Random coincidence of $2\nu2β$ decay events as a background source in bolometric $0\nu2β$ decay experiments

0.15 MB·English

by  D. M. Chernyak

Random coincidence of 2ν2β decay events as a background source in
bolometric 0ν2β decay experiments
D.M.Chernyaka,b,F.A.Danevicha,A.Giulianib,E.Olivierib,M.Tenconib,V.I.Tretyaka
aInstituteforNuclearResearch,MSP03680Kyiv,Ukraine
bCentredeSpectrome´trieNucle´aireetdeSpectrome´triedeMasse,91405Orsay,France
Abstract
3
1 Twoneutrinodoubleβdecaycancreateirremovablebackgroundeveninhighenergyresolutiondetectorssearch-
0 ing for neutrinoless double β decay due to random coincidenceof 2ν2β events in case of poortime resolution.
2
Possibilitiestosuppressthisbackgroundincryogenicscintillatingbolometersarediscussed. Itisshownthatthe

n presentbolometricdetectortechnologiesenabletocontrolthisformofbackgroundatthelevelrequiredtoexplore
a theinvertedhierarchyoftheneutrinomasspattern,includingthecaseofbolometerssearchingfortheneutrinoless
J
doubleβdecayof100Mo,whichischaracterizedbyarelativelyshorttwoneutrinodoubleβdecayhalf-life.
7
1

] 1. Introduction decay of 82Se (ZnSe [14, 16]), 116Cd (CdWO4 [17]),
et 100Mo (CaMoO4 [15] and ZnMoO4 [18, 19, 20, 21]),
d Neutrinolessdoublebeta(0ν2β)decayisakeypro- and130Te(TeO [22])areintheR&Dstage.
2
- cess in particle physics since it providesthe only ex- However,adisadvantageofcryogenicbolometersis
s
perimentallyviablepossibilitytotesttheMajoranana-
n their poor time resolution. This can lead to a back-
i ture of neutrino and the lepton number conservation, ground component at the energy Q due to random
. 2β
s establishinginthemeantimetheabsolutescaleandthe
coincidencesoflowerenergysignals,especiallythose
c
hierarchyoftheneutrinomasses[1].
i due to the unavoidable two neutrino double β decay
s One of the most important goal of the next gener-
y (2ν2β)events.
ationdoubleβdecayexperimentsistoexplorethein-
h Therandomcoincidenceof2ν2βeventsasasource
p vertedhierarchyoftheneutrinomasses.Intheinverted of background in high sensitivity 0ν2β experiments
[ scheme the effective Majorana hmνi neutrino mass is wasconsideredanddiscussedforthefirsttimein[20].
expectedtobeintheinterval 0.02 0.05eV.Inor-
1 ∼ − Inthiswork,thecontributionofrandomcoincidences
dertocheckthisrange,anexperimentalsensitivity(in
v (rc) of 2ν2β events to the counting rate in the energy
8 termsofhalf-life)forthemostpromisingnucleishould regionoftheexpected0ν2βpeakisestimated. Meth-
4 be at the level T 1026 1027 yr. This requiresa
2 detector containi1n/2g∼a large−number of studied nuclei odstosuppressthebackgroundarediscussed.
