Background modeling for the GERDA experiment
BBackground modeling for the G ERDA experiment
N. Becerici-Schmidt on behalf of the G
ERDA collaboration
Max-Planck-Institut für Physik, München, Germany
Abstract.
The neutrinoless double beta (0 νβ β ) decay experiment G
ERDA at the LNGS of INFN has started physics datataking in November 2011. This paper presents an analysis aimed at understanding and modeling the observed backgroundenergy spectrum, which plays an essential role in searches for a rare signal like 0 νβ β decay. A very promising preliminarymodel has been obtained, with the systematic uncertainties still under study. Important information can be deduced fromthe model such as the expected background and its decomposition in the signal region. According to the model the mainbackground contributions around Q ββ come from Bi,
Th, K, Co and α emitting isotopes in the Ra decay chain,with a fraction depending on the assumed source positions.
Keywords: neutrinoless double beta decay, Majorana neutrino, Ge, enriched germanium detectors, liquid argon, surface contamination
PACS: β decay; double β decay; electron and muon capture, 23.60.+e α decay, 29.85.Fj Dataanalysis INTRODUCTION
Neutrinoless double beta (0 νβ β ) decay, ( A , Z ) → ( A , Z + + e − , is a hypothetical process with an extremely lowexpected rate. For some even-even nuclei β decay is energetically forbidden. They can however simultaneously emittwo electrons and two antineutrinos via neutrino accompanied double beta (2 νβ β ) decay. These nuclei can makea 0 νβ β transition if lepton number is violated and if neutrino has a Majorana component, thus leading to physicsbeyond the standard model of particle physics [1]. The expected signal of 0 νβ β decay is a peak at the Q ββ value ofthe decay. The lower limits with 90% C.L. on the 0 νβ β half life of Ge are given by H D M and I
GEX experiments as1 . · yr [2] and 1 . · yr [3], respectively. There is also a controversial claim of observation with a half life of1 . · yr [4] from a subgroup of the H D M experiment.The GERmanium Detector Array (G
ERDA ) experiment at the National Gran Sasso Laboratory (LNGS) of INFN issearching for 0 νβ β decay of the Ge isotope [5]. The physics data taking for Phase I has started in November 2011,with the goal of testing the claim. The achieved background index (BI) around Q ββ is an order of magnitude lowerthan the one of the precursor experiment H D M. The first physics result of Phase I is a measurement of the half life of2 νβ β decay as 1 . + . − . · yr [6]. Due to the superior signal-to-background ratio, a precision comparable to latestresults which were obtained with a much more exposure has been achieved.G ERDA follows a blind analysis strategy in Phase I; events in a 40 keV window around Q ββ are not available foranalysis. The unblinding is planned for Summer 2013, when a sufficient exposure is acquired and the selection cutsare finalized. In this paper, an analysis for modeling of the observed background spectrum in Phase I is described andpreliminary results are shown. EXPERIMENTAL SETUP AND DATA TAKING
The G
ERDA experiment implements a novel technique by operating an array of high-purity germanium (HPGe)detectors directly submerged in liquid argon (LAr). The Phase I physics data taking has started in November 2011with semi-coaxial p-type HPGe detectors, eight of them enriched in Ge and three of them with natural abundance.BEGe type detectors produced for Phase II are also being tested in Phase I setup. The details of the G
ERDA experimentand Phase I data taking has been presented in [5].The analysis is performed on the data from coaxial detectors acquired until March 2013, with a total exposure of13.65 kg · yr for the sum enriched coaxial detectors ( enr Ge-coax) and 2.77 kg · yr for one natural coaxial detector ( nat Ge-coax) considered here. The surface of the detectors have a conductive lithium layer (n + contact) and a boron implantedlayer (p + contact) which are separated by a groove. They form dead layers ( dl ) on the surface measured to be nearly2 mm for the n + and expected to be less than a µ m for the p + surface (see Figure 1.) a r X i v : . [ phy s i c s . d a t a - a n ] J un IGURE 1.
Left: Schematic drawing of a coaxial type HPGe detector. Middle: A Phase I detector after reprocessing. Right: Thedetector is mounted upside down in its holder.
