COBRA - Double beta decay searches using CdTe detectors

A new approach (called COBRA) for investigating double beta decay using CdTe (CdZnTe) semiconductor detectors is proposed. It follows the idea that source and detector are identical. This will allow simultaneous measurements of 5 $\beta^-\beta^-$ - and 4 $\beta^+\beta^+$ - emitters at once. Half-life limits for neutrinoless double beta decay of Cd-116 and Te-130 can be improved by more than one order of magnitude with respect to current limits and sensitivities on the effective Majorana neutrino mass of less than 1 eV can be obtained. Furthermore, for the first time a realistic chance of observing double electron capture processes exists. Additional searches for rare processes like the 4-fold forbidden Cd-113 $\beta$-decay, the electron capture of Te-123 and dark matter detection can be performed. The achievable limits are evaluated for 10 kg of such detectors and can be scaled accordingly towards higher detector masses because of the modular design of the proposed experiment.


Introduction
The fundamental question whether neutrinos have a non-vanishing rest mass is still one of the big open problems of particle physics. In case of massive neutrinos a variety of new physical processes open up [1]. Over the last years evidence has grown for a non-vanishing mass by investigating solar and atmospheric neutrinos as well as by results coming from the LSND-experiment. They all can be explained within the framework of neutrino oscillations [2]. However oscillations only depend on the differences of squared masses and are therefore no absolute mass measurements. Besides, the question concerning the fundamental character of neutrinos, whether being Dirac-or Majorana particles, is still unsolved. A process contributing information to both questions is neutrinoless double beta decay of a nucleus (Z, A) (Z, A) → (Z + 2, A) + 2e − (0νββ-decay) (1) This process is violating lepton-number by two units and only allowed if neutrinos are massive Majorana particles. The quantity which can be extracted out of this is called effective Majorana neutrino mass m ee and given by with the relative CP-phases η i = ±1, U ei as the mixing matrix elements and m i as the corresponding mass eigenvalues. Currently the best limit is given by investigating 76 Ge resulting in an upper bound of m ee < ∼ 0.35 eV [3]. Moreover the standard model process (Z, A) → (Z + 2, A) + 2e − + 2ν e (2νββ-decay) (3) can be investigated as well. It is important to check the reliability of the calculated nuclear matrix elements. The experiment proposed here utilizes Cd-based semiconductor detectors. A big benefit of this approach is, that the double beta emitters are part of the detectors itself. The detectors can be used either in the form of only measuring the sum energy of both electrons or in a modified way as pixelised detectors, which allows simultaneous tracking and energy measurement. CdTe and CdZnTe (CZT) detectors are used in several areas of X-ray physics, astrophysics and medical applications. All isotopes of interest for β − β − -decay searches which are intrinsic in these detectors are listed in Tab.1. A few observations exist for 2νββ-decay of 116 Cd , most of them with very low statistics. The obtained half-lives center around 3 · 10 19 a [5][6][7]. The 2νββ-decay of 130 T e was only measured by geochemical methods and found to be in a range of 0.7 − 2.7 · 10 21 a, therewith a spread of a factor four among different measurements exist [8][9][10][11]. Current lower limits on 0νββ-decay half-lives for the two favourite isotopes 116 Cd and 130 T e are 7 · 10 22 a and 1.44 · 10 23 a (both 90 % CL) respectively [7,12]. Limits on the other mentioned isotopes are rather poor, a compilation can be found in [13]. In a more general scheme 0νββ-decay can be realised by several lepton number violating mechanisms. Beside massive Majorana neutrino exchange, additional mechanisms like right-handed weak currents, R-parity violating supersymmetry, double charged Higgs bosons or leptoquarks have been proposed [14][15][16].
To obtain more information on the underlying physics process, it is worthwile to look for transitions into excited states [17] and to investigate β + β + -decay [18]. Three different decay channels can be considered here where the last two cases involve electron capture. The first two are the easiest to detect because of the annihilation photons of the positron(s) emitted. On the other hand they are largely suppressed by phase space reduction (Q−4m e c 2 for β + β + and Q − 2m e c 2 for β + /EC respectively). The one with the lowest expected half-life is EC/EC -decay, but difficult to detect because only Xrays are emitted. All β + β + -decays can occur as 2νββ-decay or 0νββ-decay. For a compilation of existing limits see [13]. A first small attempt to use CdTe for rare decay searches was done by [21].

