Table Of ContentAnalysis Techniques for the Evaluation of the Neutrinoless Double-β Decay Lifetime
in 130Te with CUORE-0
C. Alduino,1 K. Alfonso,2 D. R. Artusa,1,3 F. T. Avignone III,1 O. Azzolini,4 T. I. Banks,5,6 G. Bari,7
J.W. Beeman,8 F. Bellini,9,10 A. Bersani,11 M. Biassoni,12,13 C. Brofferio,12,13 C. Bucci,3 A. Caminata,11
L. Canonica,3 X. G. Cao,14 S. Capelli,12,13 L. Cappelli,11,3,15 L. Carbone,13 L. Cardani,9,10,∗ P. Carniti,12,13
N. Casali,9,10 L. Cassina,12,13 D. Chiesa,12,13 N. Chott,1 M. Clemenza,12,13 S. Copello,16,11 C. Cosmelli,9,10
O. Cremonesi,13,† R. J. Creswick,1 J. S. Cushman,17 I. Dafinei,10 A. Dally,18 C. J. Davis,17 S. Dell’Oro,3,19
M. M. Deninno,7 S. Di Domizio,16,11 M. L. Di Vacri,3,20 A. Drobizhev,5,6 D. Q. Fang,14 M. Faverzani,12,13
G. Fernandes,16,11 E. Ferri,12,13 F. Ferroni,9,10 E. Fiorini,13,12 S. J. Freedman,6,5,‡ B. K. Fujikawa,6
A. Giachero,13 L. Gironi,12,13 A. Giuliani,21 L. Gladstone,22 P. Gorla,3 C. Gotti,12,13 T. D. Gutierrez,23
E. E. Haller,8,24 K. Han,17,6 E. Hansen,22,2 K. M. Heeger,17 R. Hennings-Yeomans,5,6 K. P. Hickerson,2
H. Z. Huang,2 R. Kadel,25 G. Keppel,4 Yu. G. Kolomensky,5,25 K. E. Lim,17 X. Liu,2 Y. G. Ma,14
6
M. Maino,12,13 L. Marini,16,11 M. Martinez,9,10,26 R. H. Maruyama,17 Y. Mei,6 N. Moggi,27,7 S. Morganti,10
1
0 P. J. Mosteiro,10 C. Nones,28 E. B. Norman,29,30 A. Nucciotti,12,13 T. O’Donnell,5,6 F. Orio,10 J. L. Ouellet,22,5,6
2 C. E. Pagliarone,3,15 M. Pallavicini,16,11 V. Palmieri,4 L. Pattavina,3 M. Pavan,12,13 G. Pessina,13
r V. Pettinacci,10 G. Piperno,9,10 S. Pirro,3 S. Pozzi,12,13 E. Previtali,13 C. Rosenfeld,1 C. Rusconi,13
p
E. Sala,12,13 S. Sangiorgio,29 D. Santone,3,20 N. D. Scielzo,29 V. Singh,5 M. Sisti,12,13 A. R. Smith,6
A
L. Taffarello,31 M. Tenconi,21 F. Terranova,12,13 C. Tomei,10 S. Trentalange,2 G. Ventura,32,33 M. Vignati,10
7 S. L. Wagaarachchi,5,6 B. S. Wang,29,30 H. W. Wang,14 J. Wilson,1 L. A. Winslow,22 T. Wise,17,18
2 A. Woodcraft,34 L. Zanotti,12,13 G. Q. Zhang,14 B. X. Zhu,2 S. Zimmermann,35 and S. Zucchelli36,7
(CUORE Collaboration)
]
x
1Department of Physics and Astronomy, University of South Carolina, Columbia, SC 29208 - USA
e
2Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 - USA
-
l 3INFN - Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila) I-67010 - Italy
c
u 4INFN - Laboratori Nazionali di Legnaro, Legnaro (Padova) I-35020 - Italy
n 5Department of Physics, University of California, Berkeley, CA 94720 - USA
[ 6Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 - USA
7INFN - Sezione di Bologna, Bologna I-40127 - Italy
3 8Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 - USA
v 9Dipartimento di Fisica, Sapienza Universita` di Roma, Roma I-00185 - Italy
4 10INFN - Sezione di Roma, Roma I-00185 - Italy
3
11INFN - Sezione di Genova, Genova I-16146 - Italy
3
12Dipartimento di Fisica, Universit`a di Milano-Bicocca, Milano I-20126 - Italy
1
13INFN - Sezione di Milano Bicocca, Milano I-20126 - Italy
0
14Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 - China
.
