Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 2009 1

The Search for Neutrinoless Double Beta Decay in CUOREL. M. Ejzak on behalf of the CUORE collaborationDepartment of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA

Understanding the nature of neutrino masses will require physics beyond the long-standing Standard Model ofparticle physics. Neutrinoless double beta decay (0νββ) experiments like the Cryogenic Underground Obser-vatory for Rare Events (CUORE) are uniquely suited for probing the remaining mysteries of neutrino mass,particularly the question of the neutrino’s Majorana nature. CUORE will be a next-generation experimentat the Laboratori Nazionali del Gran Sasso in Italy; it will consist of an array of 988 TeO2 detector crystalsoperated at ∼10 mK, following the bolometric technique established by the Cuoricino experiment. It will lookfor the energy signal produced by the theoretically-predicted 0νββ decay in 130Te, and therefore reliable energycalibration of the detector is crucial to the experiment’s success. We will present the most recent results fromCuoricino and discuss the current status of the CUORE project, with a particular emphasis on the developmentof the calibration system.

1. Introduction

Nuclear beta decay is the familiar process in whicha nucleon decays, releasing a positron (electron) andan electron neutrino (antineutrino). For some even-even nuclei of mass A and charge Z, beta decay isforbidden, since the resulting (A,Z±1) nucleus wouldbe less bound than the initial nucleus; however, ifthere is a (A,Z±2) nucleus which is more bound thanthe initial nucleus, it is possible to observe the pro-cess called two-neutrino double beta decay (2νββ), inwhich two nucleons decay simultaneously. The half-lives for 2νββ are long - typically of order 1018− 1021

years, and some are even longer - since it is a second-order weak process, but this decay has been observedin a number of isotopes [1]. The sum energy spec-trum of the emitted betas is a continuous distributionbetween zero and the Q-value of the decay, since theneutrinos carry off some of the energy.

If neutrinos are Majorana particles, there is the pos-sibility that, some small fraction of the time, theseisotopes could undergo neutrinoless double beta de-cay (0νββ) instead, in which the two (anti)neutrinoswould disappear in a virtual particle exchange insteadof being released as physical particles. The signal forthis process is a sharp peak in the beta energy spec-trum right at the Q-value of the decay, as the nucleusis so heavy that the recoil is negligible. At this time,the only feasible experimental approach to determin-ing whether or not neutrinos are Majorana particlesis to search for evidence of 0νββ. There are a numberof questions about neutrino properties that 0νββ hasthe potential to address:

1. Whether neutrinos are Majorana particles

2. Absolute neutrino mass scale

3. Neutrino mass hierarchy

The reason that 0νββ may be able to provide a han-dle on one or more of these questions is that, in the

case that 0νββ is mediated by the exchange of a vir-tual light Majorana neutrino, the 0νββ decay rate Γ0ν

is related to the neutrino mass. To be more specific,

Γ0ν = G0ν |Mnucl|2〈mν〉2, (1)

where the effective 0νββ neutrino mass is

〈mν〉 =

∣∣∣∣∣∣∑j

|Uej |2eiφjmj

∣∣∣∣∣∣ . (2)

In the above equations, G0ν is a phase space integral,Mnucl represents nuclear matrix elements, the Uej areelements of the neutrino mixing matrix, the φj arepossible complex Majorana phases, and the mj are thephysical neutrino mass eigenvalues [2]. Experimentalresults are often expressed in terms of the half lifeT 0ν

1/2 (∝ Γ−10ν ).

Unfortunately, a number of complications arise herethat limit how much the quantity that is actually be-ing measured, Γ0ν , can say about the quantities ofinterest. While G0ν can be accurately calculated, var-ious theoretical calculations of the nuclear matrix el-ements can differ by a factor of 2-3, meaning there issignificant theoretical uncertainty in determining theeffective mass from the decay rate, and additional dif-ficulty in using the effective mass to set constraintson the physical masses comes from the fact that thephases φj are completely unknown [3].