4 ( 1027 1028), with high energyresolution(atmost
. ∼ −
1 afew%attheenergyofthedecayQ2β),large(ideally 2. Randomcoincidenceof2ν2βevents
0 100%)detectionefficiency,verylow(ideallyzero)ra-
3
1 dioactivebackground. Energyspectraofβparticlesemittedin2ν2βdecay
v: cayBoesfi7d6eGseH[P2G,3e],dcerteycotgoernsiucsbeodltoomseetaerrcsh[4fo,r50]ν–2lβumdei-- a(sreeeref.lea.te[2d3t]oatnhder2e-fdsi.mtheenrseiionn)aldistribution ρ12(t1,t2)
i
X nescent[6,7,8,9,10]ornot[11,12,13]–areexcellent
r candidatestorealizelarge-scalehigh-sensitivityexper- ρ12(t1,t2)=e1p1F(t1,Z) e2p2F(t2,Z) (t0 t1 t2)5,
a iments involving different isotopes with high energy · · − − (1)
resolution (a few keV) and detection efficiency (near where t is the kinetic energy of the i-th electron (all
i
70% 90%,dependingonthecrystalcompositionand energieshereareinunitsoftheelectronmassm c2),t
− 0 0
size). istheenergyavailableinthe2βprocess, p isthemo-
i
The CUORE cryogenic experiment [12, 13], built mentum of the i-th electron p = √t(t +2) (in units
i i i
onthesuccessfulCuoricinoandsearchingfor0ν2βde- of m c), and e = t +1. The Fermi function F(t,Z),
0 i i
cayof130TewiththehelpofTeO2 detectors,isbyfar which takes into account the influence of the electric
themostadvancedbolometricsearchandisundercon- fieldofthenucleusontheemittedelectrons,isdefined
struction now, while several searches (among which as
LUCIFER [14] and AMoRE [15]), aiming to use dif-
ferent luminescent bolometers to search for double β F(t,Z)=const p2s 2exp(πη) Γ(s+iη) 2, (2)
−
· | |
ThisarticleappearedinEur.Phys.J.C(2012)72:1989andmaybefoundathttp://link.springer.com/content/pdf/10.1140/epjc/s10052-012-1989-y
where s = 1 (αZ)2,η = αZe/p,α = 1/137.036,Z
is the atomipc n−umberof the daughternucleus(Z > 0 Table1: Coefficients ai intheenergydistribution (7)fortworan-
domlycoincident2ν2βeventsfor82Se,100Mo,116Cd,130Te.
for 2β and Z < 0 for 2β+ decay), and Γ the gamma
−
function.
Thedistributionρ(t)forthesumofelectronenergies Isotope
t=t1+t2 isobtainedbyintegration ai 82Se 100Mo 116Cd 130Te
t a0 3446.59 5827.48 20093.8 15145.6
ρ(t)=Z ρ12(t−t2,t2)dt2. (3) a1 –7746.37 –14399.7 –1318.65 5554.78
0
a 22574.7 34128.1 69134.6 39930.0
2
Thisdistributionisshownfor100MoinFig.1. a3 –16189.1 –23815.5 –31971.3 –13338.5
a 8467.01 11271.7 17976.8 7689.45
4
a –2156.83 –2711.31 –3486.40 –813.887
unts/keV60000 2ν2β two coincident 210ν02Mβo aa65 –32387..9117426 –33900..8379764 –43006.5.786426 –1890.1.3013256
o 7
C40000
a 1. 1. 1. –1.
8
20000
theyaregiveninTable1.Theapproximationfor100Mo
0
0 1000 2000 3000 4000
Energy (keV) isshowninFig.1.
Therandomcoincidencecountingrate I inacho-
rc
Figure1:(Coloronline)Distributionforthesumofenergiesoftwo senenergyinterval∆E isdeterminedbythetimereso-
electrons emittedin2ν2βdecayof100Moandenergyspectrumof
lutionofthedetectorτandthecountingrateforsingle
108 two randomly coincident 2ν2β events for 100Mo obtained by
2ν2βeventsI :
MonteCarlo sampling. Theapproximation oftherandom coinci- 0
dencespectrumbytheexpression(7)isshownbythesolid(red)line.
2
ln2N
FfoerrTmZhie>fPu0nr,icmatlilaooknwoFffs-(toRt,osZis)men∼pl(iefP/yRpE)[q2a.4p(]p1,r)owtxohiimtchhaeteiisoxnpardfeeosqrsuiotahntee whereNisItrhce=nuτm·Ib02e·rεof=2βτ·decTa12y/νi22nβgnu·cεl,eiunder(in8-)
vestigation, and ε is the probability of registration of
ρPR(t ,t )=(t +1)2(t +1)2(t t t )5 (4) eventsinthe∆E interval. InEq.(8)andinthefollow-
12 1 2 1 2 0− 1− 2
ing,weassumethatiftwoeventsoccurinthedetector
andtoobtaintheformulaforρ(t)analytically: withinatemporaldistancelowerthanthetimeresolu-
tionτtheygiverisetoasinglesignalwithanamplitude
ρPR(t)=t(t t)5(t4+10t3+40t2+60t+30). (5) equaltothesumoftheamplitudesexpectedforthetwo
0
−
separated signals. The calculated probabilities at the
Theenergydistributionfortworandomlycoincident energyQ ofthe0ν2βdecayfor∆E =1keVinterval
2β
2ν2βdecaysρrc(t) canbeobtainedbynumericalcon- areequaltoε=3.5 10−4for82Seandε=3.3 10−4
× ×
volution for100Mo,116Cd,130Te.