1 15Dipartimento di Ingegneria Civile e Meccanica,
0 Universita` degli Studi di Cassino e del Lazio Meridionale, Cassino I-03043 - Italy
6 16Dipartimento di Fisica, Universita` di Genova, Genova I-16146 - Italy
1 17Department of Physics, Yale University, New Haven, CT 06520 - USA
:
v 18Department of Physics, University of Wisconsin, Madison, WI 53706 - USA
i 19INFN - Gran Sasso Science Institute, L’Aquila I-67100 - Italy
X
20Dipartimento di Scienze Fisiche e Chimiche, Universita` dell’Aquila, L’Aquila I-67100 - Italy
r 21Centre de Spectrom´etrie Nucl´eaire et de Spectrom´etrie de Masse, 91405 Orsay Campus - France
a
22Massachusetts Institute of Technology, Cambridge, MA 02139 - USA
23Physics Department, California Polytechnic State University, San Luis Obispo, CA 93407 - USA
24Department of Materials Science and Engineering,
University of California, Berkeley, CA 94720 - USA
25Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 - USA
26Laboratorio de Fisica Nuclear y Astroparticulas,
Universidad de Zaragoza, Zaragoza 50009 - Spain
27Dipartimento di Scienze per la Qualita` della Vita,
Alma Mater Studiorum - Universit`a di Bologna, Bologna I-47921 - Italy
28Service de Physique des Particules, CEA / Saclay, 91191 Gif-sur-Yvette - France
29Lawrence Livermore National Laboratory, Livermore, CA 94550 - USA
30Department of Nuclear Engineering, University of California, Berkeley, CA 94720 - USA
31INFN - Sezione di Padova, Padova I-35131 - Italy
32Dipartimento di Fisica, Universita` di Firenze, Firenze I-50125 - Italy
33INFN - Sezione di Firenze, Firenze I-50125 - Italy
2
34SUPA, Institute for Astronomy, University of Edinburgh, Blackford Hill, Edinburgh EH9 3HJ - UK
35Engineering Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 - USA
36Dipartimento di Fisica e Astronomia, Alma Mater Studiorum - Universit`a di Bologna, Bologna I-40127 - Italy
(Dated: April 25, 2016)
We describe in detail the methods used to obtain the lower bound on the lifetime of neutrinoless
double-beta (0νββ) decay in 130Te and the associated limit on the effective Majorana mass of the
neutrinousingtheCUORE-0detector. CUORE-0isabolometricdetectorarraylocatedattheLab-
oratoriNazionalidelGranSassothatwasdesignedtovalidatethebackgroundreductiontechniques
developed for CUORE, a next-generation experiment scheduled to come online in 2016. CUORE-0
is also a competitive 0νββ decay search in its own right and functions as a platform to further de-
veloptheanalysistoolsandprocedurestobeusedinCUORE.Theseincludedatacollection,event
selection and processing, as well as an evaluation of signal efficiency. In particular, we describe
the amplitude evaluation, thermal gain stabilization, energy calibration methods, and the analysis
event selection used to create our final 0νββ search spectrum. We define our high level analysis
procedures, with emphasis on the new insights gained and challenges encountered. We outline in
detail our fitting methods near the hypothesized 0νββ decay peak and catalog the main sources of
systematic uncertainty. Finally, we derive the 0νββ decay half-life limits previously reported for
CUORE-0, T0ν >2.7×1024yr, and in combination with the Cuoricino limit, T0ν >4.0×1024yr.
1/2 1/2
I. INTRODUCTION mass of ∼40kg. Cuoricino ran from 2003–2008 and until
recently held the best limits on the 0νββ decay half-life
Neutrinoless double-beta (0νββ) decay [1] is a hy- of 130Te at T10/ν2 > 2.8×1024yr (90% C.L.) [16]. Mov-
pothesized second-order weak decay in which a nu- ing from Cuoricino to CUORE, we seek to increase the
cleussimultaneouslyconvertstwoneutronsintotwopro- active mass and improve sensitivity to 0νββ decay by
tons and produces only two electrons in the process, reducing backgrounds through better material cleaning
(Z,A)→(Z+2,A)+2β−. The discovery of this decay and handling [17–19]. The CUORE-0 detector is a sin-
would conclusively indicate that lepton number is vio- gle CUORE-style tower, with comparable active mass to
lated and that neutrinos are Majorana fermions. Fur- Cuoricino, that was operated in the Cuoricino cryostat
ther, it could help constrain the absolute scale of the from 2013 to 2015. CUORE-0 serves as a technical pro-
neutrino masses and their hierarchy [2], and would lend totype and validation of the background reduction tech-
supporttothetheorythatneutrinosplayedafundamen- niquesdevelopedforCUORE,aswellasasensitive0νββ
tal role in the creation of the matter asymmetry of the decay search on its own.
Universe[3,4]. Forallthesereasons,thesearchfor0νββ
decay has recently become the center of intense experi-
mental effort utilizing a broad range of technologies [5–
7]. At present, 0νββ decay has never been decisively
observed,butseveralrecentexperimentshaveplacedup-
This paper begins by briefly describing the design and
per limits on its decay rate in 76Ge [8], 136Xe [9, 10] and
operationoftheCUORE-0detectorinSectionII;amore
130Te [11].
detailed and technical description of the detector design
The Cryogenic Underground Observatory for Rare
andperformancecanbefoundin[20],andareportonthe
Events(CUORE)[12,13]isanext-generationtonne-scale
initial performance can be found in [21]. In Section III,
bolometric detector, currently in the advanced stages of
wedescribetheproductionoftheCUORE-0energyspec-
construction at the Laboratori Nazionali del Gran Sasso
trum; this process closely follows the one used for Cuori-
(LNGS) of INFN and expected to begin operation in
cino found in [16] (hereafter referred to as CINO2011),
2016. CUORE will search for the 0νββ decay of 130Te
so here we focus on the parts of the analysis that have
using a segmented array of 988 TeO bolometric detec-
2 been further developed for CUORE-0, including the new
torsoperatedatextremelylowtemperatures. Thedetec-
data blinding procedure. In Section IV, we outline the
tors will be arranged into an array of 19 towers with 52
data selection criteria and the signal efficiency evalua-
bolometers each for a total detector mass of 741kg, or
tion. Section V summarizes our unblinding procedure.
206kg of 130Te.
In Section VI, we present our technique for searching for
CUOREbuildsontheexperienceofCuoricino[14–16],
a 0νββ decay signal and derive the limit on the half-life
which was a single tower of 62 bolometers with a total
of 0νββ decay of 130Te previously presented in [11]. In
Section VII, we detail the performance of the CUORE-0
detector,particularlyincomparisontotheCuoricinode-
∗ Present address: Physics Department, Princeton University, tector. InSectionVIIIwepresentthetechniqueforcom-
Princeton,NJ08544,USA bining the results of CUORE-0 and Cuoricino to obtain
† e-mail: [email protected] the limit on the 0νββ decay half-life of 130Te presented
‡ Deceased. in [11].