Nonetheless, it is possible to use the informationabout the neutrino mixing parameters that has beengained from oscillation experiments to determine theallowed phase space for 〈mν〉 with respect to the massof the lightest neutrino mass state. The allowed re-gion splits into two distinct regions corresponding tothe normal hierarchy and the inverted hierarchy. Thisis what gives 0νββ experiments some discriminatorypower when it comes to the mass hierarchy.

It is important to note that the above discussionapplies only in the simple case that 0νββ is mediatedby the exchange of a virtual light Majorana neutrino

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2 Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 2009

(which will be assumed for the rest of this paper). Ifsome other lepton-number-violating physics is respon-sible (e.g., exchange of a heavy Majorana neutrino orsupersymmetric particles), it becomes much more dif-ficult if not impossible to extract 〈mν〉 [2]. However,no matter what mechanism is responsible, if 0νββ isobserved then neutrinos are Majorana particles [4].

2. The Experimental Situation

Since 0νββ, assuming it happens at all, is such arare process - even more so than 2νββ, which, as dis-cussed previously, has quite a long half life to beginwith - the attempt to observe it experimentally posesa challenge. One way to characterize the sensitivityof an experiment is to introduce a figure of merit F,defined as the ratio of the number of signal events tothe Poisson fluctuation of the background:

F =Ns√Nb

= Γ0ν · f · ε ·√N · T∆E · b

(3)

where f is the isotopic fraction, ε is the detector ef-ficiency, N is the total number of nuclei (i.e., detec-tor mass), T is the live time of the experiment, ∆Eis the energy resolution of the detector, and b is theconstant background rate per atom per energy inter-val [5]. Thus a successful 0νββ experiment will needto be a long-running, low-background experiment withgood resolution and a large-mass detector.

At the moment, experiments using 76Ge(Heidelberg-Moscow, IGEX) and 130Te (Cuori-cino) hold the best limits on 〈mν〉 [5]. These limitslie in the so-called degenerate-hierarchy region, where

Figure 1: The most recent evaluation of the Cuoricinolimit (results are preliminary), representing an exposure of18 yr · kg 130Te. The left-hand peak comes from gammascaused by 60Co contamination resulting from cosmogenicactivation of the detector’s copper support structures; itis close enough to the expected Q-value that it must beincluded in the 0νββ fit. The three 0νββ contours shownare, from bottom to top: best fit, 1σ, and 90% C.L.

the absolute neutrino mass scale is much larger thanthe mass differences, and the allowed region discussedabove has not yet split into distinct regions for thenormal and inverted hierarchies. The last-publishedCuoricino limit was T 0ν

1/2 ≥ 3.1 × 1024 yr (90%C.L.) [6]. However, the current Cuoricino limit (seeFig. 1), a preliminary result including more statisticsand using an updated Q-value measurement (seesection 3.1) as compared to the last-published result,revises this number to T 0ν

1/2 ≥ 2.94 × 1024 yr (90%C.L.) [7]; this corresponds to 〈mν〉 ≤ (210−700) meV,where the range arises from the different calcula-tions of the nuclear matrix elements as tabulatedin Ref. [8]. There is also a claim to have actuallyseen 0νββ from a subset of the Heidelberg-Moscowcollaboration (the Klapdor-Kleingrothaus claim),also in the degenerate-hierarchy region [9]. It isparticularly important to test this claim using adifferent ββ isotope, with different systematics andnuclear matrix element calculations; when using agiven matrix element calculation method, Cuoricino’sresults do not exclude the Klapdor-Kleingrothausclaim [6]. Thus the goal of CUORE (the successor toCuoricino), and indeed of all next-generation 0νββexperiments, is twofold: to test the Klapdor claim,and to extend sensitivity into the inverted-hierarchyregion.

