has been evaluated for them.
In a second PSD analysis, 8 input variables calculatedfrom the charge pulse trace are used as input to theprojective likelihood method implemented in TMVA.Each input variable is the sum of four consecutive pulseheights of 10 ns spacing after baseline subtraction andnormalization by the energy. The considered trace iscentered around the time position where the derivativeof the original trace is maximal, i.e. around the maxi-mum of the current.The training is performed for two periods: before(pI) and after (pII) June 2012. Instead of DEP events,the Compton edge in the interval 2350 - 2370 keV isused as signal region and the interval 2450 - 2570 keVas background sample. The latter contains only mul-tiple Compton scattered photons and is hence almostpure MSE. The Compton edge events are a mixture ofSSE and MSE. From the two samples a likelihood func-tion for signal L sig and background L bkg like eventsis calculated and the qualifier q PL is the ratio q PL = L sig / ( L sig + L bkg ).Fig. 24 shows for the calibration data the scatterplot of the qualifier versus energy. The separation ofDEP (1593 keV) and FEP at 1621 keV is visible by thedifferent population densities at low and high qualifiervalues. The cut position is independent of energy andfixed to about 0 .
80 survival fraction for DEP events. energy [keV] li k e li hood r e s pon s e ANG3 G E RDA - Fig. 24
Likelihood response versus energy distribution for
Th calibration events. Data are shown for ANG 3.6
Table 5
Survival fractions of the projective likelihood PSDfor different event classes and the different detectors. Thecut for each subset is set to yield a DEP survival fraction of0.8. Numbers are given for calibration data (cal.) or physicsdata. pI and pII indicate the two periods. The meaning of thecolumns are identical to Table 4 and the same applies to thesize of statistical errors for the different samples.det. period SEP ROI 2 νββ K ROIcal. cal. data data dataANG 2 pI 0.47 0.57 0.61 0.35 1/3ANG 2 pII 0.50 0.56 0.57 0.37 4/10ANG 3 pI 0.49 0.58 0.60 0.36 2/7ANG 3 pII 0.52 0.61 0.64 0.40 3/11ANG 4 pI 0.52 0.60 0.65 0.54 1/1ANG 4 pII 0.50 0.62 0.71 0.51 2/5ANG 5 pI 0.45 0.57 0.62 0.42 0/8ANG 5 pII 0.40 0.51 0.61 0.31 3/21RG 1 pI 0.50 0.63 0.63 0.59 2/6RG 1 pII 0.51 0.62 0.65 0.46 2/7RG 2 pI 0.49 0.60 0.70 0.46 6/8RG 2 pII 0.51 0.61 0.63 0.50 7/9
The SEP survival fractions and for comparison alsothe ones for several other subsets are listed in Table 5.About 65 % of the events in the 230 keV window around Q ββ are rejected.Fig. 25 shows the distribution of the qualifier fordifferent event classes. The distribution for physics dataevents from the K line are well described by the FEPdistribution in calibration data and the events in the1.0 - 1.4 MeV interval are clearly enhanced in SSE asexpected for 2 νββ events.
