Neutrino masses

Authors


Corresponding author   E-mail: weinheimer@uni-muenster.de

Abstract

The various experiments on neutrino oscillation evidence that neutrinos have indeed non-zero masses but cannot provide the absolute neutrino mass scale. This scale of neutrino masses is very important for understanding the evolution and the structure formation of the universe as well as for nuclear and particle physics beyond the present Standard Model. Complementary to deducing constraints on the sum of all neutrino masses from cosmological observations, two different methods to determine the neutrino mass scale in the laboratory are pursued: the search for neutrinoless double β-decay and the direct neutrino mass search by investigating single β-decays or electron captures. The former method is not only sensitive to neutrino masses but also probes the Majorana character of neutrinos and thus lepton number violation with high sensitivity. Currently quite a few experiments using different techniques are being constructed, commissioned, or are even running, which aim for a sensitivity on the neutrino mass of inline image(100) meV. The principal methods and these experiments are discussed in this short review.

1 Introduction

The various experiments with atmospheric, solar, accelerator, and reactor neutrinos provide compelling evidence that neutrino flavor states are non-trivial superpositions of neutrino mass eigenstates and that neutrinos oscillate from one flavor state into another during flight. From these neutrino oscillation experiments the neutrino mixing matrix U containing the mixing angles as well as the differences between the squares of neutrino masses can be determined [1].

The values of the neutrino masses are very important for astrophysics and cosmology for describing the role of neutrinos in the evolution of the universe. Although neutrinos are very light they may contribute significantly to the mass density of the universe: with 336 neutrinos per cubic centimeter left over from the Big Bang they are about a billion times more abundant than atoms. Also, the values and the pattern of the neutrino masses are very important for nuclear and particle physics, since they are a very sensitive probe for physics beyond the Standard Model of particle physics at large scales. Since neutrinos are neutral there is the possibility that neutrinos are their own antiparticles and, additionally, so-called Majorana mass terms originating from large scales could play a dominant role in describing neutrino masses [2].

Clearly, neutrino oscillation experiments prove that neutrinos have non-zero masses, but these experiments – being a kind of interference experiment – cannot determine absolute masses. Therefore, we need other ways to determine the absolute value of the neutrino masses. Three methods are sensitive to the values of the neutrino mass eigenstates and their mixing angles in different ways: neutrino mass from cosmology, neutrino mass from neutrinoless double β-decay and neutrino mass from direct neutrino mass determination. These are described below.

1.1 Neutrino mass from cosmology

The relic neutrinos would have a smeared out fluctuation on small scales, depending on their mass. By analyzing the power spectrum of the universe, limits on the sum of the three neutrino mass states, e.g. inline image eV [3], have been obtained, which are to some extent dependent on model and analysis.

1.2 Neutrino mass from neutrinoless double β-decay (inline image)

Some even–even nuclei can only decay via double β-decay into a nucleus with higher binding energy. This second-order weak process was proposed more than 70 years ago [4] and has been experimentally confirmed for around a dozen nuclei over a period of more than 20 years (left-hand panel of Fig. 1). If – in the case of a inline image-decay – the electron antineutrino going out at one vertex is absorbed at the other vertex as a neutrino (right-hand panel of Fig. 1), the double β-decay will be neutrinoless. This would violate lepton number conservation by two units. Therefore, neutrinoless double β-decay is forbidden in the Standard Model of particle physics. It could occur only if the neutrino is its own antiparticle (“Majorana neutrino” in contrast to “Dirac neutrino”). Secondly, the left-handedness of neutrinos and the right-handedness of antineutrinos in charge current weak interactions provide a second obstacle for neutrinoless double β-decay. A finite neutrino mass is the most natural explanation for the production, in the chirality-selective weak interaction, of a neutrino with a small component of opposite handedness on which this neutrino exchange is based. Then the decay rate will scale with the absolute square of the so-called effective neutrino mass, which takes into account the neutrino mixing matrix U:

display math(1)

In the case of neutrinoless double β-decay the neutrino mixing matrix U also contains two so-called Majorana phases in addition to the normal CP-violating phase δ. The latter is important for neutrino oscillation whereas the former do not influence neutrino oscillation but mee. A significant additional uncertainty entering the relation of mee and the decay rate comes from the uncertainties of the nuclear matrix elements of the neutrinoless double β-decay [5].