3
II. DETECTOR DESIGN & DATA COLLECTION as both the source of the decays of interest and detector
oftheirenergy. Inthis“source=detector”configuration,
The CUORE-0 experiment is a segmented array of 52 MonteCarlosimulationsshowthat≈88%of0νββ decay
bolometric detectors arranged into a tower of 13 floors events deposit all of their energy in the crystal in which
with4bolometersperfloor(seeFig.1(a)). Eachbolome- the decay occurred. Thus the signal we are searching for
ter has three primary components: an energy absorber, isamonoenergeticpeakattheQ-valueofthe130Tedecay,
a temperature sensor, and a weak thermal link to the Qββ =2527.518±0.013keV [23]. This energy is above
copper frame that acts both as the structural tower sup- that of the majority of the naturally occurring environ-
port and the thermal bath (see Fig. 1(b)). When energy mentalγ radiation,butbetweentheprominent2615keV
is deposited in the absorber, its temperature increases line from the decay of 208Tl and its Compton edge. In
suddenly by this region, the primary backgrounds are due to multi-
scatteredγeventsanddegradedαdecayswhichreachour
δT =E/C(T), (1) detectorsfromthesurfacesofmaterialsnearthecrystals.
Adetaileddescriptionoftherelevantbackgroundscanbe
where C(T) is the (temperature-dependent) heat capac-
found in [24].
ity and E is the amount of energy deposited. As the en-
TheCUORE-0towerhasatotalactivemassof39.1 kg
ergy slowly leaks out into the thermal bath, the bolome-
for a total 130Te mass of 10.9kg. The tower is cooled in
tergraduallyreturnstoitsinitialtemperature. Thistem-
the cryostat that housed the Cuoricino experiment. The
peraturepulseisconvertedtoavoltagepulsebythether-
cryogenic installation, shielding, and anti-radon system
mometer (see Fig. 1(c)) and by measuring its amplitude
are identical to Cuoricino (see [20] for details) and the
we can determine the amount of energy deposited in the
backgrounds associated with this infrastructure is simi-
bolometer.
larly unchanged (see Sec. VII).
We monitor the temperature of each bolometer by
measuring the resistance of a neutron transmutation
doped (NTD) Ge thermistor glued to each crystal. The
NTDhasaresistivitythatisexponentiallydependenton
its temperature, making it a very sensitive thermome-
ter [25–27]. We further instrument each crystal with a
silicon resistor, which we use as a Joule heater to pro-
(b)
ducefixed-energyreferencepulsesforstabilizingthegain
of the bolometers against temperature variations. Each
bolometer is held in the copper frame with a set of poly-
V)-3200
m tetrafluoroethylene (PTFE) supports. These, as well as
e (-3400 the25µmgoldwiresthatinstrumenttheNTDandJoule
g
olta-3600 heater, form the weak thermal link to the thermal bath.
V-3800 WebiaseachNTDthroughtwolow-noiseloadresistors
-4000
and measure the output voltage signal using a specially
-4200 designedlow-noiseroomtemperaturepreamplifier,apro-
-4400 grammable gain amplifier, and a 6-pole Thomson-Bessel
(a) -4600 low-pass filter with a programmable cutoff frequency set
0 1 2 3 4 5
Time (s) to 12Hz. The data-acquisition system (DAQ) continu-
(c) ouslysampleseachwaveformat125S/swith±10.5Vdy-
namic range and 18bit resolution. We trigger each data
streaminsoftwareandstoreeventsin5secondwindows:
FIG. 1. (a) CUORE-0 tower array rendering. The tower
consists of 13 floors of 4 bolometers, mounted in a copper theonesecondofdataprecedingthetriggerandthefour
frame. (b)SchematicofasingleCUORE-0bolometershowing seconds after. Particle pulses — pulses coming from en-
thethermistor(T),theheater(H),andtheweakthermallink ergy deposits in the crystals — have typical rise times
(L) between TeO crystal and copper thermal bath (not to of ∼0.05s and two decay time components, a fast decay
2
scale). (c) An example of a bolometer signal with an energy timeof∼0.2sandaslowerdecaytimeof∼1.5s. Thefor-
of approximately 2615 keV. The rise and fall times of this merdecaytimeisdeterminedbytheheatcapacityofthe
signal are 0.05s and 0.2s respectively. Figure from [21].
crystalandthethermalconductivitytothethermalbath,
and the latter decay time by the heat capacity of the of
In CUORE-0, the energy absorber is a 750g the auxiliary components (i.e. the PTFE spacers and
5×5×5cm3 natTeO crystal which we cool to an nearby copper frame). The rise time is determined pri-
2
operating temperature of T ≈ 12mK. The typi- marily by the roll-off of the Bessel filter. Typical trigger
0
cal heat capacity at this temperature corresponds to thresholdsrangefrom30keVto120keV.Every200s,we
∆T/∆E ∼10−20µK/MeV. Thenaturalisotopicabun- collect 5 second waveforms simultaneously on all chan-
danceof130Teisa =34.167%[22],thusthecrystalacts nels with no signal trigger and use these to study the
I
4
noise behavior of the detector. 1. measurethe amplitudeof thesignal B whilemini-
i
We collect data in one-day-long runs, which are inter- mizingtheeffectofthenoiseterminordertomax-
ruptedfor2-3hoursevery48hourstorefilltheliquidHe imize the energy resolution of our detector (pulse
bath and perform other maintenance on the cryogenic amplitude evaluation);
system. Roughly once per month, we calibrate the en-
2. stabilize the temperature-dependent gain term
ergyresponseofthedetectorbyinsertingthoriatedtung-
G (T) against temperature drifts of the detector
stenwiresinsidetheexternalleadshieldingandusingthe i
characteristic γ lines from the 232Th decay chain. These (thermal gain stabilization);
calibration runs typically last for three days. The data
3. determine an energy calibration that models the
are combined into datasets that contain roughly three
form of A (E), allowing us to extract the energy
i
weeks of 0νββ decay physics runs flanked at the begin-
for each event (energy calibration);
ningandtheendbyasetofcalibrationruns. Eachcrystal
has a typical event rate of ∼1mHz in the physics runs 4. blind the region of interest (ROI) in order to pre-
and ∼60mHz in the calibration. vent any bias in the later stages of our analysis
During the tower assembly, one NTD and one heater (data blinding).
couldnotbebonded, andanotherheaterwaslostduring
the first cool down. Thus of the 52 bolometers, 49 are 1. Amplitude Evaluation: To evaluate the ampli-
fully instrumented (working heater and thermistor), two tude of the pulse Bi, we employ two parallel approaches.