In a third approach, only two variables are used to se-lect single site events for the semi-coaxial detectors. Asdiscussed above, the
A/E variable alone is not a goodparameter for semi-coaxial detectors. However, if
A/E is combined with the pulse asymmetry, the PSD se-lection is much more effective. The asymmetry A s isdefined as A s = Σ i = n m i =0 I ( i ) − Σ i< i = n m I ( i ) Σ i< i =0 I ( i ) (3)Here I ( i ) is the current pulse height, i.e. the differenti-ated charge pulse at time i , and n m the time positionof the maximum. A window of 200 samples (i.e. a 2 µ stime interval) around the time of the trigger is analyzed.To reduce noise, different moving window averagingwith integration times of 0 (no filter), 20, 40, 80, 160and 320 ns for the charge pulse are applied. For eachshaping time, A/E and A s are determined. Empirically,the combination q AS = A/E · ( c + A s ) (4) likelihood response r e l a t i v e i n t en s i t y physics data ROIcalibration DEPcalibration FEP spectrum bbn
2 peak g K ~ 80% efficiency GERDA 13-06
Fig. 25
Likelihood response for
Th calibration DEP(green dotted) and FEP (dark blue dashed) events for ANG 3.The distributions from Compton events at these energies aresubtracted statistically using events in energy side bands.Also shown in black are the qualifier values of events fromphysics data taking from a 230 keV window around Q ββ .The grey vertical line marks the cut position. Shown are alsodistributions of physics data events from the K γ line (lightblue) and from the interval 1.0 - 1.4 MeV (red, dominantly2 νββ ). exhibits good PSD performance. For SSE, the currentpulse might contain more than one maximum (Fig. 3).To reduce ambiguities, A S is shaped with larger inte-gration times.An optimization is performed by comparing the DEPsurvival fraction (cid:15) DEP from calibration data to the frac-tion of background events f bkg between 1700 and 2200 keV(without a 40 keV blinded interval around Q ββ ) thatremains after the PSD selection. The lower cut value ofthe qualifier q AS is determined by maximizing the quan-tity S = (cid:15) DEP / (cid:112) f bkg + 3 /N bkg ; the upper cut is fixedat ≈ +4 σ of the Gaussian width of the DEP qualifierdistribution (see Fig. 26). All combinations of shapingtimes for A/E and A s are scanned as well as differentvalues for c in the range of 1 - 4. The one with thehighest S is selected.The term 3 /N bkg with N bkg being the total numberof background events is added to avoid an optimiza-tion for zero background. For N bkg ≈
40 the optimiza-tion yields a DEP survival fraction of 0.7 - 0.9 (seeTable 6) and about 75 % of the events in the interval1.7 - 2.2 MeV are rejected.Fig. 27 shows a scatter plot of the PSD qualifierversus the energy. A separation between the DEP andmulti site events at the energy of the FEP or SEP is vis-ible. Fig. 26 shows qualifier distributions for DEP and asymmetry classifier -3 -2 -1 0 1 2 3 r e l a t i v e i n t en s i t y f r a c t i on @ D EP [ % ] accepted regionphysics datacalibration FEPcalibration DEP peak g K spectrum bbn G E RDA - Fig. 26
Distribution of qualifier for DEP (dotted green) andFEP (dashed dark blue) calibration events for ANG 3 aftera statistical subtraction of the Compton events below thepeaks. The grey band marks the acceptance range. Overlayedare also the PSD qualifier for physics data in the 230 keVwindow around Q ββ (black), data events from the 1525 keV K peak (light blue) and from the interval 1.0 - 1.4 MeV(dark green dotted). The DEP survival fraction is displayedin red (right scale).
FEP calibration events after Compton events below thepeaks are statistically subtracted. Overlayed is also thePSD qualifier for physics data in the 230 keV windowaround Q ββ (black histogram), from the 1525 keV γ line (light blue) and the interval 1.0 - 1.4 MeV (yel-low). The right scale shows the DEP survival fraction(red) as a function of the cut position. The grey areaindicates the accepted range. The qualifier distributionof physics data around Q ββ has a larger spread thanthe one of FEP events. This is the reason why eventsat Q ββ are rejected stronger than MSE (see Table 6).A possible explanation is that the physics data containa large fraction of events which are not MSE. Thesecan be for example surface p+ events. The “maximal”background model of Gerda [1] is compatible with asignificant fraction of p+ events. A pulse shape simu-lation also shows that the selection corresponds to avolume cut: events close to the p+ contact and in thecenter of the detectors are removed.4.4 Summary of PSD analysis for coaxial detectorsFor the semi-coaxial detectors three different PSD meth-ods are presented following quite different concepts.The one based on an artificial neural network will be Table 6