t Counting rates of detectors with 100 cm3 volume
ρ (t)= ρ(t x)ρ(x)dx, (6)
rc Z − (typical for large mass bolometers) at the energy of
0
0ν2βdecayfordifferent2βcandidatesandcompounds
orwithaMonteCarlomethodbysamplingenergyre-
arepresentedinTable 2. We assume100%isotopical
leases in two independent2ν2β events in accordance
enrichmentfor 82Se, 100Mo, 116Cd, and naturalabun-
withthedistribution(3)andaddingthem. Theenergy
dance (34.08%) for 130Te. The time resolution of a
spectrum obtained by sampling 108 coincident 2ν2β
detector is assumed as τ = 1 ms. The reported rates
eventsfor100MoisshowninFig.1. (Weassumehere
scalelinearlywiththetimeresolution.
anidealenergyresolutionofthedetector.) Thisdistri-
Background B causedbyrandomcoincidencesof
butioncanbeapproximatedbythefollowingcompact rc
2ν2β events has the following dependenceon the en-
expression,1similartothatreportedinEq.(5):
ergy resolution R, the volume of the detector V, the
abundanceorenrichmentδofthecandidatenucleicon-
8
ρ (t)=t3(2t t)10 ati. (7) tainedinthedetector:
rc 0 i
− X
i=0 B τ R (T2ν2β) 2 V2 δ2. (9)
rc ∼ · · 1/2 − · ·
However,the coefficientsa are differentfordiffer-
i
entisotopes; for82Se, 100Mo,116Cd, 130Te (whichare 1Onecanexpectapolynomialof21-stdegreebecauseofthefor-
the nearest aims of the bolometric 2β experiments), mulae(5)and(6).
2
One can conclude from Table 2 that the most impor- facing the detectorsor by the detectorsurfaces them-
tantrandomcoincidencebackgroundisfor100Modue selves, are expected to be the dominant contribution
totherelativelyshort2ν2βhalf-life. However,anon- in all high Q -value candidates, for which the sig-
2β
negligible contribution is expected also for other iso- nal falls in a region practically free of γ background.
topes in case of big volume and poortime resolution The α background component however can be made
ofthesingledetectors. negligibleusingscintillatingoringeneralluminescent
Obviouslyanyothersourceofbackgroundwithen- (including Cherencov light [10, 22]) bolometers. In
ergyhighenoughcancontributeduetorandomcoinci- fact, since the α light yield is generally appreciably
dences. Forexample,the presenceof 234mPa(belong- differentfromtheβ/γlightyieldatequaldepositeden-
ingtotheseriesof238U)witharelativelyhighactivity ergy,whilethethermalresponseissubstantiallyequiv-
of 1 mBq/kg in 100 cm3 ZnMoO crystal will result alent,thesimultaneousdetectionoflightandheatsig-
4
in additional background due to random coincidence nals,andthecomparisonoftherespectiveamplitudes,
with 2ν2β events of 3.8 10 5 counts/(keVkgy) at represents a powerful tool for α/β discrimination and
−
× · ·
100MoQ energy. Thiscontributionishowevermuch therefore for α background rejection [6, 7, 8]. Scin-
2β
less importantthan that due to the 2ν2β decay alone. tillation photons are usually detected by a dedicated
In addition, our simulationsshow that coincidenceof bolometer, in the form of a thin slab, opaque to the
2ν2β signals with low energy events is not problem- emitted light and equipped with its own temperature
atic, because of the quite steep shape of 2ν2β spec- sensor. The light absorber, normally a Ge, Si or Si-
trum near Q . Low energy signals due to spurious coatedAl O slab, isplacedclosetoaflatfaceofthe
2β 2 3
sources, like microphonicnoise, which can in princi- mainscintillatingcrystal.