are functional but without heater (thermistor only), and We apply the same optimum filtering (OF) technique
one cannot be read (no thermistor). described in [CINO2011, 28] as well as a new decorre-
The detector was assembled in March 2012 and first lating optimum filter (DOF). Both filters are frequency-
cooled down in August 2012, with data collection start- based and designed to maximize the signal-to-noise ra-
ing in March 2013. The first data-taking campaign tio (SNR), assuming a predetermined detector response
(Campaign I) lasted until September 2013 (8.5kg·yr of function si(t) and noise spectrum (see Fig. 2). These fil-
TeO , corresponding to 2.0kg·yr of 130Te). We then ters leverage the entire waveform to create an amplitude
2
paused data collection for about 2 months to perform estimate rather than just a few points around the peak
maintenance on the cryostat. Data collection resumed of the pulse.
in November 2013 and Campaign II lasted until March Uptoamultiplicativegain,anOFpulsecanbewritten
2015. Combining both campaigns, the total exposure is in frequency space as
35.2kg·yr of TeO , corresponding to 9.8kg·yr of 130Te.
2 S∗(ω)
VOF(ω)∝eiωtmax i V (ω), (4)
i N (ω) i
i
III. FIRST-LEVEL DATA PROCESSING
whereV (ω)andS (ω)istheFouriertransformofthesig-
i i
nal v (t) and temporal detector response function s (t)
The low-level data processing takes the CUORE-0 i i
respectively for bolometer i; N (ω) is the noise power
data from a series of triggered waveforms to a cali- i
spectral density of the underlying noise sources; ω is
brated energy spectrum that will be the input into the
the angular frequency and t is the time at which the
higher-level analysis. The data processing procedure for max
pulse reaches its maximum. The expected detector re-
CUORE-0 closely follows that of Cuoricino, outlined in
sponse s (t) is computed for each bolometer over each
CINO2011, but with several additions newly developed i
dataset by averaging many events in the 2615keV cal-
for CUORE-0.
ibration line. The exact number of events depends on
Inordertoestimatetheenergyofeachevent,wemodel
the counting rate and the amount of calibration data in
the time-waveform v (t) of each bolometer, i, as the sum
i a given dataset, but is typically several hundred events.
of a known detector response function s (t) and an un-
i The noise power spectral density N (ω) is similarly esti-
known additive noise term n (t) i
i mated for each bolometer on each dataset by averaging
v (t)=B s (t)+n (t), (2) the noise power spectral densities of noise samples col-
i i i i
lected throughout each run.
where Bi is the amplitude of the signal response. To a The DOF generalizes Eqn. (4) by accounting for noise
very good approximation, this amplitude can be decom- correlations between neighboring bolometers [29, 30].
posed as The DOF pulse for an event on bolometer i is given by
Bi =Gi(T)·Ai(E), (3) VDOF(ω)∝eiωtmax(cid:88)S∗(ω)C−1(ω)V (ω), (5)
i i ij j
where A (E) depends only on the energy deposited into
i j
the bolometer E, and G (T) is a bolometric gain which
i
depends on the operating temperature of the bolometer where C−1(ω) is the i,j component of the inverted noise
ij
T. The low-level data processing performs the following covariancematrixatfrequencyωandthesumrunsovera
steps on each triggered waveform in order to extract the list of correlated bolometers. In CUORE-0, we limit this
deposited energy: list to the 11 nearest geometric neighbors for bolometers
5
tion runs are essential to determining the energy resolu-
V)500 Raw Amplitude tion input to our 0νββ decay analysis, so this makes the
m DOF problematic. Despite this, for some bolometers,
2 OF Amplitude
0. the benefit of the decorrelation outweighs the degrada-
nts / (400 DOF Amplitude tion due to the higher event rate in the calibration data.
u Thus the final CUORE-0 dataset utilizes both the OF
o
C
300 and the DOF, depending on which performed better on
the 2615keV 208Tl line in the calibration data. In order
200 to use the DOF over the OF the improvement in energy
resolutionat2615keVmustbestatisticallysignificantat
the (cid:38)90% level. With this requirement, 20% of the final
100
CUORE-0 data production utilizes the DOF.
Once filtered, the amplitude of each pulse is deter-
0- 6 - 4 - 2 0 2 4 6
Amplitude (mV) mined by interpolating the three data points around the
peak of the filtered pulse and evaluating the maximum
FIG. 2. The distribution of amplitudes of the noise pulses of that parabola.
collected from a single channel during the physics data of a 2. Thermal Gain Stabilization: The thermal gain
dataset from Campaign I. The widths of the above distri- stabilization (TGS) compensates slow variation in the
butions are indicative of the amount of noise remaining af- gain of the bolometers G (T) due to drifts of the operat-
i
ter filtering. The channel presented is one where the DOF
ing temperature of the detector. As with the amplitude
performed well. The raw unfiltered RMS is 2.7mV (black
evaluation, we use two techniques in parallel: a heater-
dotted histogram); the RMS after OF is 1.1mV (blue solid
based TGS and a calibration-based TGS.
histogram); the RMS after DOF is 0.8mV (red dashed his-
togram). Theheater-TGSisidenticaltothetechniquedescribed
in CINO2011 and described further in [31]. This ap-
proach uses the heater attached to each bolometer to in-
in the middle floors of the tower (i.e., the four bolome- ject fixed-energy reference pulses every 300s during each
ters from the floor above, the four from the floor below, run. Since the energy of the reference pulse is constant,
and the three on the same floor as the triggered bolome- any variation in its measured amplitude Biref is due to
ter) or the 7 nearest neighbors for bolometers on the top a change in the bolometric gain Gi(T). We use the av-
andbottomfloors. Thisfiltercanbethoughtofaswork- erage value of the baseline, measured in the one second
ing in two stages: it first subtracts the noise common of data preceding the trigger, as a proxy for the bolome-
to all bolometers and then performs a regular OF on ter temperature at the time of the event. By regressing
the bolometer of interest with the expected noise spec- thereferenceamplitudeBiref asafunctionofthebaseline
trum after removing common-mode noise. The key is value, we can determine Gi(T) — up to a multiplicative
that the neighboring bolometers provide an estimate of constant that can be folded into Ai(E). We then factor
thecommon-modenoise. Notethatifthecovariancema- Gi(T) out of the measured amplitude Bi to stabilize our
trix is calculated with only the bolometer of interest and bolometric response against thermal drifts.