3. Moving from Cuoricino to CUORE

The CUORE experiment will be a search for evi-dence of neutrinoless double beta decay. It will usethe bolometric technique established with its prede-cessor, Cuoricino, and should be able to achieve ap-proximately a two-orders-of-magnitude improvementin sensitivity to the 0νββ half-life T 0ν

1/2 over Cuori-cino’s current limit; CUORE’s predicted limit afterabout five years of running is T 0ν

1/2 ≤ 2.1 × 1026 yr(90% C.L.), corresponding to 〈mν〉 ≤ (24− 83) meV,assuming the 0.01 counts/[keV · kg · y] goal for thebackground rate is met (see discussion in section 3.2below).

3.1. The Cuoricino and CUORE Detectors

The design of the CUORE detector is based on thebolometric principle (see Fig. 2), as tested in the pi-lot experiment, Cuoricino. The detector is an arrayof (dielectric and diamagnetic) TeO2 crystals, so thatthe detector itself contains the source (130Te) that itis studying. Let C be the heat capacity of one crystal,which is thermally coupled to a heat sink of tempera-ture T by a thermal conductance of G. Under the as-sumption that the crystal is a perfect calorimeter and∆T (t) � T for all times t, whenever an event occurs

Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 2009 3

Figure 2: A side-by-side comparison of a schematicbolometer with a close-up photograph of the top face of aCuoricino crystal mounted in its copper support structure.The chip glued to the crystal is the thermistor; the whiteblock labeled in the figure as the ‘thermal coupling’ is aPTFE standoff.

in a crystal, the energy ∆E it deposits is converted tophonons and manifests as a small temperature rise

∆T (t) =∆EC

e(−t/τ) (4)

with recovery time constant

τ =C

G. (5)

According to the Debye law, at low temperatureC ∝ T 3; therefore, the array is housed in a cryostatwhich keeps the crystals at 8-10 mK, reducing theirheat capacity and thereby improving both the mag-nitude of the temperature response and the recoverytime constant [10]. Each crystal is equipped with athermometer, or, to be more specific, a thermistor -a resistor whose resistance changes rapidly with tem-perature:

R(T ) = R0e√T0/T (6)

A bias current I is applied across the thermistor, andthe change in the resultant voltage V across it as thethermistor’s resistance changes with temperature isread out. The detector’s exact response depends onthe point on its V − I load curve at which it is op-erating, known as the working point, which in turndepends on the base temperature of the bolometer.The thermistors therefore produce voltage data, whichmust be calibrated to signals of known energies to ob-tain a voltage-to-energy conversion.

Both Cuoricino and CUORE use TeO2 crystals tostudy the decay of 130Te. Tellurium is an advan-tage in this instance because of the relatively highnatural abundance (33.8%) of the 0νββ candidateisotope, which means that enrichment is not neces-sary to achieve a reasonably large active mass. Also,the Q-value of the decay falls between the peak andthe Compton edge of the 2615 keV gamma line of208Tl, the highest-energy gamma from the natural de-cay chains; this leaves a relatively clean window in

Figure 3: Left: A photo of the Cuoricino detector tower.Right: A 3D scale model of the CUORE detector (an arrayof 19 Cuoricino-like towers) and cryostat. The lavenderstructures are lead shielding.

which to look for the signal. Two recent measure-ments give the Q-value as 2527.01 ± 0.32 keV [11]and 2527.518 ± 0.013 keV [12], a marked improve-ment in precision over the previously-accepted valueof 2530.3 ± 2.0 keV [13]. Cuoricino was comprised ofa single tower of crystals, with a total detector massof 40.7 kg and a 130Te mass of 11.34 kg. By contrast,CUORE will consist of an array of 988 5× 5× 5 cm3

TeO2 bolometer crystals, arranged in 19 towers of2 × 2 × 13 crystals apiece; the total detector masswill be 741 kg, which corresponds to a 130Te mass of203 kg.