Figure 1.

Normal double β-decay with the emission of two antineutrinos (left) and neutrinoless double β-decay (right). The diagrams are shown for the case of a inline image decay.

In the case of inline image decays there are two alternative processes including one or two electron capture (EC) processes: inline image and ECEC. However, the modes involving positrons are phase-space suppressed and only six possible inline image emitters are known. Since in the case of neutrinoless double β-decay the inner neutrino propagator is not observable, the exchange could be based on a completely different particle allowing this lepton number-violating process, e.g. a particle from theories beyond the Standard Model, which leads to a very interesting interplay with new Large Hadron Collider data [6], because at the TeV scale the contribution to double β-decay can have a similar amplitude to the light neutrino exchange. Among others there are heavy Majorana neutrinos, right-hand W bosons, and double-charged Higgs bosons, which are getting constrained by measurements of ATLAS and CMS [7-10]. But there is a general theorem that there will always be a Majorana neutrino mass term observed in the case neutrinoless double β-decay [11]. Diagrams like the one shown in the right-hand panel of Fig. 1 are also applicable for other out-going leptons in theories beyond the Standard Model [12].

There are many recent reviews on neutrinoless double β-decay and neutrinoless double β-decay searches (e.g. [6, 13]).

1.3 Neutrino mass from direct neutrino mass determination

Direct neutrino mass determination is based purely on kinematics or energy and momentum conservation without further assumptions. In principle there are two methods: time-of-flight measurements and precision investigations of weak decays. The former requires very long baselines and therefore very strong sources, which only cataclysmic astrophysical events like a core-collapse supernova could provide. From the supernova SN1987a in the Large Magellanic Cloud, upper limits of 5.7 inline image (95% CL) [14] or of 5.8 inline image (95% CL) [15] on the neutrino mass have been deduced, which depend somewhat on the underlying supernova model. Unfortunately nearby supernova explosions are too rare and seem to be not well enough understood to compete with the laboratory direct neutrino mass experiments.

Therefore, the investigation of the kinematics of weak decays and more explicitly the investigation of the endpoint region of a β-decay spectrum (or an electron capture) is still the most sensitive model-independent and direct method to determine the neutrino mass. Here the neutrino is not observed but the charged decay products are precisely measured. Using energy and momentum conservation the neutrino mass can be obtained. In the case of the investigation of a β-spectrum usually the “average electron neutrino mass squared” inline image is determined [16]:

display math(2)

This incoherent sum is not sensitive to phases of the neutrino mixing matrix in contrast to neutrinoless double β-decay.

In β-decay, e.g. inline image, the out-going electron is sharing the decay energy with the out-going electron antineutrino. Therefore the shape of the β-spectrum near its endpoint E0, i.e. the maximum energy of the electron in the case of zero neutrino mass, is sensitive to the neutrino mass as shown in Fig. 2. A recent review of this topic has been published [17].

Figure 2.

Expanded β-spectrum of an allowed or super-allowed β-decay around its endpoint E0 for inline image (red line) and for an arbitrarily chosen neutrino mass of 1 eV (blue line). In the case of tritium β-decay, the gray-shaded area corresponds to a fraction of inline image of all tritium β-decays.

1.4 Comparison of the different neutrino mass methods

Figure 3 demonstrates that the different methods are complementary to each other and compares them. It shows that the cosmological relevant neutrino mass scale inline image has a nearly full correlation to inline image determined by direct neutrino mass experiments. The observable of neutrinoless double β-decay, the effective neutrino mass mee, does not allow a very precise neutrino mass determination, e.g. to determine inline image, due to the unknown CP and Majorana phases and the uncertainties of the nuclear matrix elements [5]. In the case of normal hierarchy and small neutrino masses the effective neutrino mass mee can even vanish (left-hand panel of Fig. 3), which is not possible in the case of inverted hierarchy (right-hand panel of Fig. 3). On the other hand, the combination of all three methods gives an experimental handle on the Majorana phases. As already mentioned, in addition the exchange of supersymmetry particles may be the dominant process of neutrinoless double β-decay, which would spoil the complete information on the neutrino mass. Nevertheless, the search for the neutrinoless double β-decay is the only way to prove the Majorana character of neutrinos and one of the most promising ways to search for lepton number violation.