no neighboring bolometers (i.e., if C (ω) is diagonal), For the two bolometers without functioning pulser
ij
then Eqn. (5) reduces to Eqn. (4). heaters the heater-TGS can not be applied. These two
The DOF typically outperforms the OF in reducing bolometers amount to about 4% of our total exposure.
the RMS of the noise in the physics runs but performs Moreover,forsomebolometerstheheater-TGSalgorithm
worse in the calibration runs. The higher event rate of consistently failed to stabilize the gain over very large
the calibration runs leads to a higher probability of an temperature drifts. This was due partly to deviations
event occurring on a neighboring bolometer within the from linearity and partly to differences in the way en-
5s triggered window which yields an incorrect estimate ergy is deposited by particle interactions versus heater
of the common-mode noise. This results in two scenar- pulses(i.e.,differencesinthepulseshapesresultingfrom
ios: either the energy deposited is small (i.e., not much particle interactions and heater pulses). A failure of the
abovethenoise),thepulsegoesuntriggered,andisinad- heater-TGS manifests as a shift in the location of the
vertently included in the sum in Eqn. (5); or the event calibration peaks between the initial and final calibra-
is triggered and the waveform is excluded from the sum tion runs, visible as two distinct peaks in the calibration
andthefilterisnolonger“optimal”(i.e.,thetermsinthe spectrum. In this case, we consider the entire dataset
sumarenotoptimizedforthesmallersetofbolometers). invalid for that particular bolometer. These shifted cal-
Both scenarios degrade the performance of the DOF. ibration datasets correspond to about 7% of our total
This effect is only prominent in the calibration runs exposure.
where the event rate is about 60 times higher than in In order to address these issues, we developed a TGS
thephysicsrunsandthus,intheory,doesnotworsenthe algorithm based on calibration data and independent
DOF performance on the physics data and in our 0νββ from the heater. This approach uses the 2615keV γ-
analysis. However,asweshowinSectionVI,thecalibra- line in the calibration runs in lieu of the monoenergetic
6
strongest γ peaks from the 232Th decay chain. This
consists of fitting each peak position using a Gaussian
lineshape plus a first degree polynomial background and
performing a linear regression on the expected energies
of the calibration peaks against their reconstructed po-
sitions using a second-order polynomial with zero inter-
cept.
In Section VI, we show that a Gaussian line shape
does not provide a good fit to the reconstructed peak
shapes. This discrepancy leads to a small bias in the
reconstructed event energies, but rather than correcting
for this bias at the calibration stage, we adjust the po-
sition at which we search for a 0νββ decay signal (this
is detailed in Section VI). For CUORE, we plan to im-
prove our energy reconstruction by accounting for these
non-Gaussian peak shapes during the data processing.
FIG.3. Exampleofthecalibration-TGS.Thepointsaretaken
4. Data Blinding: The final step of the first level
duringthecalibrationrunsforoneoftheCUORE-0datasets.
data processing is the blinding of the ROI. Our blind-
The cluster of points on the right are from the calibration
ing procedure is designed to mask any possible signal
runs which opened the dataset, while the cluster on the left
are from the closing calibration runs. The solid blue points or statistical fluctuation at Qββ, while maintaining the
have energies around the 2615keV 208Tl peak and are used spectral integrity so that we can use the blinded energy
for calibration-TGS. By regressing the measured amplitudes spectrumfortestingourlateranalyses. Weuseaformof
of these points against the NTD voltage we can determine a data salting that randomly shifts the reconstructed en-
stabilization curve (red dashed line) which is then applied to ergyofafractionofeventsfromwithin10keVofthe208Tl
the physics runs taken between calibrations. 2615keV peak by −87keV to around Q and the same
ββ
fraction of events from within 10keV of Q by +87keV
ββ
toaroundthe208Tlpeak. Becausetherearesignificantly
pulser to map the temperature-dependent gain G (T). more events around the 208Tl peak, this creates an arti-
i
Weregressthegaindependencemeasuredinthecalibra- ficial peak at Qββ with the shape of a true signal peak.
tion runs (see Fig. 3) and use this to correct the ampli- The fraction of events is blinded and random but chosen
tudes of events in both the calibration and physics runs. from a range such that the artificial peak is unrealisti-
Since calibration-TGS is interpolated across an entire cally large (see Fig. 7(b)). Each event’s true energy is
dataset, it requires carefully measuring and accounting encrypted and stored, to be decrypted later during un-
fortheappliedandstrayvoltageoffsets. Thiscalibration- blinding. This procedure is pseudo-random and repeat-
TGSallowedustorecoverabout80%ofthelostexposure able. Thecalibrationrunsarenotblinded. Thestepsfor
onthetwobolometerswithbrokenheaters. Additionally, unblinding are detailed in Section V.
in cases of large temperature drifts, the calibration-TGS
routinely outperformed the heater-TGS and resulted in
little or no shift between the peak positions in the initial IV. DATA SELECTION & SIGNAL EFFICIENCY
and final calibration runs, as measured on the 2615keV
line. This allowed us to recover much of the 7% of expo- A. Data Selection
surethatwouldhavebeenrejectedwiththeheater-TGS;
and further it improved the resolution of other bolome- Once the first level data processing is complete, we
ters that showed a marginal peak shift between initial selecttheeventsofinterestwithasetofeventcuts. These
and final calibration runs, but one not large enough to cuts fall into three types:
be considered invalid. All told, we used the calibration-
1. Time-basedcutsthatremoveperiodsoftimewhere
TGS on 12% of the total CUORE-0 exposure.
the data quality were poor or the data processing
For the majority of the CUORE-0 data, applying the
failed.