The design and construction of the cryostat thatwill be used to maintain the detectors at the neces-sary cryogenic temperatures is a rather unique un-dertaking. It is based on the comparatively recently-developed technology of the cryogen-free dilution re-frigerator, which utilizes pulse tube (PT) pre-coolinginstead of a liquid helium bath; this should allow im-proved stability of the base temperature of the detec-tors as compared to the traditional 3He/4He refrigera-tor (used for Cuoricino). It will be the first cryostat ofits kind big enough to house and cool the large detec-tor mass represented by the CUORE array (∼1 ton).

In addition to the increase in scale from Cuori-cino to CUORE, in order for CUORE to reach itsanticipated sensitivity, improvement is foreseen intwo crucial aspects of detector performance: resolu-tion and background. The average FWHM resolu-tion at 2615 keV of the Cuoricino bolometers wasapprox. 8 keV; the goal for CUORE is 5 keV. Testsof the first batches of crystals produced for CUOREhave shown that this goal has already been met, bymeans of improvements in the crystal quality, detec-tor mounting structure, and reproducibility of thethermistor-crystal couplings. The average flat back-ground in the region-of-interest seen in Cuoricino was

4 Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 2009

0.18 counts/[keV · kg · yr]; the goal for CUORE is toreach 0.01 counts/[keV · kg · yr]. See section 3.2 be-low for further discussion of Cuoricino backgroundsand efforts to reduce them for CUORE. Projections ofCUORE’s sensitivity generally assume 5 keV resolu-tion and 0.01 counts/[keV ·kg ·yr] background; an op-timistic background rate of 0.001 counts/[keV ·kg ·yr]has also been considered.

3.2. Backgrounds

0νββ experiments must be low-background exper-iments, and CUORE is no exception. Backgroundsare the crucial limiting factor which controls the sen-sitivity which can be reached, and they must there-fore be reduced and controlled as much as possible.The CUORE detector, like Cuoricino before it, willbe located underground in the Laboratori Nazionalidel Gran Sasso (LNGS) in Italy in order to reduce therate of cosmic ray events; the cryostat will also containshielding constructed from ancient low-radioactivitylead (see Fig. 3) and be surrounded by additionallead to block environmental radioactivity from reach-ing the detector, and the detector structure itself willbe composed of low-background materials and han-dled entirely in clean room conditions.

In Cuoricino, the main sources of the 0.18 ±0.01 counts/[keV · kg · y] background were the naturaluranium and thorium decay chains from contamina-tion of the detector materials. There were two maincomponents to this background: surface contamina-tion of the detector components, and bulk contamina-tion of the cryostat materials. The surface contami-nation produced a flat α background in the region ofinterest; the main contributors were the surfaces of thecopper support structures facing the bolometers (re-sponsible for 50± 20% of the total background in the0νββ region) and of the crystals themselves (10±5%).The principal background contribution due to bulkcontamination was the tail of the 2614.5 keV gammaproduced by the decay of 232Th in the cryostat mate-rials (30 ± 10%). These values have been verified byextensive Monte Carlo studies [6].

The goal that CUORE is striving to reach is0.01 counts/[keV · kg · y]. In order to reach this goal,more stringent material selection, production, clean-ing, handling, and storage procedures have been es-tablished for all detector components to be used in theconstruction of CUORE. The cleaning of the coppersupport structures in particular has been the subjectof an intense R&D program which is currently in itsfinal stages. Thus far, test runs have demonstratedbackground levels within a factor of 2-4 of the goalwhen extrapolated to CUORE.

To some extent, the array can self-veto againstpenetrating background particles like muons (whichwould cause simultaneous events in multiple adjacent

crystals), and spurious events due to detector noisecan be filtered out through pulse-shape analysis; how-ever, in the end, the only real data, and therefore theonly real handle on event identification, that bolo-moters provide is energy information. This is quitesuitable for a 0νββ experiment, since an energy sig-nal is precisely what is sought, but it does mean thatreliable, precise energy calibration is absolutely essen-tial to the experiment’s ability to provide meaningfuldata.