Figure 3.

Observables of neutrinoless double β-decay mee (open blue band) and of direct neutrino mass determination by single β-decay inline image (red) versus the cosmologically relevant sum of neutrino mass eigenvalues inline image for the case of normal hierarchy (left) and of inverted hierarchy (right). The width of the bands/areas is caused by the experimental uncertainties (2σ) of the neutrino mixing angles [1] and in the case of mee also by the completely unknown Majorana CP phases. Uncertainties of the nuclear matrix elements, which enter the determination of mee from the measured values of half-lives or of half-life limits of neutrinoless double β-decay, are not considered.

The remainder of this article is structured as follows. Section 'Search for neutrinoless double β-decay' reports on the various searches for neutrinoless double β-decay. In Section 'Direct neutrino mass experiments' the neutrino mass determinations from tritium and inline image β-decay as well as from inline image electron capture are presented. The conclusions are given in Section 'Conclusions'.

2 Search for neutrinoless double β-decay

There are 35 double β-decay isotopes with the emission of two electrons. The strong dependence of the phase space on the Q-value makes only 11 of them (Q-value larger than 2 MeV) good candidates. For most of them, normal double β-decay with neutrino emission has been observed. For neutrinoless double β-decay there is only one claim for evidence at inline image inline image by part of the Heidelberg–Moscow collaboration [18, 19]; all other experiments so far set upper limits. A couple of experiments with sensitivity inline image(100) meV are being set up to check this claim or have started data taking recently. Common to all these experiments is the use of ultrapure materials with very little radioactivity embedded in a passive and an active shield placed in an underground laboratory. Most of them use isotopically enriched material as well.

The most important signature of neutrinoless double β-decay is that the sum of the energy of both decay electrons (in the case of double inline image decay, positrons for double inline image decay) is equal to the Q-value of the nuclear transition. The current proposed or running double β-decay search experiments are given in Table 1.

Table 1. The 11 candidate isotopes with a Q-value larger than 2 MeV. Given are the natural abundances and Q-values as determined from precise Penning trap measurements. The last column shows the experiments addressing the measurement of the corresponding isotope. For some experiments only the “default” isotope is mentioned as these experiments have the option of exploring several isotopes. Several additional research and development projects are ongoing
 Natural abundanceQ-value 
Isotope(%)(keV)Experiment
48Ca0.1874262 ± 0.84CANDLES
76Ge7.82039.006 ± 0.050GERDA, MAJORANA
82Se9.22997.9 ± 0.3SuperNEMO, LUCIFER
96Zr2.83347.7 ± 2.2
100Mo9.63034.40 ± 0.17AMoRE, LUMINEU, MOON
110Pd11.82017.85 ± 0.64
116Cd7.52813.50 ± 0.13COBRA, CdWO4
124Sn5.642292.64 ± 0.39
130Te34.52527.518 ± 0.013CUORE
136Xe8.92457.83 ± 0.37EXO, KamLAND-Zen, NEXT
150Nd5.63371.38 ± 0.20SNO+, MCT

Neutrinoless double β-decay is also sensitive to different scenarios with sterile neutrinos [20]. The sum in Eq. (1) will then run over more than four neutrino mass states and the corresponding mixing matrix elements. The experimental approaches can be classified into two methods (Fig. 4) [21] as described below.

Figure 4.

Two different experimental configurations in the search for neutrinoless double β-decay.