TGS caused temperature-dependent gain drifts to be-
come a subleading cause of degradation in the energy 2. Event-basedcutsthatremovepoorlyreconstructed
resolution of our detector. However, in 2.7% of the final and non-signal-like events to maximize sensitivity
exposure both TGS algorithms failed significantly, usu- to 0νββ decay.
ally due to an abnormally large or sudden drift in tem-
3. Anti-coincidence cuts that remove events that oc-
perature or a change in electronic operating conditions.
cur in multiple bolometers and are thus less likely
These data were discarded for the rest of the analysis.
to come from a 0νββ decay.
3. Energy Calibration: For each dataset, we cali-
bratetheenergyresponseofeachbolometerA (E)using 1. Time-Based Selection: The first set of cuts re-
i
the reconstructed positions of at least four of the seven moves intervals of time where the data collection was
7
poor. This typically removes periods of excessive noise
fromanindividualbolometer(e.g. amalfunctioningelec-
tronicchannel),orperiodsoftimewhentheentiredetec-
tor temperature was fluctuating quickly (e.g. during an
earthquake). This cut introduces a dead time that re-
duces our total exposure by 3.5%. We further remove
intervals of time when the data processing failed. The
most significant component of this was a failure of the
TGSalgorithmstostabilizegainvariationsovertoolarge
a temperature drift. These excluded periods lead to the
reductioninourtotalexposureof2.7%mentionedinthe
previous section.
2. Event-Based Selection: We implement a set of
event based cuts that remove events that are either non-
signal-like or are in some way not handled well by the
data processing software. This includes a set of basic
quality cuts that removes events that are clearly prob-
lematic, such as events that exceed the dynamic range
of the electronics or events that overlap with one of the
injected heater pulses. We further implement a pile-up
cut that rejects an event if more than one trigger oc-
cursinthesamebolometerwithin3.1sbeforeor4safter
FIG.4. Plotofthetwoabsorbedenergiesindouble-crystalco-
the event trigger. This 7.1s window allows any previ-
incidences during physics data collection. The diagonal lines
ous event enough time to return to baseline and ensures correspond to events where a γ scatters in one crystal and is
that any following event does not occur within the event then fully absorbed in another. The vertical and horizontal
window. linesarecascadeeventswhereoneγ isfullyabsorbedandthe
In addition to these basic quality checks, we have de- other is scattered. This can be seen for the two 60Co γ-rays,
208Tl 2615keV + 583keV γ-rays, and 208Tl pair production
veloped a set of pulse shape cuts, which remove events
eventswhereoneannihilationphotonescapesandisabsorbed
onthebasisofsixpulseshapeparameters. Theseinclude
in another bolometer.
the slope of the baseline as well as the time in the event
window that the signal reaches its maximum. Cutting
on these two parameters is useful for removing events
whose amplitudes are poorly reconstructed by the pro-
146 – 2615keV, and the background is measured in the
cessing software. The pulse shape cuts also cut on the
energy regions around the peaks. To avoid biasing our
pulse rise and decay times, which are useful for identi-
selection, we use a randomly selected half of the data for
fying pile-up events that failed to cause a second trigger
tuning the selection and the remaining events for deter-
and events that have very fast time constants and are
mining the selection efficiency (reported in Table I). We
believed to be due to energy depositions in the thermis-
exclude the 0νββ decay ROI from both calculations.
tor itself, fast temperature variations due to vibrations,
or electronic noise. The last pulse shape cut selects on 3. Anti-coincidence Selection: Since the desired
two parameters referred to as “Test Value Left” (TVL) 0νββ decay events have their full energy absorbed in a
and “Test Value Right” (TVR). These are effectively χ2 singlebolometer,weuseananti-coincidencecuttoreject
values between the normalized OF filtered pulse shape any event that occurs within ±5ms of another event in
and the expected filtered detector response shape on ei- any other bolometer in the tower. This cut primarily re-
ther the left or right side of the signal peak. These last jects α-decays that occur on the surfaces of our bolome-
two parameters are useful for identifying events whose ters, γ-rays that scatter in one bolometer before being
shape deviates significantly from the expected detector absorbedinanother, cascadeγ-raysfromradioactivede-
response shape. cays, and muons passing through the tower and their
All pulse shape parameters have an energy depen- secondary neutrons. A plot of the energies of double-
dence,whichwenormalizebyinterpolatingacrossevents crystal coincidence events — events where two bolome-
thatliewithinpeaksinthecalibrationspectrumoverthe tersaretriggered—isshowninFig.4. InCINO2011,the
range 146keV to 2615keV. As a result, the efficiency of anti-coincidencewindowwas±50ms,andin[21]weused
the cuts on these variables is independent of energy to a window of ±100ms. Here we have significantly nar-
within statistical uncertainty over this range. We tune rowed this window by accounting for the constant differ-
thesepulseshapecutsbymaximizingthesignalefficiency ences in detector rise times between different bolometers
over the square root of the background in the physics when measuring the time between two events on differ-
spectrum, where the signal efficiency is measured as the entbolometers(seeFig.5). Thiscorrectionimprovesthe
fraction of selected events in the γ peaks over the range timing resolution by a factor of ≈50.
8
After implementing all cuts, 233 out of 411 triggered as a Gaussian peak around 3−3.5MeV. We determine
eventsremainintheROIforthe0νββ analysisdescribed ourenergyreconstructionefficiencybyfittingthisheater
in Sec. VI. peak with a Gaussian line shape and counting the frac-
tion of events that reconstruct within 3σ. This calcula-
D T (ms) tion is done for each bolometer for each physics run and
Sync
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 averaged,weightedbyexposure,todetermineasingleef-
ents3500 ficiency for the entire detector. The bolometers without
v
E3000 working heaters are excluded from this calculation and
are assigned the same efficiency as the other bolometers
2500
— thus they are assumed to have the average efficiency
2000 of the other bolometers.
