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Two-Neutrino Double-Beta Decay Ruben Saakyan Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom; email: [email protected]

Annu. Rev. Nucl. Part. Sci. 2013. 63:503–29

Keywords

First published online as a Review in Advance on August 7, 2013

nuclear matrix elements, low-background technologies, underground detectors

The Annual Review of Nuclear and Particle Science is online at nucl.annualreviews.org This article’s doi: 10.1146/annurev-nucl-102711-094904 c 2013 by Annual Reviews. Copyright  All rights reserved

Abstract Two-neutrino double-β decay is a radioactive process with the longest lifetime ever observed. It has been a subject of experimental research for more than 60 years and remains an important topic in modern nuclear and particle physics. This review examines the process in detail, covers its theoretical and experimental aspects, and describes the results obtained so far and future challenges.

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Contents

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1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. PHENOMENOLOGY OF TWO-NEUTRINO DOUBLE-BETA DECAY . . . . . 2.1. Double-Beta Decay in Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Double-Beta Decay Rate, Phase Space, and Electron Spectra . . . . . . . . . . . . . . . . . 3. NUCLEAR MATRIX ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. EXPERIMENTAL METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Indirect Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Direct Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Isotope Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. BACKGROUNDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Natural α, β, and γ Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Neutrons from Natural Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Cosmic Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Shielding for Double-Beta Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. EXPERIMENTAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. First Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. 76 Ge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. NEMO3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. 48 Ca and 116 Cd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. 136 Xe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. Transitions to Excited States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Two-Neutrino ECEC, ECβ + , and β + β + Transitions . . . . . . . . . . . . . . . . . . . . . . . . 7. DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Experimental Nuclear Matrix Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Time Variation of the Fermi Coupling Constant and Two-Neutrino Double-Beta Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. CONCLUSION AND OUTLOOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

504 505 505 507 510 512 512 513 514 515 515 517 517 517 518 518 520 520 521 522 523 525 525 525 526 526

1. INTRODUCTION Two-neutrino double-β decay (2νββ) is a rare nuclear transition in which two neutrons inside a nucleus are simultaneously transformed into two protons accompanied by the emission of two electrons and two antineutrinos. The process was first suggested in 1935 by Goeppert-Mayer (1), who estimated the half-life of such a process, by using the then-recently-formulated Fermi theory of β decay, to be >1017 years. The reason for the rarity of such a decay is that, although allowed, it is a second-order process in the Standard Model of electroweak interactions. Almost 80 years later, 2νββ has been observed in 12 nuclei with half-lives ranging from ∼1019 to 1024 years. As is well known, a neutrinoless version of the double-β decay (0νββ) provides a powerful instrument that allows one to investigate the most fundamental questions of particle physics. This process violates the total lepton number and therefore is forbidden in the Standard Model: (A, Z) → (A, Z + 2) + 2e − . Considerable experimental efforts are being dedicated to the detection of 0νββ. This interest is well justified because such experiments represent the only practical way of establishing the 504

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a u d d

b V–A

W–

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V–A

W–

u d u e –L νR

νL

d d u

u d d

e –L

νR

V–A

u d u

νR

e –L W–

u d u

d d u

V–A

W–

e –L u d u

Figure 1 Feynman diagrams of (a) 0νββ decay with light Majorana neutrino exchange and (b) 2νββ decay.

nature of neutrino mass—namely whether a neutrino is identical to its antiparticle (a Majorana particle)—and therefore of shedding light on the mechanism of the tiny (but nonzero) neutrino mass generation established by neutrino oscillation experiments (2). Light Majorana neutrinos represent the most-discussed mechanism of 0νββ (Figure 1a) and provide one of the most sensitive tools with which to determine the absolute neutrino mass. Regardless of the underlying mechanism, 0νββ violates the full lepton number and therefore provides a unique window into physics beyond the Standard Model. This review focuses on the version of the process that is allowed in the Standard Model: 2νββ (Figure 1b). The study of this process is important in its own right because it provides a tool for testing a possible higher-order Standard Model process and provides insights into nuclear structure. Importantly, 2νββ provides vital information for the 0νββ search. In particular, it provides experimental access to the values of nuclear matrix elements (NMEs) that can then be used to inform NME calculations for the 0νββ mode, which in turn is necessary to extract the particle physics parameters responsible for lepton number violation. Also, knowledge about 2νββ rates and the spectral shapes of electron energies emitted in the decay can mitigate this ultimate background for 0νββ. This review is structured as follows. Section 2 is dedicated to the phenomenology of the 2νββ transition. We review criteria for its occurrence and the basic formulae determining its probability. Various models used to calculate the aforementioned NMEs are briefly reviewed and compared in Section 3. Section 4 describes experimental methods, both direct and indirect, that are used to search for 2νββ decay. Key backgrounds that have to be considered when searching for this rare process are discussed in Section 5, and Section 6 reviews the main results obtained during 60 years of experimental research. We discuss the implications of 2νββ in Section 7 and conclude in Section 8.