2.1 “Source = detector” configuration

In the “source = detector” configuration the double β-decay nuclei are part of the detector, which measures the sum of the energy of both β-electrons. The experimental implementations of these calorimeters are semiconductors (e.g. isotopes: 76Ge, 116Cd; experiments: GERDA, MAJORANA, COBRA), cryo-bolometers (e.g. isotopes: 130Te, 82Se; experiments: CUORE, LUCIFER), and liquid scintillators (e.g. isotopes: 48Ca, 136Xe, 150Nd; experiments: EXO-200, SNO+, NEXT, KamLAND-Zen, CANDLES). In general, this method allows more easy installation of a large target mass.

Currently the most sensitive limits come from the EXO-200 and KamLAND-Zen experiments using a large amount of enriched 136Xe. EXO-200 is a liquid xenon time projection chamber with a fiducial target mass of 80 kg installed at the WIPP in New Mexico, USA. Coincident drifted charge and scintillation light read-out allows one to improve the energy resolution and to reduce the background. EXO-200 gave a half-life limit on neutrinoless double β-decay [22] of

display math(3)

The KamLAND-Zen experiment uses the KamLAND detector, which was built for long-baseline reactor neutrino oscillation measurements, in which a nylon-based inner balloon of 3 m in diameter was inserted. This balloon is filled with 13 t of xenon-loaded liquid scintillator. The scintillation light coming from decays in this balloon is detected by the photomultipliers surrounding the KamLAND detector. For the neutrinoless double β-decay search a fiducial volume with 2.70 m diameter containing 179 kg of 136Xe was used yielding a half-life limit [23] of

display math(4)

Both the EXO-200 and the KamLAND-Zen results exclude the claimed evidence of part of the Heidelberg–Moscow collaboration for a large part of matrix element calculations.

The GERDA experiment [24] at the Gran Sasso underground laboratory is proceeding in two phases with the option of a third phase together with the MAJORANA experiment [25]. GERDA uses enriched germanium1 embedded in a shielding cryostat filled with liquid argon, which itself sits in a water veto tank (Fig. 5). This new shielding technique allows an improvement in the background rate by an order of magnitude compared to the Heidelberg–Moscow experiment. For a second phase, point contact BEGe detectors for optimized pulse shape analysis are currently produced aiming for another factor of 10 in background reduction. The GERDA experiment started data taking in November 2011 and first new results in the form of a new 2ν double β-decay half-life have been obtained [26]. The GERDA collaboration just recently unblinded their phase I data with a total accumulation of 21.6 kg yr[27]. The number of events agrees well with the background expectation.The experiment sets an lower limit at 90∼%C.L. of the neutrinoless double β-decay half-life of

display math(5)

by GERDA data alone and of

display math(6)

by using data from former Germanium experiments in addition. With its about an order of magnitude lower background compared to previous Germanium experiments the GERDA experiment clearly disfavors the claim by part of the Heidelberg–Moscow collaboration.

Figure 5.

View of the GERDA liquid argon cryostat within water shielding which is instrumented as muon veto. (Courtesy of the GERDA collaboration.)

Recently there has been a revived interest in neutrinoless double electron capture [28] because of potential resonance enhancement with an excited state of the daughter nucleus [29, 30]. Due to the sharpness of the resonance major action was taken with Penning traps to provide better atomic masses, and indeed some systems like 152Gd seem to fulfill the requirement for resonance enhancement (e.g. [31]). There is still a lack of understanding as to what the signal of neutrinoless double electron capture to the ground state could be.

2.2 “Source ≠ detector” configuration

In the this configuration the double β-decay source is separated from two tracking calorimeters, which determine direction and energy of both β-electrons separately (e.g. isotopes: 82Se, 100Mo; experiments: NEMO3 and its much larger successor SuperNEMO, ELEGANT, MOON).