ple contribute with a high rate, are in general easily A wealth of prelimimary experimental results [9,
rejected in bolometersthanks to pulse shape discrim- 16, 17, 18, 19, 20, 21] show that this method is ef-
ination. In conclusion, while a generic source can be fective and α rejection factors even much better than
reducedbycarefulshielding,purificationofmaterials, 99.9%canbeachieved. Oncethatthisdiscrimination
improvementof the noise figure and anti-coincidence capability of scintillating bolometer is taken into ac-
technique, the random coincidence of 2ν2β events is count, a detailed background analysis, based on rea-
a background hard to suppress, as it is related to the sonable assumptions on internal radioactive contam-
presenceitselfoftheisotopeunderinvestigation. The ination, shows that a residual background level of
∼
possibilitiestodecreasethistypeofbackgroundatan 10 4counts/(keVkgy)canbesafelyassumed[20,21],
−
· ·
acceptablelevelarediscussedinthenextSection. opening the opportunity to explore the inverted hier-
archy region of the neutrino mass pattern. However,
the random coincidences of 2ν2β events discussed in
3. Pile-uprejectioninscintillatingbolometers
Section2needtobekeptundercontrol. Accordingto
A cryogenic bolometer [26] consists of an energy Eq. (8), the rate of rc-2ν2β events is proportional to
absorber (a single diamagnetic dielectric crystal in thetimeresolutionofthedetector. Thereforethetime
0ν2β applications) thermally linked to a temperature propertiesofthesignalfromacryogenicdetectorplay
sensor, that in some cases may be sensitive to out of acrucialroleinthisformofbackground.
equilibriumphonons.Theheatsignal,collectedatvery The large mass ( 800 g), high energy resolution
∼
lowtemperatures(typically<20mKforlargebolome- ( 3 4keVFWHMat2615keV)detectorsdeveloped
∼ −
ters),consistsofatemperatureriseofthewholedetec- forCuoricinoandCUORE[11,12]representasortof
tordeterminedbyanuclearevent. paradigma for 0ν2β decay bolometers, inspiring also
Themajorityofthemostpromisinghigh Q -value other proposed experiments and the related R&D ac-
2β
(> 2.5MeV)candidatescanbestudiedwiththebolo- tivities. As temperature sensors, Neutron Transmuta-
metric technique in the “source=detector” approach, tionDoped(NTD)Geelementsareused,characterized
joininghighenergyresolutionandlargeefficiency[4, byahighimpedance(1-100MΩ)andahighsensitivity
5].Ultra-purecrystalsupto100 1000gcanbegrown ( dlogR/dlogT 10).Otherpromisingsolutionsfor
− − ∼
with materials containing appealing candidates. Ar- thethermalsensorshavebeenused[15,28,29,30],but
raysofthesinglecrystallinemodulesallowachieving forthemomentonlytheenergyresolutionandthere-
totalmassesoftheorderof100 1000kg[12,13,14], liabilityprovidedbyNTD-Ge-basedbolometersseem
−
necessarytoexploretheinvertedhierarchyregion. to be compatible with a large-scale 0ν2β experiment.
Anexcellentchoiceforthebolometricmaterial,per- In these devices, the NTD Ge thermistor is glued to
formedintheCuoricinoandCUOREexperiments[11, theTeO crystalbymeansofatwo-componentepoxy.
2
12], consists of TeO (tellurite) that has a very large Theirtimeresolutionisstrictlyrelatedtothethermal-
2
(27% in mass) natural content of the 0ν2β candidate signalrisetime.
130Te. In terms of background, the experience pro- The temporal behaviour of the thermal pulse, and
videdbyTeO searches[27]showsclearlythatenergy- therefore its risetime, can be understood thanks to a
2
degradedαparticles, emittedbythe materialsurfaces thermalmodelforthe whole detector, describedelse-
3
Table 2: Counting rate oftwo randomly coincident 2ν2β events in cryogenic Zn82Se, 40Ca100MoO4, Zn100MoO4, 116CdWO4 and TeO2
detectorsof100cm3volume.Enrichmentof82Se,100Moand116Cdisassumed100%,whileforTethenaturalisotopicabundance(34.08%)
istaken.Cisthemassconcentrationoftheisotopeofinterest,ρisthedensityofthematerial(g/cm3),Nisthenumberof2βcandidatenuclei
inonedetector,andBrcisthecountingrateatQ2β(counts/(keVkgyr))underassumptionof1mstimeresolutionofthedetectors.