2. PHENOMENOLOGY OF TWO-NEUTRINO DOUBLE-BETA DECAY 2.1. Double-Beta Decay in Nuclei The stability of the nucleus is determined by its binding energy or, equivalently, its mass. Weizs¨acker (3) made the first successful attempt to describe the mass of a nucleus in what is www.annualreviews.org • Two-Neutrino Double-Beta Decay

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Even-A

M(A,Z)

Odd-odd

Even-even β–

(b)

(d) β+

(a) β–β–

(e)

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β+β+

(c) Z–2

Z–1

Z

Z+1

Z+2

Figure 2 Mass parabolas for nuclear isobars with even A. Due to the pairing term in the semiempirical mass formula, even-even nuclei have lower masses than do odd-odd nuclei. Thus, β − decay is impossible from point a to point b, whereas in a second-order process, β − β − decay is energetically possible from point a to point c. Similarly, β + β + decay or double–electron capture decays can occur between point e and point c.

widely known as the semiempirical mass formula (SEMF): M (A, Z) = Zm p + N mn − a V A + a S A 2/3 + a C

Z2 (N − Z)2 + δ(A, Z), + a A A 1/3 A

where the first two terms are simply the mass of all protons and of all neutrons in the nucleus and the remaining terms represent the binding energy that holds the nucleus together. Whether the nucleus undergoes a weak decay depends on the last pairing term, δ(A,Z), which is zero for odd-A nuclei, negative for even-even nuclei, and positive for odd-odd nuclei. Consequently, even-A nuclear isobars can be described with two parabolas in M(A,Z) versus Z plots, as shown in Figure 2. Even-even nuclei generally have lower masses than do their odd-odd counterparts, and as a result, simple β decay is energetically forbidden (Figure 2). However, in a second-order process, double-β decay may be possible. Depending on the relative numbers of protons and neutrons in the nucleus, four different possibilities are allowed in the Standard Model: β − β − : (A, Z) → (A, Z + 2) + 2e − + 2ν¯ e , β + β + : (A, Z) → (A, Z − 2) + 2e + + 2νe , ECEC : 2e − + (A, Z) → (A, Z − 2) + 2νe , ECβ + : e − + (A, Z) → (A, Z − 2) + e + + 2νe , where EC stands for electron capture (usually a K-shell electron is captured). The energy release in the decay is distributed between the lepton products and the recoil of the nucleus, which usually can be neglected. For β − β − decay, this energy is Q ββ = M (A, Z) − M (A, Z + 2), where M(A,Z) is the atomic mass of the isotope with mass number A and atomic number Z. The Qββ values are smaller in the case of β + β + , ECEC, and ECβ + ; they are M(A,Z) − M(A,Z − 2) − 4me c2 , M(A,Z) − M(A,Z − 2) − 2ε , and M(A,Z) − M(A,Z − 2) − 2me c2 − 2ε , respectively 506

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Table 1 The most experimentally feasible isotopes and their key features

Annu. Rev. Nucl. Part. Sci. 2013.63:503-529. Downloaded from www.annualreviews.org by Universidad Nacional Autonoma de Mexico on 08/12/14. For personal use only.

Isotope

Abundance (%)

Qββ (MeV)

G2ν (10−18 year−1 )

48 Ca

0.187

4.263

76 Ge

7.8

2.039

0.0482

82 Se

9.2

2.998

1.60

96 Zr

2.8

3.348

7.83

100 Mo

9.6

3.035

4.13

116 Cd

7.6

2.813

3.18

130 Te

34.08

2.527

1.53

136 Xe

8.9

2.459

1.43

150 Nd

5.6

3.371

15.6

36.4

The phase-space factors G2ν are from Reference 4. G2ν for 96 Zr, 100 Mo, and 116 Cd are calculated within the single-state dominance model (see Section 3).