With this method the most sensitive limit comes from the NEMO3 experiment [32] in the Modane underground laboratory. NEMO3 used thin source foils of a total area of 20 m2. These foils contained 7 kg of the double β-decay isotope 100Mo and 1 kg of the double β-decay isotope 82Se. The foils were surrounded by a tracking chamber in a magnetic field composed of 6400 drift cells working in Geiger mode and a calorimeter made out of 1940 plastic scintillators. The recent upper limits on neutrinoless double β-decay from NEMO3 are [32]:

display math

Although it requires much larger detectors to accumulate similar large target masses as in the “source = detector” case, there is the advantage that the independent information of both electrons allows one to study double β-decay processes with two neutrinos in detail. In the case of neutrinoless double β-decay being detected, the angular correlation of both electrons will allow some conclusions to be drawn on the underlying process.2

3 Direct neutrino mass experiments

The signature of a non-zero neutrino mass is a tiny modification of the spectrum of the β-electrons near its endpoint (Fig. 2), which has to be measured with very high precision. To maximize this effect, β-emitters with low endpoint energy (e.g. inline image keV, $E0$(3H) = 18.57 keV) are favored [33].

3.1 “Source ≠ detector” configuration: tritium β-decay experiments

Tritium is the standard isotope for this kind of study due to its low endpoint of 18.6 keV, its rather short half-life of 12.3 yr, its super-allowed shape of the β-spectrum, and its simple electronic structure. Tritium β-decay experiments using a tritium source and a separated electron spectrometer have been performed in the search for the neutrino mass for more than 60 years [16, 17] yielding a sensitivity of 2 eV in the experiments at Mainz [34] and Troitsk [35]. The huge improvement of these experiments in the final sensitivity as well as in solving the former “negative inline image” problem with respect to previous experiments is mainly a result of the use of new spectrometers of MAC-E filter type and of careful studies of the systematics.

To further increase the sensitivity to the neutrino mass down to 200 meV by a direct measurement the KArlsruhe TRItium Neutrino experiment (KATRIN) [36, 37] is currently being set up at the Karlsruhe Institute of Technology. Since inline image is the observable, this requires an improvement by two orders of magnitude compared to the previous tritium β-decay experiments at Mainz and Troitsk. The KATRIN design is based on the successful MAC-E filter spectrometer technique combined with a very strong windowless gaseous molecular tritium source (WGTS) [37]. Figure 6 illustrates the whole 70 m long setup.

Figure 6.

Schematic of the 70 m long KATRIN experiment consisting of calibration and monitor rear system (yellow), windowless gaseous tritium source (a), differential pumping and cryo-trapping section (b), small pre-spectrometer (c), large main spectrometer (d), and segmented PIN-diode detector (e). Not shown is the separate monitor spectrometer. (Courtesy of the KATRIN collaboration.)

The WGTS essentially consists of a 10 m long tube of 9 cm in diameter kept at 30 K. Molecular tritium gas injected in the middle of this tube freely streams to both ends of the beam tube. The tritium gas is pumped back by huge turbo-molecular pumps placed at pump ports intersected with straight sections. The β-electrons are guided by superconducting solenoids housing the beam tubes. A so-called WGTS demonstrator has been set up to prove that the new concept of ultra-stable beam-pipe cooling works: gaseous and liquid neon is sent through two tubes welded onto the beam tube. By stabilizing the pressure of this two-phase neon the temperature of the beam tube can be stabilized well below the requirement of 10−3 [38]. The input pressure is chosen to obtain a total column density of 5 × 1017 molecules per square centimeter allowing a near maximum count rate at moderate systematic uncertainties [39]. Currently the WGTS demonstrator is being upgraded into the full WGTS.

The electron guiding and tritium retention system consists of a differential and a cryogenic pumping unit. It has been demonstrated that tritium flow reduction by differential pumping is about as large as expected by Monte Carlo simulations [40]. Inside the differential pumping sections Fourier transform ion cyclotron resonance Penning traps will be installed to measure the ion flux from the tritium source [41]. Ions will be ejected from the beam by a transverse electric field. The principle of the cryogenic pumping section based on argon frost at 3–4.5 K has been demonstrated in a test experiment [42]. The overall tritium reduction amounts to 10−14.