Experimental considerations
The proposed experiment, running under the name COBRA 1 , should consist in a first stage of 10 kg of material in form of either CdTe or CdZnTe detectors. For double beta decay searches especially two experimental parameters have to be primarily considered, namely energy resolution and the expected background. A possible setup is shown schematically in Fig.1. The central detector is an array of about 1600 CdTe crystals, because the largest available crystal size is of the order of 1 cm 3 . In case of a cubic arrangement it would have a size of 12×12×12 cm 3 . The detectors will be installed within a NaI detector for two reasons: First, it can act as an active veto against penetrating particles and secondly it can be used as a detector for γ-rays, coincidence measurements between a CdTe detector and the NaI can be done. It has been demonstrated by several dark matter groups that such detectors can be built as low-level devices [22,23]. Coincidences among the various CdTe crystals can be formed as well. This inner part is surrounded by a shield of very clean oxygen free high conductivity (OFHC) copper in combination with low-level lead, a setup common to low-level experiments. The complete apparatus will be covered by an active veto against muons made out of high efficiency scintillators. Clearly the experiment should be located in one of the existing underground facilities. A further shielding against thermal neutrons might be necessary, because of the large cross section of 113 Cd(n, γ) 114 Cd reactions. Common background to all low level experiments are the uranium and thorium decay chains as well as 40 K contaminations. Some parts of the chains might be eliminated by subsequent detections within one crystal, clearly identifying the origin of the event. As an example take a sequence from the 226 Ra decay chain (from the 238 U decay): This β − α coincidence within one crystal can be used to estimate this background contribution. Studies on radioisotope production in CdTe due to cosmic ray activation have been performed using proton beams [24]. The intrinsic background from 113 Cd -decay is of no concern because its endpoint is around 320 keV, much below the 0νββ-decay lines. A measurement of the energy spectrum in the range 2-3 MeV obtained with a test setup using a conventional 1 cm 3 CdTe is shown in Fig.2.
The smallness of the CdTe detectors makes it possible to construct the experiment in a modular design, making future upgrades easy.
The principle readout of one CdTe detector will focus on electron collection only, to avoid smearing in the energy because of the bad hole mobility in CdTe. Energy resolutions of about 1 % for the 137 Cs line at 662 keV have already been achieved [25]. This is sufficient to assure no overlap between the 0ν region of 130 T e with possible background lines at 2447.7 keV ( 214 Bi) and 2614.4 keV ( 208 Tl). A further improvement of the energy resolution might be achieved by a slight cooling of the CdTe detectors to temperatures of roughly − 20 degrees centigrade. As a modification the usage of pixelized detectors is envisaged. In addition to an energy measurement this allows tracking of the two emitted electrons and therefore a handle on background reduction. However, it has to be investigated experimentally in more detail whether the additional pixel bonds are not causing relatively more impurities. On the other hand this is a very attractive method to search for transitions to final states using separate pixels within one crystal. Pulse shape analysis techniques might be performed as well for background subtraction. A more detailed treatment of experimental details and simulation studies can be found in [26].

Expected sensitivities for β − β − -decays
The dominant 2νββ-decays are coming from 116 Cd and 130 T e . With an assumed half-life of 3 · 10 19 a this produces a count rate of 94 events/day. Therefore a high statistics measurement of this decay is possible. For 130 T e with an assumed half-life range of 0.7 −2.7 · 10 21 a 6 -23 events/day are expected. This corresponds to a 6.4 % -24.5 % contribution to the 116 Cd spectrum. Clearly a decision among the lower and higher half-lives for 130 T e can be made. A detection and proof of the geochemical half-life obtained for 128 T e will be very difficult, because it would roughly result in only about 1 event/a. The rather poor limit of T 2ν 1/2 > 9.2 · 10 16 a for 114 Cd can certainly be improved, in case of using CZT for the first time a limit on the 2νββ-decay of 70 Zn can be obtained. With regard to neutrino mass limits again the main focus lies on 116 Cd and 130 T e . Achievable half-life limits after 5 years of measurement are shown in Fig.3. In case of building a background free detector, the corresponding halflives scale linear with measuring time, resulting in an even better sensitivity. Using the parameters given in Tab.1, a limit on m ee in the region below 1 eV can be achieved. For an extensive discussion of the status of the necessary nuclear matrix element calculations see [27,28]. If no signal is observed, the observed limit on m ee would strengthen the believe in the result already obtained with Ge, because of the uncertainties coming from nuclear matrix element calculations. Clearly a further improvement can be achieved by adding more detectors, which is possible because of the modular design of the experiment. Also transitions to excited states can be investigated because of the good sensitivities of CdTe detectors for γ-rays. Current bounds for such transitions are in the order of 10 21 a [29,30]. The modular layout of this experiment would allow to perform a high sensitivity search. The coincident detection of the deexcitation photon in one CdTe crystal and the corresponding electron signal in a neighbouring detector forms a clear signal. This will significantly reduce the background in searches for these channels.