(here, ε is the excitation energy of the atomic shell of the daughter nucleus). Consequently, these processes have a lower probability compared with β − β − decay due to a smaller phase space, and experimentally they are much more challenging to observe. This review therefore focuses primarily on β − β − transitions. The study of isotopes that have higher abundance and larger Qββ values is preferred in experimental research due to their higher expected rates and smaller backgrounds. Table 1 lists the most feasible of the commonly studied ββ isotopes, their natural abundance, their Qββ values, and their two-neutrino mode phase-space factors (4).

2.2. Double-Beta Decay Rate, Phase Space, and Electron Spectra The energy sum of the two electrons in the two-neutrino mode has a continuum spectrum with an end point at Qββ due to neutrinos carrying away part of the energy. In the neutrinoless mode, this spectrum is a δ function at Qββ because all the transition energy goes into the kinetic energy of the two electrons. The exception is a zero-neutrino mode with the emission of a light or massless goldstone boson, majoron B (0νββB) (Figure 3). The rate of 2νββ can be calculated by invoking the recipe of the Fermi golden rule for simple β decay. To a good approximation, the kinematic part (the phase space of the leptons emitted in the decay) and the nuclear part (the matrix element responsible for the transition probability between two nuclear states) can be factorized as  2ν =

1 = G2ν (Q ββ , Z)|M 2ν |2 , 2ν T 1/2

where G2ν is obtained by integration over the phase space of four leptons emitted in the decay and can be calculated exactly. The NME M2ν deals with the nuclear structure of the transition and is much more difficult to evaluate. The rate of the zero-neutrino mode, forbidden in the Standard Model, can be factorized as  0ν =

1 = G0ν (Q ββ , Z)|M 0ν |2 η2 , 0ν T 1/2

where η2 is the lepton number–violating parameter that represents New Physics. The mostdiscussed mechanism involves a light Majorana mass exchange, <mν >, but there are many other www.annualreviews.org • Two-Neutrino Double-Beta Decay

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100Mo

0νββ

0.7

2νββ 0νββB

Arbitrary units

0.6 0.5 0.4 0.3

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0.2 0.1 0

0

500

1,000

1,500

2,000

2,500

3,000

3,500

Energy (keV) Figure 3 Theoretical spectra of the summed energy of two electrons emitted in 2νββ, 0νββB, and 0νββ modes of the 100 Mo double-β decay.

possibilities (see, e.g., Reference 5 for a relevant discussion). Knowledge about M 0ν is clearly necessary to extract the New Physics parameters. Unfortunately, there is no direct experimental observation available to independently pin down M 0ν . We have to rely on nuclear models to do that. Any experimental input into these models is, of course, important. One of these inputs comes from 2νββ. The formula for  2ν shows that once 2νββ is observed, the experimental value of the corresponding NME can be extracted. The nuclear models used for M 2ν calculations can therefore be directly probed. General methods for phase-space factor calculations in double-β decay have been developed (6–8). The phase-space factor is obtained by integration over all possible energies and angles of the leptons emitted in the decay. For the two-neutrino mode, these leptons are the two electrons and the two (anti)neutrinos:  E0 −me  E0 −Ee1 F (Z, Ee1 ) p e1 Ee1 dEe1 × F (Z, Ee2 ) p e2 Ee2 dEe2 G2ν ∝ me E0 −Ee1 −Ee2

 ×

0

me 2 p ν1 (E0 − Ee1 − Ee2 − p ν1 )2 d p ν1 ,

which is written in the natural units  = c = 1, where E0 = Qββ + 2me , F(Z,E) is the Fermi function that describes the Coulomb effect on the outgoing electrons and Ee , pe , and pν are the energy and momentum of the electrons and neutrinos emitted in the decay. In the Primakoff–Rosen approximation (9) for the nonrelativistic Coulomb correction, the spectrum of the individual electrons can be analytically calculated from the phase-space integral (10): dN ∼ (T e + 1)2 (T 0 − T e )6 [(T 0 − T e )2 + 8(T 0 − T e ) + 28]. dT e Here, Te is the kinetic energy of the electron in the units of electron mass and T0 is its maximum value: T0 = Qββ − 2. The single-electron energy spectrum is shown in Figure 4 for the isotope 508

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a

0.7

Probability (arbitrary units)

0.1

Probability (arbitrary units)

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0.6 SSD HSD 0.4

0.2

b

0.6 0.5 0.4 0.3 0.2

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0.1 0

0

0.5

1.0

1.5

Ee – me

2.0

c2 (MeV)

2.5

0 0

3.0

0.5

1

1.5

2

2.5

3

E1 + E2 – 2mec2 (MeV)