4. The CUORE Detector CalibrationSystem

Since the thermistors read out the temperaturechanges in the bolometer crystals as voltage data, en-ergy calibration must be performed in order to deter-mine the relationship between the energy depositedin the crystal and the voltage signal subsequently ob-tained. This must be done for each bolometer indi-vidually, before the spectra can be summed togetherand analyzed for evidence of 0νββ. In order to dothis, a gamma source with a known spectrum is usedto illuminate the crystals. Although the most criticalenergy region that must be calibrated is the regionof interest around the 0νββ Q-value, the whole spec-trum should be calibrated as well as possible for reli-able identification of backgrounds. For this purpose,Cuoricino used 232Th as its calibration source, sinceits decay chain produces a number of gamma lines upto 2615 keV that are strong enough to be used for cali-bration; the 2615 keV peak is particularly strong, andcan be used to ensure solid calibration in the regionof interest (see Fig. 4). The calibration uncertainty inthe region of interest is a systematic error in the deter-mination of T 0ν

1/2. In Cuoricino, this uncertainty wasnegligible with respect to the ±2 keV uncertainty onthe Q-value; however, with the improved precision inrecent Q-value measurements, the performance of theCUORE calibration system is of greater importance.

The thermistors which are used to read out the crys-

Figure 4: The summed spectrum of all Cuoricino bolome-ters, from a calibration run with 232Th. Each bolometerhas been calibrated individually, then summed together af-ter the calibration was applied. Note the strong 2615 keVgamma line from the decay of 208Tl, which provides a solidhandle on the calibration near the 0νββ Q-value, 2530keV.

Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 2009 5

Figure 5: Some images illustrating the calibration system concept. Left: 3D model of the calibration system as itinterfaces with the cryostat flanges and vessels. Center: source positions relative to detector towers and cryostat shields.Top right: 3D model of the drive spool (as seen from inside the motion box). Bottom right: schematic of a single sourcecapsule; photograph of a section of a prototype source string.

tals are very sensitive and their response will changewith small variations in the working point of the detec-tor. Between calibrations, the response of the bolome-ters is stabilized by means of periodic heater pulses ofknown energy, and the base temperature of the detec-tor is stabilized with a DC feedback loop; however, itis still necessary to perform a calibration every monthor two with minimal disruption of the detector andcryostat. ‘Minimal disruption’ means that the calibra-tion system must not compromise the low-backgroundenvironment of the detector, nor place excessive ther-mal load on the cryostat such that the detector warmsup, changing the working points of the bolometers.

One of the most dramatic changes that has to bemade in scaling up from the single tower of Cuoricinoto the 19 towers of CUORE is that the calibrationsystem must grow in complexity. In Cuoricino, whichcomprised a single tower of crystals, two radioactivesource wires were inserted inside the external shieldingon either side of the cryostat. In CUORE, the outertowers will shield the inner towers, so some calibrationsources must be routed all the way into the detectorarea and between the towers (see bottom-center im-age in Fig. 5) in order to achieve even illumination,which is important in order to be able to successfullycalibrate the entire detector in a reasonable amountof time without causing an excessively high event ratein some crystals - since bolometers are inherently slow(each pulse lasts several seconds), a high rate causespileup and raises the baseline temperature of the de-

tectors, leading to increased dead time and degrada-tion of the energy resolution.