A pre-spectrometer will transmit only the interesting high-energy part of the β-spectrum close to the endpoint into the main spectrometer [43], in order to reduce the rate of background-producing ionization events therein. The big main spectrometer is of MAC-E filter type as is the pre-spectrometer. It is essentially an electric retarding spectrometer with a magnetic guiding and collimating field [44]. In order to achieve a strong energy resolution of 1:20,000 the magnetic field in the analyzing plane in the center of the spectrometer has to be 20,000 times smaller than the maximum magnetic field of 6 T provided by the pinch magnet. Due to conservation of the magnetic flux from the WGTS to the spectrometer it needs to have a diameter of 10 m in the analyzing plane. To avoid background by scattering of β-electrons inside the spectrometer, extreme requirements for the vacuum pressure of inline image mbar are necessary [45]. The β-electrons which have enough energy to pass the MAC-E filter are counted with a state-of-the-art segmented PIN detector. The spatial information provided by the 148 pixels allows one to correct for the residual inhomogeneities of the electric retarding potential and the magnetic fields in the analyzing plane. Active and passive shields minimize the background rate at the detector.

Of crucial importance is the stability of the retarding potential. KATRIN uses a twofold way to achieve the necessary redundancy: a custom-made ultrahigh-precision high-voltage divider [46] developed together with the Physikalisch-Technische Bundesanstalt and a state-of-the-art 8.5 digit digital voltmeter measure directly the retarding voltage. In addition the retarding voltage is applied to a third MAC-E filter, the so-called monitor spectrometer reusing the former MAC-E filter at Mainz. The line position of ultra-stable electron sources based on the isotope inline image [47] is continuously compared to the retarding voltage of the main spectrometer. Both methods reach the required parts per million precision.

The sensitivity limit of 200 meV on the neutrino mass for the KATRIN experiment is based on a background rate of 10−2 counts per second, observed under optimal conditions in the experiments at Mainz and Troitsk using similar MAC-E filters. To reach this low background rate with the much larger KATRIN instrument requires new methods. At Mainz the main residual background originated from secondary electrons ejected from the walls/electrodes at high potential by passing cosmic muons or by γ-rays from radioactive impurities. Although there is very effective magnetic shielding by the conservation of magnetic flux, small violations of the axial symmetry or other inhomogeneities allowed a fraction of about 10−5 of these secondary electrons to reach the detector and to be counted as background. A new method to reject these secondary electrons from the electrodes has been developed and successfully tested at the Mainz spectrometer [48]: nearly mass-less wires are installed in front of these electrodes, which are put at a more negative electrical potential than the electrode potential by −100 to −200 V. For KATRIN a double-layer wire electrode system consisting of 248 modules with 23,440 wires in total has been developed, which should reduce the secondary electron background by a factor of 100 [49]. Its installation (Fig. 7) was completed in early 2012.

Figure 7.

Wire electrode system inside the KATRIN main spectrometer during installation. (Photo: M. Zacher.)

Other relevant background sources are decays of radioactive atoms in the spectrometer volumes, e.g. the fast-decaying radon isotope 219Rn from emanation out of the non-evaporable getter pumps [50] or small amounts of tritium originating from the WGTS [51]. They create electrons, which might be stored by the magnetic mirror effect and/or by the negative potentials of the two MAC-E filters or within the non-avoidable Penning trap between the pre-spectrometer and the main spectrometer. For these backgrounds new methods have been developed to avoid storage of electrons or to eject them [52-54].

Since the KATRIN experiment will investigate only the very upper end of the β-spectrum, quite a few systematic uncertainties will become negligible because of excitation thresholds. Others systematics like the inelastic scattering fraction or the source intensity will be controlled very precisely by measuring the column density online using an angular-selective electron gun [55, 56], by keeping the temperature and pressure within the tritium source constant at the per mille level [39], and by determining the tritium fraction of the gas in the source using laser Raman spectroscopy to the sub-per mille level [57]. An important consistency check of the correct systematic corrections will be comparison of the endpoint energy E0 fitted from the β-spectrum with a precision value derived from ultrahigh-precision ion cyclotron resonance mass spectroscopy in a multi-Penning trap setup measuring the 3He–3H mass difference [58] with the final goal of using the measured Q-value in the neutrino mass fit. KATRIN's sensitivity will allow full investigation of the quasi-degenerate neutrino mass regime to distinguish between different neutrino mass models as well as full investigation of the cosmological relevant neutrino mass range, where neutrino masses would shape significantly structure formation. In addition, the KATRIN experiment will be sensitive to contributions to sterile neutrinos [59-61] as suggested by the so-called reactor anomaly.