Figure 4 Theoretical electron energy distributions for 2νββ decay of 100 Mo to the ground state of 100 Ru obtained using the single-state dominance (SSD) and higher-state dominance (HSD) models (19). (a) Single-electron energies. (b) Energy sum of two electrons. The single-electron energy spectra have a much more significant discriminating power.

of 100 Mo. The summed kinetic energy of the two electrons, which is often the only quantity detected in an experiment, is given by   K3 K4 4K 2 dN ∼ K (T 0 − K )5 1 + 2K + + + , dK 3 3 30 where K is the summed kinetic energy in the units of electron mass (Figures 3, 4b). Finally, by integrating the equation for dN/dT e over Te we can find the dependence of the 2νββ transition probability on T0 and therefore Qββ :   T0 T2 T3 T 04 + 0 + 0 + . W (2ν) ∼ T 07 1 + 2 9 90 1,980 The important result is the very strong dependence of the 2νββ probability on the Qββ value through its dependence on the phase space: W 2ν ∝ G2ν ∝ Q 11 ββ . An analogous calculation for the zero-neutrino decay shows a weaker dependence, G0ν ∝ Q 5ββ . To first order, the phase-space factor determines the shape of the electron spectra as well as their angular distribution. The angle between the two electrons follows the 1 − β 1 β 2 distribution for 0+ → 0+ transitions and the 1+β 1 β 2 /3 distribution for 0+ → 2+ transitions (here β = p/E). The contribution of the NME to the shape of the energy and angular distribution is small, and it affects primarily the absolute value of the transition probability. An exhaustive list of phase-space factors can be found in Reference 11. The phase-space factors were recalculated for most β − β − nuclei of interest (4) by taking advantage of modern developments www.annualreviews.org • Two-Neutrino Double-Beta Decay

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Jπ 1+ 2–

223 keV

1+

0+ QEC = 168.4(18)

15.3 s 100 Tc

100Mo

Qββ = 3,034.40(17)

g.s.

Qβ – = 3,202.8(17)

0+

1,130 keV

0+ 100 Ru

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Figure 5 Nuclear-level diagram for the isotope of 100 Mo (83). Abbreviation: g.s., ground state.

in the numerical evaluation of the Dirac wave function for electrons. The results are particularly interesting for heavy nuclei, in which relativistic and screening corrections play a major role. The results for light nuclei (such as 48 Ca and 76 Ge) are consistent with previous calculations, whereas those for heavy nuclei (such as 136 Xe and 150 Nd) are ∼30% lower than previous values.

3. NUCLEAR MATRIX ELEMENTS NMEs define the nuclear-structural part of the probability for the double-β transition between the parent and daughter nuclei. NMEs are notoriously difficult to calculate even in the case of a single-β decay. Considering that making such a calculation involves mapping out all possible transitions between the two complex multibody systems (initial and final nuclei), it is not surprising that this is a difficult task. As mentioned above, 2νββ allows one to experimentally verify nuclear models used for the M 2ν calculation. Although there is no one-to-one correspondence between M 2ν and M 0ν , this experimental input is essential for M0ν evaluation, which in turn is crucial for pinning down the New Physics parameters responsible for full lepton number violation. Figure 5 shows a nuclear-level diagram of the double-β decay transition for the isotope of 100 Mo. The transition between the parent and daughter even-even nuclei goes through a virtual odd-odd nucleus. It is necessary to evaluate the wave functions of both the initial and final nuclei and to evaluate the operator that connects them. This operator is responsible for a simultaneous conversion of two neutrons bound in the ground (0+ ) state of the parent even-even nucleus into two protons bound in the ground (0+ ) or excited (2+ ) state of the daughter even-even nucleus. Due to the isospin conservation, the NME of the two-neutrino mode contains only the Gamow–Teller (GT) part (unlike the zero-neutrino mode, wherein the Fermi part should also be included). A general formula for the two-neutrino NME for ground-state transitions is 2ν = M GT

+ + +  0+f ||τ + σ ||1+ m 1m ||τ σ ||0i  m

Em − (M i + M f )/2

,

where the summation goes over all possible 1+ states of energy, Em , of the intermediate oddodd nucleus. The interpretation of the above formula is straightforward. The last factor in the numerator is the amplitude of the β − decay of the initial nucleus, and the first factor represents