The CUORE detector calibration system addressesthis requirement in the following way: the system con-sists of 12 flexible source carriers, routed through thelevels of the cryostat by means of guide tubes, andstored and deployed by four motion boxes containingthree spools each which sit on top of the 300 K flangeof the cryostat. This approach allows the sources tobe stored entirely outside the cryostat during normaldata-taking, and to traverse the complicated routesthrough the interior of the cryostat (see Fig. 5) neces-sary to reach the detector area. Motion in cryogenicand vacuum conditions is challenging, because of themechanical and thermal effects of friction and vibra-tion; additional complication arises from the fact thatthe calibration sources must travel through regions ofdiffering temperatures, from 300 K to 8-10 mK, with-out failing under thermal cycling or thermally over-loading the cryostat. The system has been carefullydesigned to meet this challenge; a more detailed dis-cussion than that which follows can be found in [14].

The source carrier is conceived as a collection ofsmall, individual active sources, chained together toform a single flexible unit that is capable of slidingdown through the guide tubes into calibration posi-tion under its own weight when fed off a spool (seeFig. 5). The source carrier will be built by attachingindividual source capsules to a continuous string. Asource capsule is comprised of a copper tube crimped

6 Proceedings of the DPF-2009 Conference, Detroit, MI, July 27-31, 2009

to the string, and covered with PTFE heat-shrink tub-ing to reduce the friction against the guide tube dur-ing source motion. Each capsule will house a lengthof thoriated tungsten wire. The source isotope willthus be 232Th, as it was in Cuoricino; however, thissource carrier design is adaptable enough to allow thepossibility of using different isotopes in the case thatit is deemed useful to do so.

The guide tubes route the source carriers throughthe cryostat, and also provide a thermal connection tovarious stages of the cryostat. Heat will be dissipatedinto the cryostat by the friction of the source carriersmoving through the bends. Additionally, since theguide tubes essentially form a penetration through allthe thermal stages of the cryostat, the thermal gra-dient that will develop along them represents anotherthermal load; the materials for the guide tubes musttherefore be chosen on the basis of both thermal con-ductivity, to minimize thermal load, and radiopurity,to minimize background events induced in the detec-tor. As a conservative approach, the system has beendesigned to operate within the static heat budget ofthe cryostat wherever possible, even during source mo-tion, since we do not know the dynamic recovery timeconstant of which the cryostat will be capable.

Calculations have shown that, in order for the ther-mal radiation from the source carriers to be at an ac-ceptable level when they are in the detector area, thesource carriers must be thermalized to 4 K during theinsertion process. A thermalization clamp has beendesigned in order to ensure sufficient thermal contactbetween the sources and the guide tubes; four of theseclamps will be mounted below the 4 K flange of thecryostat, one for each group of three guide tubes.

Extensive room-temperature motion, friction, andcontrol tests have been conducted of a prototype guidetube system. Motion has been shown to be reliable,and instrumentation (including a motor encoder, aproximity sensor, and a load cell operated as a ten-sion meter) allows monitoring of the sources’ travelthrough the tubes and automatic failsafes against thesource string escaping the tubes or damage to the mo-tor. Vacuum and cold tests of the system will be con-ducted as part of the commissioning of the CUOREcryostat.

5. Conclusions and Status of theExperiment

CUORE is in the construction phase. The facili-ties at LNGS are under construction and more than200 crystals have been received and stored at LNGS.In early 2010, assembly and installation of the firstCUORE tower in the Cuoricino cryostat will begin;this tower will take data independently as CUORE-0,providing an ‘engineering run’ to verify CUORE as-

sembly procedures as well as allowing statistics com-patible with those of Cuoricino to continue to accrueuntil the full CUORE array is operational. Also inearly 2010, assembly of the CUORE cryostat will be-gin, allowing a battery of hardware tests at both roomtemperature and at cold (including cold tests of thecalibration system) to be performed. CUORE detec-tor construction will continue throughout 2010 and2011; data taking with the full CUORE array will be-gin in 2012.

CUORE is a next-generation 0νββ experimentwhich will utilize the bolometric detection techniqueproven in its predecessor, Cuoricino. It is now in theconstruction phase, and will be one of the first 0νββexperiments to probe the inverse hierarchy mass re-gion.

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