The commissioning of the KATRIN spectrometer and detector system started in May 2013. The tritium source as well as the electron transport and tritium elimination section will be put into operation in 2014. First tritium data with the full KATRIN setup are expected in 2015.

There is also research and development involving rather different approaches, like Project-8, which intends to measure the endpoint spectrum of tritium β-decay by detecting the radio emission of coherent cyclotron radiation from a KATRIN-like tritium source [62, 63]. Its main idea is that the cyclotron frequency inline image scales inversely with γ, only the radiated power but not the frequency depending on the angle of the emitted β-electron with respect to the magnetic field. Measuring the β-spectrum by synchrotron radiation has the principal advantage that the radiofrequency photons can leave a tritium source which is already opaque for electrons, thus allowing much larger source strengths. Currently the Project-8 collaboration is investigating whether this very low-intensity coherent cyclotron radiation can be detected.

3.2 “Source = detector” configuration: 187Re β-decay and 163Ho electron capture experiments

3.2.1 187Re β-decay experiments

Compared to tritium, the isotope inline image has a 7 times lower endpoint energy of 2.47 keV resulting in a 350 times higher relative fraction of the β-spectrum in the interesting endpoint region. Unfortunately inline image exhibits a very complicated electronic structure and has a very long half-life of 4.3 × 1010 yr. This disadvantage can be compensated for by using it as a β-emitter in cryo-bolometers, which measure the entire energy released in the absorber, except that of the neutrino.

A cryo-bolometer is not an integral spectrometer like the MAC-E filter but measures always the entire β-spectrum. Pile-up of two random events may pollute the endpoint region of a β-decay on which the neutrino mass is imprinted. Therefore cryo-bolometers with milligram masses are required to suppress pile-up by four or more orders of magnitude. Unfortunately large arrays of cryo-bolometers are then required to reach the necessary sensitivity to the neutrino mass. Another technical challenge is the energy resolution of the cryo-bolometers. Although cryo-bolometers with an energy resolution of a few eV have been produced with other absorbers, this resolution has not yet been achieved with rhenium.

Two groups have started in the field of inline image β-decay experiments. The MANU experiment at Genoa used one metallic rhenium crystal of 1.6 mg working at a temperature of 100 mK and read out with a germanium-doped thermistor. The β-environmental fine structure was observed for the first time giving rise to a modulation of the shape of the β-spectrum by the interference of the out-going β-electron wave with the rhenium crystal [64]. The spectrum near the endpoint allowed setting an upper limit on the neutrino mass of inline image eV [65]. The MiBeta collaboration at Milan used 10 crystals of AgReO4 with a mass of about 0.25 mg each [66]. The energy resolution of a single bolometer was about 30 eV. One year of data taking resulted in an upper limit of inline image eV [66].

Both groups are now working together with additional groups in the MARE project [67] to further the development of sensitive micro-calorimeters investigating inline image β-decay. MARE consists of two phases [68]. MARE-1 aims to investigate alternative micro-calorimeter concepts to improve energy resolution, to shorten the rise time of the signals, and to develop possibly a multiplexing read-out. A summary of the sensitivity reached dependent on these detector properties can be found in [69]. Among the possible technologies for MARE are transition edge and neutron-doped thermistors for temperature read-out, but also new technologies based on magnetic micro-calorimeters [70]. These new detectors are being tested in medium-size arrays with up to 300 cryo-bolometers enabling MARE-1 to reach a sensitivity to the neutrino mass of a few inline image. After selection of the most successful technique a full-scale experiment with sub-eV sensitivity to the neutrino mass will then be set up in MARE phase 2 comprising about 50,000 detectors.