Survival fractions of the PSD based on the currentpulse asymmetry for different event classes and the differentdetectors. Numbers are given for calibration data (cal.) orphysics data. pI and pII stand for the two periods. The DEPsurvival fractions are listed in the third column. Note thatthe selection of data files is slightly different for this analysissuch that the total observed event counts (last column) aredifferent compared to the other PSD methods. The mean-ing of the different columns is explained in Table 4 and thesame applies to the size of statistical errors for the differentsamples.det. time DEP SEP 2 νββ K ROIcal. cal. data data dataANG 2 pI 0.69 0.32 0.52 0.28 1/5ANG 2 pII 0.70 0.40 0.50 0.33 4/6ANG 3 pI 0.90 0.51 0.74 0.55 3/13ANG 3 pII 0.69 0.22 0.49 0.23 1/7ANG 4 pI 0.78 0.28 0.63 0.41 1/9ANG 4 pII 0.78 0.45 0.66 0.41 2/8ANG 5 pI 0.81 0.33 0.65 0.39 2/13ANG 5 pII 0.67 0.16 0.65 0.39 2/8RG 1 pI 0.92 0.64 0.78 0.65 2/9RG 1 pII 0.69 0.23 0.55 0.38 3/6RG 2 pI 0.86 0.38 0.71 0.44 2/11RG 2 pII 0.86 0.38 0.65 0.56 1/6 used for the 0 νββ analysis. It has been tuned to yield90 % survival fraction for DEP events of the 2.6 MeV γ line of Tl decays. Most of these events are SSElike 0 νββ decays. For the study of a possible volumeeffect and energy dependence of the efficiency, 2 νββ de-cays ( (cid:15) νββ = 0 . ± .
02) and events with energy close energy [keV] a sy mm e t r y c l a ss i f i e r -3-2-10123 ANG3
GERDA 13-06
Fig. 27
Distribution of the ANG 3 qualifier versus energyfor
Th calibration data for the PSD based on the pulseasymmetry.8 the Compton edge (efficiency between 0.85 and 0.95)have been used. We conclude that the 0 νββ efficiencyis (cid:15)
ANN = 0 . +0 . − . .The event selection of the neural network is crosschecked by two other methods. One is based on a like-lihood ratio. Training is performed with events at theCompton edge (SSE rich) and at slightly higher ener-gies (almost pure MSE). For a cut with a DEP survivalfraction of about 0.8 only 45 % of the events around Q ββ remain.Another method is only based on the A/E parame-ter and the current pulse asymmetry A S . Different sig-nal shapings are tried and an optimization of a signalover background ratio is performed. The DEP survivalfraction varies between 0.7 and 0.9 for the different de-tectors and periods. The background is reduced by afactor of four.Of the events rejected by the neural network analy-sis in the 230 keV window around Q ββ , about 90 % arealso identified as background by both other methods.This gives confidence that the classification is meaning-ful. The neural network analysis rejects about 45 % of theevents around Q ββ for the semi-coaxial detectors andthe A/E selection reduces the corresponding numberfor BEGe detectors by about 80 %. With a small lossin efficiency the
Gerda background index is hence re-duced from (0 . ± . · kg · yr) to (0 . ± . · kg · yr). These values are the averagesover all data except for the period p2, the “silver” dataset, that covers the time period around the BEGe de-ployment and which corresponds to 6 % of the Phase Iexposure [1].The estimated 0 νββ decay signal efficiencies for semi-coaxial detectors are 0 . +0 . − . and for BEGe detectors0 . ± .
02. Despite this loss of efficiency, the
Gerda sensitivity defined as the expected median half life limitof the 0 νββ decay improves by about 10 % with the ap-plication of the pulse shape discrimination.
Acknowledgments
The
Gerda experiment is supported financially by theGerman Federal Ministry for Education and Research(BMBF), the German Research Foundation (DFG) viathe Excellence Cluster Universe, the Italian IstitutoNazionale di Fisica Nucleare (INFN), the Max PlanckSociety (MPG), the Polish National Science Centre (NCN),the Foundation for Polish Science (MPD programme), the Russian Foundation for Basic Research (RFBR),and the Swiss National Science Foundation (SNF). Theinstitutions acknowledge also internal financial support.The
Gerda collaboration thanks the directors andthe staff of the LNGS for their continuous strong sup-port of the
Gerda experiment.We acknowledge guidance concerning the n+ surfacelayer modeling from D. Radford. References
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