· ·
Isotope T2ν2β(yr)[25] Detector(ρ) C N B
1/2 rc
82Se 9.2 1019 Zn82Se(5.65) 55.6% 2.31 1024 5.9 10 6
−
× × ×
100Mo 7.1 1018 40Ca100MoO (4.35) 49.0% 1.28 1024 3.8 10 4
4 −
× × ×
Zn100MoO (4.3) 43.6% 1.13 1024 2.9 10 4
4 −
× ×
116Cd 2.8 1019 116CdWO (8.0) 31.9% 1.32 1024 1.4 10 5
4 −
× × ×
130Te 6.8 1020 TeO (5.9) 27.2% 0.76 1024 1.1 10 8
2 −
× × ×
where[31, 32, 33, 34]. The modelpredictsthatlarge tothefastresponseprovidedbythelightdetector.
mass detectors with NTD-Ge readout have risetimes
oftheorderoftensofmilliseconds. Thisisconfirmed
experimentally in the Cuoricino detectors, which ex-
hibited pulse risetimes of the order of 50 ms [11].
∼
Similarvaluesareexpectedforanycryogenicbolome-
ters with a volume of the order of 100 cm3 and
basedonNTD Gethermistors. Fasterrisetimescould
be observed if an important component of the en-
ergy reaches the thermistors in the form of athermal
phonons,butthis possibility dependscriticallyon the
nature of the main crystal and of the crystal-glue-
thermistorinterface. The mostconservativeapproach
consists in assuming the slow risetime evaluated and
observedinTeO bolometers.
2
Thetimeresolutionofthemaincrystalcanbemade
substantially shorter than the risetime, taking advan-
tage of the excellent signal-to-noise ratio expected at
the0ν2βenergy[35],whichisoftheorderof2000to1
inTeO crystals.(However,thishighvalueisstilltobe
2
provedforotherbolometricmaterialsrelevantfor0ν2β
decay.)Eventhoughthetimeresolutionprovedshorter
byafactor10withrespecttothepresentTeO2risetime Figure2: (Coloronline)Simulatedpiled-uppulses(solid/redlines)
values, and therefore around 5 ms, the background usingrealpulseshapeandnoisefromaworkinglightdetectorcou-
values reported in Table 2 should be multiplied by a pledtoaZnMoO4scintillatingbolometer: (a)pile-upoftwopulses
factor5,bringingthemabove10 3counts/(keVkgyr) shifted by 3 ms with equal amplitude; (b) pile-up of two pulses
− · · shiftedby3mswithamplituderatioequalto4(thesmallerpulseoc-
for100Mo. Backgroundduetorandomcoincidenceof cursfirst);(c)asinglepulse. Thetypicalsingle-signalpulseshape,
2ν2β events would be then dominant. The advantage obtainedbyfittinganaveragepulse,isplottedaswell(dashed/blue
ofscintillatingbolometers,whichpromisetokeepthe lines). Inallcases, thesignal-to-noise ratioisthatexpected fora
0ν2βsignal. Thedifference inshapebetween piled-up andsingle
othersourcesaroundorbelow10 4counts/(keVkgyr)
− · · pulsesissmall,especiallyforunequalamplitudes,butappreciable.
[20,21],wouldbesubstantiallycompromised.