Experimental sensitivities for β + β + -decays
A wide range of results can be obtained for the various decay modes of β + β + -decays given in Tab. 2. As already stated, the lowest expected half-life belongs to the EC/EC -decay mode. The filling up of the two K-shell holes in 106,108 Pd coming from the decay of Cd-isotopes will result in a peak at 48.6 keV. A recent calculation for 106 Cd EC/EC results in a theoretical predicted half-life of 4 · 10 20 a [31]. The expected count rate then is about 550 events/a, which should result in a clear observation. A corresponding peak for the EC/EC of 120 Te to 120 Sn would be at 58.4 keV. There is only a limit on the β + /EC of 4.2 · 10 12 a [32], which can be improved by many orders of magnitude, because the expected number for COBRA is 1.2·10 7 events/day. Transitions to excited states for 106 Cd and 120 Te can be explored in a similar fashion. While limits of the order of 10 18 a exist for 106 Cd [35], nothing is known so far for 120 T e .
5 Additional physics -dark matter searches and 113 Cd , 123 T e -decay As most low-level double beta detectors also CdTe could be used for dark matter searches. Detectors with thresholds of about 1 keV at a temperature of − 20 degrees are available. From the theoretical point of view, 125 Te together with 129 Xe is among the theoretically most preferred isotopes to study spin-dependent interactions [37,38]. With 10 kg of CdTe it will be possible to probe the DAMA evidence [39] within reasonable time scales. Unfortunately no theoretical calculation for the usage of Cd-isotopes for dark matter searches exists. A long standing discussion is connected with the β-decay of 123 T e . This second forbidden unique electron capture occurs with a transition energy of 51.3 ± 0.2 keV to the ground state of 123 Sb. Measurements concentrating on the detection of the 26.1 keV photons of K X-rays from 123 Sb resulted in a half-life of the order 10 13 years [33]. However, a new measurement claims a value of 2.4 ± 0.9 ·10 19 a [36], six orders of magnitude higher. The discrepancy might be associated with confusing the above X-ray line with the Te K X-ray line at 27.3 keV. Having a decay within the CdTe detector itself, in contrast to the above measurements, this problem can be solved because the full transition energy can be measured with high efficiency and good energy resolution. Even the long half-life would correspond to 19 decays per day. Last but not least there is the β-decay of 113 Cd . This 4-fold forbidden decay has an uncertain half-life of about 8 · 10 15 a and a Q-value of about 320 keV. Two measurements exist [34,35], but are within their errors in slight disagreement. In the COBRA-setup discussed here a very high statistics measurement can be done, having about 10 decays per second with good energy resolution.

Summary and conclusion
In this paper the physics potential of CdTe or CdZnTe detectors for double beta decay searches and other rare processes is discussed. CdTe detectors profit from the fact that source material and detector are identical. An experimental advantage of the described setup is the good energy resolution (in contrast to scintillators) also in combination with possible tracking and the possibility to perform the experiment at room temperature or only slightly below (in contrast to cryogenic detectors). The unique chance of investigating in total 5(4) β − β − and 4(3) β + β + -emitters at the same time in case of using CZT (CdTe) can be realised. For neutrinoless double beta decay an improvement on the existing half-life limits for the most promising isotopes 116 Cd and 130 T e by more than one order of magnitude with respect to current limits could be obtained. Thus for both isotopes a neutrino mass limit of m ee < ∼ 1 eV would result. A high statistics measurement of the 2νββ-decays of both isotopes is possible. Furthermore, a detailed investigation of β + β + -decays can be done and for the first time an attempt to measure EC/EC -decays in the theoretically predicted range can be performed. Sensitive searches for a large number of excited state transitions are feasible as well. As further topics a high statistics measurement of the 4-fold forbidden β-decay of 113 Cd can be conducted, the six orders of magnitude discrepancy for the electron capture of 123 T e can be solved and a sensitive search for dark matter can be done. The given numbers scale with the used mass and because of the modular design of the experiment a corresponding upgrade for improvements is possible as discussed for a 100 kg solution.

Acknowledgements
I would like to thank Y. Ramachers for valueable discussions, D. Münstermann for working together on building up the test setup and performing the measurements and C. Gößling for his support. Also I thank the mechanical workshop and T. Villett of the University of Dortmund for their help in building the test setup.  Table 2 β + β + -isotopes of relevance in CdTe and CZT detectors. Given are the Q-values of the transition and the natural abundance. Also given are the possible decay modes.

NaI
Veto system Pb Cu Fig. 1. Schematic layout of the proposed COBRA experiment. An array of CdTe detectors is installed within two NaI detectors, serving as active veto and part of coincidence measurements. This will be installed inside an OFHC copper shield, surrounded by low level lead. As a veto the complete setup will be surrounded by a muon veto consisting of high efficiency plastic scintillators.  MeV. The measuring time corresponds to 135.5 hours. The detector was installed in a shielding of 10 cm standard grade copper surrounded by an additional shield of 20 cm of spectroscopy lead. The whole apparatus was surrounded by a 4π veto made of plastic scintillators. The total shielding depth was about 5 mwe. For more details see [26]. Expected 0νββ-decaylines are at 2529 keV ( 130 T e ) and 2805 keV ( 116 Cd ).