ANALYSIS OF THE BACKGROUND SPECTRUM
The main background sources in G
ERDA
Phase I, identified by their characteristic γ lines or by other features in theobserved energy spectrum, are Co, K, Ar and K ( Ar) due to LAr, 2 νβ β decay of Ge,
Ra (
U-series),
Ac and
Th (
Th-series). At any rate, presence of these sources in the setup was known mainly due to thescreening of materials for radio purity tests or due to the LAr surrounding the bare detectors.This section describes the analysis for modeling the observed background energy spectrum. Firstly, the energyregion above 3.5 MeV (Q β of K) is analyzed. Practically no significant contribution from sources other than α decays is expected in this region. After obtaining an α model that describes the spectrum at high energies, a largerenergy window is analyzed that includes the Q ββ region. Analysis of the α -induced background A very prominent peak structure around 5.3 MeV with a tail towards lower energies has been observed in theenergy spectrum of the enr
Ge-coax (depicted in Figure 2) due to Po α decays. Also a significant number of eventsobserved above 5.3 MeV reveals that there are other sources than Po contributing to the spectrum. Other peakstructures observed with lower intensities, i.e., around 4.7 MeV, 5.4 MeV and 5.9 MeV, indicate a contribution fromthe successive α decays in Ra decay chain. α particles with energies between 4 MeV and 9 MeV have several tens of µ m range in Ge and in LAr. Therefore,they can only deposit energy in the active volume if they decay on or close to the p + surface ( dl < 1 µ m ) of thedetectors and can induce events at Q ββ after their energies degrade in LAr and dl .In the following, analyses of the event rate distributions and of the energy spectrum of events above 3.5 MeVare described. While the source of the events which are dominant in different regions can be inferred from the timeanalysis, a model of the energy spectrum can allow to estimate their contributions around Q ββ . energy (keV)2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 c oun t s / ( k e V ) yr × enriched coaxials, 13.65 kg G E RDA FIGURE 2.
Energy spectrum of the enr
Ge-coax in high energy region measured in G
ERDA
Phase I. ayesian inference
The probability of the model and its parameters, the posterior probability is given from Bayes theorem as P ( (cid:126) λ | (cid:126) n ) = P ( (cid:126) n | (cid:126) λ ) P ( (cid:126) λ ) (cid:82) P ( (cid:126) n | (cid:126) λ ) P ( (cid:126) λ ) d (cid:126) λ (1)where P( (cid:126) n | (cid:126) λ ) denotes the likelihood and P ( (cid:126) λ ) the prior probability of the parameters. When analyzing the binneddistributions of data arising from a Poisson process, the likelihood is written as the product of the probability of datagiven the model and parameters in each bin P ( (cid:126) n | (cid:126) λ ) = ∏ i P ( n i | λ i ) = ∏ i e − λ i λ n i i n i ! (2)where n i is the observed number of events and λ i is the expected number of events in the i -bin bin.The analysis of both event rate and energy distributions is carried out by fitting the binned distributions due to themethod described. One of the merits of Bayesian analysis is the possibility to add initial knowledge to the analysisin order to get a better answer. This is done by giving prior probabilities on the parameters whenever available. Thecomputation is done using the Bayesian Analysis Toolkit BAT [7]. Event rate analysis
The event rate distributions are obtained for two different energy regions; 3.5 – 5.3 MeV where
Po is dominantand 5.3–7.5 MeV where events only due to
Ra decay chain are expected. The distribution for the first regionfollows an exponential decrease as expected from an initial
Po ( T / = . Po) and exponential plus a constant rate (allowingother contributions) by giving a Gaussian prior on the half life parameter with a mean value of 138.4 days and astandard deviation of 0.2 days. Note that a constant component can be due to
Pb ( T / = . Ra( T / = Ra and fitted only with aconstant.The expected number of events, λ i , is corrected for the live time fraction. While performing a fit with an exponentialfunction it is written as λ i = ε i (cid:90) i ∆ t ( i − ) ∆ t N · e − ln2 t / T / dt (3)where ε i is the value in the i -bin bin of the live time fraction distribution, ∆ t is the bin width, N , the initial event rateand T / , the half life are the parameters of the model. The distribution for the 3.5 – 5.3 MeV region was describedbetter with the second model with a small constant term of (0.57 ± ± ± ± Po. The distribution for the 5.3 – 7.5 MeV region is described very well with a constant rate of(0.09 ± Ra source.Figure 3 shows the results of the performed fits, i.e. data (what has been measured) together with the expectation(what is expected to be measured given the live time fraction) due to the best fit model (what was supposed to bemeasured for a 100% live time fraction). Comparison of data and expectation due to model is done by giving 68%,95% and 99.9% probability intervals for the expectation.