3.2.2 163Ho electron capture experiments

MARE is not only aimed at inline image β-decay but also at investigating the electron capture of inline image, triggered by the persisting difficulties with superconducting metallic rhenium absorbers coupled to the sensors [71]. The isotope inline image could be implanted into well-suited cryo-bolometers. The very upper end of the electromagnetic de-excitation spectrum of the inline image daughter 163Dy looks similar to the endpoint spectrum of a β-decay and is sensitive to the neutrino mass [72]. Additionally, the ECHO collaboration has been set up to investigate the direct neutrino mass search with inline image implanted in magnetic micro-calorimeters [73]. In these detectors, the temperature change following an energy absorption is measured by the change of magnetization of a paramagnetic sensor material (Au:Er) sitting in an external magnetic field. This change of magnetization is read out by a superconducting quantum interference device. A first inline image spectrum has been presented [70]. Again much work has been undertaken to develop a multiplexing read-out technology to allow the running of large arrays of these magnetic micro-calorimeters.

4 Conclusions

The absolute neutrino mass scale is addressed using three different methods. The analysis of large-scale structure data and the anisotropies of the cosmic microwave background radiation are very sensitive but model dependent. The search for neutrinoless double β-decay requires neutrinos to be their own antiparticles (Majorana neutrinos) and measures a coherent sum over all neutrino masses contributing to the electron neutrino with unknown phases. Therefore – even without the contribution of other beyond the Standard Model physics processes – the value of the neutrino mass cannot be determined very precisely. On the other hand, the discovery of neutrinoless double β-decay would involve the detection of lepton number violation, which would be an extraordinarily important discovery. A few double β-decay experiments of the second generation like EXO-200 KamLAND-Zen and GERDA phase I have already delivered exciting new data; much more, e.g. from these and other experiments, will come in the near future. Among the various ways to address the absolute neutrino mass scale, investigation of the shape of β-decay spectra around the endpoint is the only real model-independent method, independent of other beyond the Standard Model physics processes. The KATRIN experiment is being set up at Karlsruhe and will start data taking in 2015, whereas the MARE experiment is commissioning a small array of detectors starting with MARE-1 and ECHO is developing a new technology for electron capture experiments. The field of cryogenic calorimeters is also driven by the field of astronomy, where arrays of cryogenic bolometers with inline image (1000) pixels have been established already. From both laboratory approaches, the search for neutrinoless double β-decay and the direct neutrino mass determination, we expect in the coming years sensitivities on the neutrino mass of inline image (100) meV.

Acknowledgements

The work of the authors is supported by the German Ministry for Education and Research (BMBF) and the German Research Society (DFG).

  1. 1

    The enrichment of the double β-decay isotope 76Ge is about 86%; the total mass of the phase one detectors amounts to 18 kg.

  2. 2

    A theorem by Schechter and Valle [11] requires the neutrinos to have non-zero Majorana masses, if neutrinoless double β-decay is proven to exist, but the dominant process could still be different, e.g. based on other beyond Standard Model physics like right-handed weak charged currents, which would show a completely different angular distribution of the two electrons with respect to a neutrino mass term.

Biographies

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    Christian Weinheimer studied physics and mathematics at Mainz University and received his Ph.D. degree in physics in 1993. He was CERN Fellow from 1995 to 1996. Since 2004 he has been full professor at Münster University. His research focuses on neutrino masses, dark matter, and fundamental interactions with the experiments KATRIN, XENON, SpecTrap, and WITCH.

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    Kai Zuber studied physics at Würzburg and Heidelberg University and received his Ph.D. degree in 1992. He spent postdoctoral periods in Heidelberg and Dortmund from 1993 to 2002 and was Heisenberg Fellow of DFG at Oxford University from 2002 to 2005. Since 2008 he has been full professor at TU Dresden with main research interests in neutrinos (masses, solar, and general), fundamental interactions, with the experiments COBRA, GERDA, SNO+, HALO, Borexino, and ISOLTRAP.