We estimate the efficiency of the signal cuts (i.e., pile-
1500
up and pulse shape) using the 208Tl 2615keV peak in
1000 the physics data. The vast majority of events that re-
constructinthepeakareproperlyreconstructed; pile-up
500
eventsandeventswithnon-standardpulseshapesrecon-
struct somewhat randomly with a much wider distribu-
0
0 10 20 30 40 50 60 70 80D T90 (ms1)00 tion. We estimate our cut efficiency by measuring the
Raw
rate within 5σ of the 2615keV peak and subtracting the
FIG. 5. Distribution of measured time between coincident backgroundratemeasuredinbandsaroundthepeak. We
eventsbeforecorrectingfordifferentdetectors’risetime(black compare this signal rate before and after applying the
solid, ∆TRaw) and after (red dashed, ∆TSync). cuts to determine the fraction of signal events that are
accidentally removed by the signal cuts.
The anti-coincidence efficiency accounts for the rejec-
tionofvalideventsduetoaneventbeingcloseenoughin
timetoanunrelatedeventonanotherbolometersoasto
B. Signal Detection Efficiency
accidentally be considered a coincidence. This efficiency
isestimatedinasimilarfashiontothesignalcutefficien-
The signal detection efficiency for a 0νββ decay is a
cies—comparingthesignalratebeforeandafterthecut
productofconditionalprobabilities: theprobabilitythat
— except that it is calculated around the 1460keV line
the full energy of the decay is contained in a single crys-
from electron capture in 40K. While the 208Tl 2615keV
tal, the probability that the event is then triggered and
γ-ray can be part of cascade and is expected to occa-
properly reconstructed, the probability that the event
sionally occur in coincidence with other γ-rays, the 40K
then passes the signal cuts, and the probability that the
1460keV only occurs in coincidence with a 3keV X-ray
event is not then accidentally in coincidence with an un-
which is well below the trigger threshold of our bolome-
related event in a different bolometer. These efficiencies
ters. Thusanyeventincoincidencewithafullyabsorbed
are summarized in Table I.
1460keV γ-ray constitutes an accidental coincidence.
We use a Geant4-based [32] Monte Carlo simulation
Combining these, we determine the total signal effi-
to estimate the fraction of events that deposit their full
ciency of the CUORE-0 detector to be 81.3±0.6%.
energy in a single crystal. This simulation models the
mostsignificantenergylossmechanisms: electronescape,
X-rayescape,andtheescapeofBremsstrahlungphotons.
TABLE I. CUORE-0 signal detection efficiency. See the text
Thesimulationalsomimicsthedetectorresponsebycon-
for how these are calculated.
volving the spectrum with a Gaussian to reproduce the
Source Signal Efficiency (%)
expected shape near Q . We calculate the efficiency by
ββ 0νββ energy confinement 88.345±0.040(stat)±0.075(syst)
fitting the resulting 0νββ decay peak and dividing the
Trigger & Reconstruction 98.529±0.004
fitted area by the number of simulated decays. The effi- Pile-up & Pulse Shape cuts 93.7±0.7
ciency evaluates to 88.345±0.040(stat)±0.075(syst)%. Anti-coincidence cut 99.6±0.1
The systematic uncertainty is from the variation in the Total 81.3±0.6
crystal dimensions, the uncertainty in decay energy, and
thestepchoiceforsecondarypropagationintheGeant4
simulation.
We evaluate the trigger and energy reconstruction ef-
ficiencies using the pulser heater events. The DAQ au- V. DATA UNBLINDING
tomatically flags each heater event in the data, and then
passes the event through the standard signal trigger al- Theunblindingprocedurewasdecideduponbeforeany
gorithm. Thefractionofheatereventsthatalsogenerate data were unblinded. After fixing the data selection cuts
a signal trigger provides an estimate of our signal trig- and the 0νββ decay analysis procedure (described in the
ger efficiency. The heater events typically reconstruct next section), we unblinded the data in two stages: first
9
r) 102 3
y
g
V k 1 2 6 6 2 5 5 2 4
ke 10
( 2
s / 4 2 2
nt 4 2
u 2
o 1
C
10- 1
10- 2
500 1000 1500 2000 2500
Reconstructed Energy (keV)
FIG. 6. The final CUORE-0 physics spectrum (blue) and calibration spectrum (red). The calibration spectrum has been
normalized to match the rate of the physics spectrum around the 2615 keV 208Tl peak. The most prominent peaks in the
physics spectrum are from the decay of known radioactive backgrounds: (1) e+e− annihilation, (2) 214Bi, (3) 40K, (4) 208Tl,
(5) 60Co and (6) 228Ac. Figure adapted from [11].
we unblinded 17 of 20 datasets (or 8kg·yr of 130Te expo- strainthebackgroundratewithoutintroducingunneces-
sure) and began the 0νββ decay analysis while we con- sary peaks into the analysis. The range is bounded by
tinued to collect the final three datasets (or 1.8kg·yr of a 214Bi line at 2448keV and a small peak at 2585keV
130Te exposure). The last three datasets were blinded from a 2615keV 208Tl γ-ray minus a 30keV Te X-ray
duringcollection,weresubjectedtothesameproduction escape (see Fig. 7(a)). The ROI contains the potential
procedureandcutsastherestofthedata,andweretobe 0νββ decaysignalat2527keVaswellasapeakfromthe
includedregardlessoftheireffectonthefinalresult. The single-crystalcoincidenceofthetwoγ-raysfrom60Code-
unblinded spectrum is shown in Fig. 6, and the blinded caywhichliesonly21keVbelow. Weattributethis60Co
andunblindedspectraintheROIareshowninFig.7(b). contaminationtotheactivationofthecopperframesand
As a cross-check, we also reproduced all of the internalshielding[24]. Wehavemeasuredtheproduction
CUORE-0 data without the blinding/unblinding steps rate of 60Co inside the TeO crystals to be small [33], so
2
and compared them to the data that had been blinded we expect a negligible background from the β +γ +γ
and unblinded to confirm it had no effect on the final coincidence.
spectrum. Indeed, the blinding/unblinding procedure
Our0νββ decayanalysisproceedsthroughthreesteps.