However, the simultaneous detection of light and The above discussion is simplified: the capability
heatwhichcharacterizesscintillatingbolometersoffers todiscriminatetwoclose-in-timeeventscannotbere-
thepossibilityto controlthisproblematicbackground duced to a single parametersuch as the detectortime
source as well. In fact, a much faster risetime in the resolutionτ.Infact,itdependssmoothlyonthetempo-
light-detectorsignalisexpected,duetothemuchlower raldistancebetweenthetwoeventsandontheratiobe-
heat capacity of the energy absorber, which has now tween theirtwo amplitudesas well. Furthermore,the
a mass of only a few grams at most. Following the pile-up discrimination capability is influenced by the
bolometer thermal model [31, 32, 33, 34], the light- signal-to-noise ratio in the light detector [35] and by
detectorrisetimecanbereduceddownto 1ms. As- thepulseshapeandnoisefeatures. Acompleteanaly-
∼
sumingasimilartimeresolution,the2ν2βbackground sis,whosedetailswillbereportedelsewhereinaded-
contributionis in the ranges shown in Table 2 thanks icated publication, has been performed. In this letter,
4
wepresentthemainresultsofthisinvestigationandthe goodpulses. Theothertwoindicatorsprovideequiva-
mostimportantconclusions. lentorevenbetterresults. However,wepreferhereto
An experiment based on modules of Zn100MoO consider conservatively the results obtained with the
4
crystals was considered. We have used pulse shapes methodof the risetime, as this parameteris an intrin-
andnoisefromareallightdetector,ofthesametypeas sic property of each signal that does not require the
thosedescribedin[19,20],coupledtoaZnMoO scin- comparison with a standard shape. This comparison
4
tillatingcrystal. Thepile-upphenomenonwasstudied infactimpliesadelicatesynchronizationbetweenthe
by generating light pulses with the observed experi- single pulse and the standard-shapepulse thatwill be
mental shape on top of experimentalnoisy baselines. discussedinthementionedmorecompletework.
In particular, pair of pulses were generated with ran- Theresultsofthesimulationshowthatthecontribu-
domtimedistanceswithaflatdistributionupto10ms tion to the background of the piled-up events is sub-
–infact,theinterarrivaltimedistributionispractically stantiallyequivalenttothatobtainedwhenassuminga
constant over the [0,10] ms range (this is the rele- time resolution τ of 1 ms in Eq. 9 (since 80% – 90%
vant time interval since it allows to fully explore the of the pulsesare rejectedin the regionof 0ν2β decay
most problematic pile-up case, i.e. that occurring on insideapile-uprelevantrangeof10ms),andtherefore
the pulse risetime which is of the order of 3 ms). In confirmingtheevaluationforZnMoO reportedinTa-
4
Fig. 2, two pile-upemblematiccases(bothwith 3 ms ble2.
timeseparation)extractedfromtheperformedsimula-
tionareshown,alongwithasinglepulseasareference.
As a first step, we defined a 90% efficiency in ac-
ceptingapulsefromthelightdetectorasapotentially
good 0ν2β pulse using opportune signal filtering and
three differentpulse-shape indicators: (i) the risetime
from15%to90%ofthemaximumamplitude;(ii)the
χ2evaluatedusinganaveragepulseasastandardshape
function;(iii)thepulseshapeparameterdefinedin[36]
whichalso usesa standardpulse-shapefunction. The
rejectionefficiencyofpiled-uppulseswasthentested.
In each pulse pair, the amplitude of the first pulse A
1
wasextractedbysamplingthe2ν2βdistribution,while
the amplitude of the second pulse A was chosen as
2
Q2β(100Mo) A1+∆E,where∆E isarandomcompo- Figure3: (Coloronline)Risetimedistribution fortwopopulations
−
nentintheinterval[ 5,+5]keV. of5000generatedeventseach. Thesolid(red)linereferstosingle
Thegeneratedpul−seamplitudeswerechosensoasto pulses;thedashed(blue)lineisobtainedwithpiled-uppulsessepa-
ratedbyatimedistancecoveringuniformlytheinterval[0,10]ms,
fix thesignal-to-noiseratioatthelevelexpectedfora
withamplitudessamplingthe2ν2βspectrumandaddingsoastofall
0ν2βsignal,i.e. oftheorderof30,asshowninFig.2; intheregionofthe0ν2βexpectedpeak.
in fact, the typical light energy collected by the light
detectorsinZnMoO scintillatingbolometersrealized Wecanconcludethereforethatlightdetectorsatthe
4
sofarisoftheorderof1keVfor1MeVenergyinthe present technological level are compatible with next-
heat channel [18, 19, 20, 21], while the typical RMS generation0ν2βdecayexperimentsbasedonZnMoO
4
noiseofthelightdetectorcanbeconservativelytaken crystalswithbackgroundinthe10 4counts/(keVkgy)
−
· ·
as 100 eV, althoughvalues as low as 30 eV were ob- scale,confirmingthatthisclassofexperimentshasthe
served[19]. potentialtoexploretheinvertedhierarchyregionofthe
The piled-up pulses generated in the simulation neutrinomasspattern[20,21].