Spectral analysis
Analysis of the energy spectrum is done under the assumption that events above 3.5 MeV come from Po α decaysand from the successive α decays in the Ra decay chain. While former is only assumed on the p + surface, the latterstarting from Rn assumed also in LAr. This is expected since
Rn emanates into LAr from materials with
Racontamination in the close vicinity of the detectors. The expected energy spectrum of all the components are obtained days0 50 100 150 200 250 300 350 400 c oun t s / ( da ys ) li v e t i m e f r a c t i on sumENREfficiencyBest fitError band days0 50 100 150 200 250 300 350 40050100150200250 DataData (0 events)Expectation68%95%99.9% days0 50 100 150 200 250 300 350 400 c oun t s / ( da ys ) li v e t i m e f r a c t i on sumENREfficiencyBest fitError band days0 50 100 150 200 250 300 350 400510152025 DataData (0 events)Expectation68%95%99.9%
FIGURE 3.
Results of fitting the event rate distribution for the 3.5–5.3 MeV region with an exponential plus constant (left) andfor the 5.3–7.5 MeV region with a constant. The best fit model with 68% uncertainty band and the live time fraction distributionare shown in the upper panels. The observed and the expected number of events in the lower ones. Also shown are the smallestintervals containing the 68%, 95% and 99.9% probability for the expectation in green, yellow and red regions, respectively [8]. through MC simulations in M A G E [9] by using a detailed description of the G ERDA
Phase I setup. Spectra for different dl thicknesses (100 nm – 1 µ m ) are simulated to derive the effective dl thickness.The simulated spectra are fitted to the observed spectrum with a 50 keV binning in 3.5–7.5 MeV region by givingflat priors on the parameters. The analysis is also done for the nat Ge-coax which shows a similar spectral featuresbut a lower
Po rate and enhanced structures from
Ra decay chain. The model describes both spectra very well(see Figure 4). The results are stable wrt. the choice of bin width. According to the model the expected backgroundcontribution in Q ββ ± ± · − cts/(keV · kg · yr) ( ∼ enr Ge-coax mostly (7%) coming fromLAr decays resulting in a linear spectrum with a small slope unlike surface decays. The contribution of α inducedevents depends on the analyzed data set, since the surface contaminations are detector dependent and initial Po rateis decreasing in time. e v en t s / ( k e V ) datamodelPo on surface Ra & daughters on surface
Rn & daughters in LAr
GERDA preliminary G E RDA energy (keV)3500 4000 4500 5000 5500 6000 6500 7000 7500 da t a / m ode l r a t i o data/model68%95%99.9% e v en t s / ( k e V ) datamodelPo on surface Ra & daughters on surface
Rn & daughters in LAr
GERDA preliminary G E RDA energy (keV)3500 4000 4500 5000 5500 6000 6500 7000 7500 da t a / m ode l r a t i o data/model68%95%99.9% FIGURE 4.
The upper panels show the best fit model (black histogram) and observed spectrum (black markers) for enr
Ge-coax(left) and nat
Ge-coax(right). Individual components of the model are shown as well. The lower panel shows the ratio of data andmodel and the smallest intervals containing 68%, 95% and 99.9% probability for the model expectation. global model for the background spectrum
The α induced event model alone successfully describes the observed energy spectrum down to 3.5 MeV. Below3.5 MeV many other background components contribute to the spectrum, some of them also relevant around Q ββ .The analysis window is therefore expanded down to 570 keV to obtain a full background decomposition at Q ββ . Thepart where the beta spectrum of Ar (Q β =565 keV) is the dominating component without any relevance at Q ββ is notincluded in the analysis. All the components – namely, 2 νβ β decay of Ge, K, K, Bi,
Th, Co and the α model – that are expected to contribute in this energy window are considered in a global fit. Some parameters aregiven an informative prior probability, e.g. a Gaussian prior probability distribution for the expected Bi decays onthe p + surface is given according to the α model. The best fit model together with the observed spectrum is shown inFigure 5, which is rather a qualitative demonstration of the success of the model. Many cross-checks and systematicuncertainties are still under study. Therefore, the details of the analysis and its results are intentionally neither shownnor discussed. Nevertheless, one important conclusion can be made: The main contributions around Q ββ come from Bi,
Th, K, Co and α emitting isotopes in the Ra decay chain, with a fraction depending on the assumedsource position and distribution. energy (keV)1000 2000 3000 4000 5000 6000 7000 e v en t s / ( k e V ) dataglobal model GERDA preliminary
FIGURE 5.
Data (filled histogram) from the enriched coaxial detectors and the best fit model (black histogram). The red bandmasks the region of interest.
CONCLUSIONS
A model for the observed background energy spectrum in G
ERDA
Phase I is obtained. The model allows to have adecomposition of the background at Q ββ . Other important informations that can be deduced from the backgroundmodel are, the expected number of background events and the spectral shape of background around Q ββ . These areessential inputs for a reliable result in the upcoming 0 νβ β analysis. After all the necessary cross checks are performedand systematic uncertainties are evaluated, the results will be presented in a paper from the G ERDA collaboration.
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