had no effect on our final spectrum. This confirmation
Wefirstconstructadetectorresponsefunctionρ foreach
ofourblinding/unblindingprocedurevalidatesthistech- i
BoDs, which characterizes the expected spectral shape
nique moving forward to CUORE.
of a particular bolometer’s response to a mono-energetic
energy deposition during a particular dataset. We then
use this set of ρ to fit other prominent peaks in the
i
VI. 0νββ ANALYSIS
physics spectrum. This allows us to understand how our
detector response depends on energy. Finally, we fit the
The CUORE-0 physics spectrum over the range 300– ROI by postulating a peak at the 0νββ decay energy
2700keVisshowninFig.6. TheCUORE-0dataconsists and constraining its amplitude with a detector response
of 20 datasets collected on 51 active bolometers. After functionproperlyscaledinenergy. Theresultingbest-fit
implementing all cuts, 1,008 bolometer-dataset (BoDs) amplitude provides insight into the 0νββ decay rate.
pairs remain for a total TeO exposure of 35.2kg·yr,
2
or 9.8kg·yr of 130Te. Our 0νββ decay analysis treats
eachoneoftheseasasemi-independentexperimentwith
some parameters unique to each BoDs, some parameters
shared across datasets (i.e., constant in time), and other
A. Detector Energy Response
parameters shared globally (i.e., constant in time and
uniform across the detector).
We define the ROI for our 0νββ decay analysis as Wemodelthedetectorresponsetothemono-energetic
therange2470–2570keV;thisregioncontains233events. 0νββ decay signal based on the measured response to
This is the widest possible range that allows us to con- the γ peaks. This is done for each BoDs, i, using the
10
nts / (keV kg yr) 110 (a) 208Tl Counts / keV111024 (b) UBlnibnldiendded
ou 214Bi
C 8
60Co 60Co
10-1 6
4
X-ray
10-2 Escape 2
0
2350 2400 2450 2500 2550 2600 2650 2700 2470 2480 2490 2500 2510 2520 2530 2540 2550 2560 2570
Reconstructed Energy (keV) Energy (keV)
FIG. 7. (a) The CUORE-0 spectrum around the ROI. This is a zoomed view of Fig. 6. The shaded region corresponds to the
energyrangeusedintheROIfit. ThebackgroundintheROIisnowdominatedbythescattered-γ backgroundratherthanthe
flat α background. (b) Comparison of the blinded (dashed) and unblinded (solid) spectra in the ROI. The peak in the dashed
spectrum is the artificial peak created by the blinding procedure. Q is indicated by the dotted line.
ββ
functional form We estimate the best-fit detector response for each
BoDs by fitting the intense 208Tl 2615keV calibration
ρi(E;µi,σi,δi,ηi)≡ peak. This fit is over the range 2560–2650keV and in-
(1−ηi)Gauss(E;µi,σi) (6) cludesthreemoreelementstomodelthebackgroundun-
+ηiGauss(E;δiµi,σi). der the detector response: (i) a smeared step function,
modeled as an Erfc function, to model γ-rays that scat-
This function produces a primary Gaussian centered at ter in the shields before interacting with a bolometer or
µi and a secondary Gaussian at a slightly lower energy scatter multiple times in a single bolometer before exit-
δiµi, with δi ∼ 0.997. This smaller secondary peak ac- ing; (ii) a Gaussian peak roughly 30keV below the pri-
counts for ηi ∼ 5% of events and models an energy loss mary peak to model an event in which a 2615keV γ-ray
mechanismwhoseoriginispresentlyunderinvestigation. is absorbed and one of the characteristic Te K shell X-
The presence of this substructure is unaffected by the rays, which have energies that range from 27–31keV, is
choice of pulse filtering technique or TGS algorithm and producedandescapesthecrystal;(iii)aflatbackground.
is present on all channels. It is not clustered in time The best fit for a single BoDs is shown in Fig. 8(a).
or a result of pile-up of events. It also does not ap-
The full calibration peak model is given by
pear to be correlated with any shape parameter used in
the above cuts. A visual inspection of pulses selected
fTl(E) = RTlρ (E;µ ,σ ,δ ,η )
from the primary and secondary peaks reveals no obvi- i i i i i i i
ous difference in the pulse shape. The Cuoricino data +rScatterRiTlErfc(E√−2σµii) (7)
showsahintofthisasymmetriclineshape; however,itis +rEscapeRiTlGauss(E;δEscapeµi,σi)
the improved resolution of the CUORE-0 detector that +bCal,
has made this effect clear. We tested multiple models
to reproduce the line shape, including a Gaussian dis- whereRTl representsaBoDsdependent208Tlpeakevent
i
tribution with an asymmetric tail and a triple Gaussian rate in counts/(kg·yr), which is a free parameter in the
lineshape which modeled escapes of 4keV characteristic fit. The event rates of both the scattered γ-rays and the
X-rays from Te. Ultimately, we settled on the double- X-rayescapepeakaregivenasfractionsofthepeakevent
Gaussian shape which reproduced the data well across a rate, r and r respectively. Both of these are
Scatter Escape
broad range of energies. globalphysicalparametersthatcouldbeestimatedusing
Each BoDs has its own peak position, µ , and a sin- Monte Carlo, but since modeling them requires carefully
i
gle resolution parameter, σ , for both the primary and accounting for detector thresholds (to accurately predict
i
secondary Gaussian peaks. The data suggest that the the fraction that are flagged as a coincidence) these pa-
position and amplitude of the secondary Gaussian peak rameters are instead left unconstrained in the fit. The
may vary between bolometers and in time, thus indicat- position of the X-ray escape peak is described as a frac-
ingthatthisispossiblyadetectorrelatedeffect. Bothδ tion of the primary peak energy, δ , and is also left
i Escape
and η are free to vary from bolometer to bolometer, but unconstrained in the fit. The final parameter bCal is a
i
tolimitthenumberoffreeparametersbothareconstant global flat background rate in counts/(keV·kg·yr), also
in time within each of the two data-taking campaigns. unconstrained.