wereanalyzedwiththementionedpulse-shapeindica-
tors. Using the risetime (after low-pass filtering), an
4. Conclusionsandprospects
excellentpile-uprejectionefficiencywas obtained. A
comparisonbetweentherisetimedistributionforgen- Randomcoincidenceof 2ν2β eventsis an irremov-
uinesinglepulsesandpiled-uppulsesgeneratedasde- ablebackgroundsourceinalargescale2βexperiments
scribedaboveisshowninFig.3. Morequantitatively, usingdetectorswithslowresponsetime,suchaslarge
the same procedure that retains 90% of genuine sin- masscryogenicbolometerswithNTDGereadout.
gle pulses rejects 80%–90% of piled-up pulses when Advancement of time resolution of cryogenic de-
their sum amplitude is in the region of Q and the tectors plays a key role to suppress the background.
2β
differencebetweenthe arrivaltimesofthe two pulses However, we have shown that the present technology
covers uniformly the interval [0,10] ms. For exam- is already compatible with searches at the sensitivity
ple, the analysis of the sample reported in Fig. 3 ex- frontier. For further improvements, experimental ef-
cludes83%ofpiled-uppulseswhenaccepting90%of fortsshouldbeconcentratedonthetimepropertiesof
5
the light signal, potentially much faster than the heat [19] J.W. Beeman et al., J. Low Temp. Phys. (2012).
pulses of a scintillating bolometer. Achieving a time doi:10.1007/s10909-012-0573-z
[20] J.W.Beemanetal.,Phys.Lett.B710,318(2012)
resolution below 0.1 ms could make the background
[21] J.W. Beeman et al., Astropart. Phys. (2012). doi:
totally negligibleeven forthe difficult case of 100Mo.
10.1016/j.astropartphys.2012.02.013
Suchaperformancecouldbeobtainedbyusingsensors [22] J.W.Beemanetal.,Astropart.Phys.35,558(2012)
sensitivetoout-of-equilibriumphononsorintrinsically [23] V.I.Tretyak,Yu.G.Zdesenko,At.DataNucl.DataTables61,
43(1995)
fast[28,29,30].
[24] H.Primakoff,S.P.Rosen,Rep.Progr.Phys.22,121(1959)
Amoredirectwaytodecreasethepile-upeffectisto [25] A.S.Barabash,Phys.Rev.C81,035501(2010)
reducethevolumeof themain absorber(andincreas- [26] A.Giuliani,PhysicaB280,501(2000)
ingcorrespondinglythenumberofarrayelements),on [27] M.Pavanetal.,Eur.Phys.J.A36,159(2008)
[28] A.Fleischmannetal.,AIPConf.Proc.1185,571(2009)
which the randomconcindencerate dependsquadrat-
[29] G.Angloheretal.,Astropart.Phys.31,270(2009)
ically, as shown in Eq. (9). Cryogenicdetectors with [30] C.Nonesetal.,J.LowTemp.Phys.151,871(2008)
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further. [32] A.Alessandrelloetal.,Czech.J.Phys.46-S5,2893(1996)
[33] M.Pedrettietal.,PhysicaB329-333,1614(2003)
[34] L.Foggettaetal.,Astropart.Phys.34,809(2011)
[35] H.Spieler, SemiconductorDetectorSystems(OxfordUniver-
5. Acknowledgments
sityPress,2005)
[36] T.Fazzinietal.,Nucl.Instr.Meth.A410,213(1998)
The work of F.A. Danevich and V.I. Tretyak
was supported in part through the Project
“Kosmomikrofizyka-2” (Astroparticle Physics) of
the National Academy of Sciences of Ukraine. The
light detector results used for the pile-up simulation
have been obtained within the project LUCIFER,
funded by the European Research Council under
the EU Seventh Framework Programme (ERC grant
agreement n. 247115). The background study in
ZnMoO scintillating bolometers is part of the pro-
4
gram of ISOTTA, a project receiving funds from
the ASPERA 2nd Common Call dedicated to R&D
activities.
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