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the amplitude of the β + decay of the final nucleus. Therefore, the M 2ν description is equivalent to the description of the full β strength functions of both the initial and final nuclei. Note that M 2ν is very sensitive to nuclear structure because the ground state–to–ground state transitions exhaust only a small fraction of the double-GT sum rule. There are two basic approaches to the evaluation of M 2ν : the nuclear shell model (NSM) and the quasiparticle random phase approximation (QRPA). Each has its own strengths and weaknesses. The NSM is perhaps the most straightforward way of solving the NME problem. In this approach, one assigns a set of valence single-particle states and finds an effective Hamiltonian that is based on the free nucleon–nucleon interaction but modified to describe the effective nuclear interaction for that particular set. All configurations are used in the diagonalization of the Hamiltonian and the evaluation of the NME. The Hamiltonian is adjusted using the information from nuclear spectroscopy (energy levels and transition probabilities) of the relevant nuclei. Unfortunately, due to computational constraints only a limited set of single-particle states can be included in the NSM. The effects of single-particle states that are not included are simulated by use of effective operators, bringing uncertainties into these calculations. Consequently, the NSM is most successful in evaluating the NMEs of lighter nuclei with fewer valence nucleons. The doubly magic nucleus of 48 Ca, for example, has served as a benchmark calculation for the NSM. Some of the most advanced calculations involving the NSM were carried out in References 12 and 13. In a sense, the QRPA explores the opposite approach. It includes essentially all relevant singleparticle states but limits itself to certain types of correlations, thereby reducing complexity. This method does not use the free nucleon–nucleon interaction but instead exploits phenomenological interactions with several adjustable parameters, such as the repulsive particle–hole spin–isospin interaction and the attractive particle–particle interaction. As a result, the experimental values for M2ν can be reproduced for several isotopes if the empirical parameter g p p , the strength of the particle–particle interaction, is adjusted. The dependence of the QRPA on the g p p parameter, which sometimes leads to the collapse of its solutions, is a frequent subject of criticism. Nevertheless, different QRPA calculations of M 0ν for a particular isotope can converge (14) if the gpp parameter is taken from the experimentally measured M 2ν for that particular isotope. This observation is one example of how an experimental measurement of the 2νββ half-life could be used to constrain M 0ν calculations. Recent QRPA calculations have also attempted to account for the deformation of the nuclei involved in the transition (15). Other methods have recently become available for NME evaluation; these include the projected Hartree–Fock–Bogoliubov model, the microscopic interacting boson model, and the energy density functional method. Although there have been attempts to use these models to evaluate M2ν (16), so far they have focused primarily on M 0ν , so they are not discussed further here. In summary, evaluation of the 2νββ NMEs presents a formidable challenge and could help improve the reliability of M 0ν calculations. The greatest advantage of the two-neutrino mode is that the NME calculations can be directly verified in an experiment by measuring the 2νββ half-life. In many respects, the M 2ν evaluation is more complex due to its sensitivity to the nuclear structure of the intermediate nucleus. This sensitivity can be addressed experimentally by looking at chargeexchange and muon-capture reactions to determine the strength of the parent–intermediate and intermediate–daughter transitions (see, e.g., Reference 17). In certain double-β nuclei, transitions through a single intermediate state can dominate, leading to important consequences for NME evaluation and experimental observables. This topic is addressed in more detail below. The double-β transition can be considered a two-step process: (a) from the parent nucleus to an intermediate state (the so-called left leg) and (b) from that intermediate state to the ground (or

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excited) state to the final nucleus (the right leg) (Figure 5). In 2νββ, these transitions can proceed only via 1+ intermediate states. The important problem for the theoretical evaluation of 2νββ is the question of the particular intermediate states that produce a sizable contribution to the decay rate. In certain nuclei the lowest (ground) 1+ 1 state may dominate the decay (18, 19). This suggestion is known as the single-state dominance (SSD) hypothesis. Among the β − β − candidates in which this situation is likely to occur are 96 Zr, 100 Mo, 110 Pd, and 116 Cd, in which protons occupy primarily the 1g9/2 level and neutrons mainly the 1g7/2 level. Another candidate is 128 Te, in which the protons occupy primarily the 2d5/2 level and neutrons the 2d3/2 level. M2ν calculations under the SSD hypothesis have been performed (19) for several isotopes. This study showed that appreciable differences arise in the decay rates and decay product (electron) distributions under the SSD model when compared with a mode that assumes that higher-lying 1+ states produce a noticeable contribution—known as the higher-state dominance (HSD) hypothesis. Although it would be challenging, there is a possible way to experimentally verify the SSD model. Figure 4 shows the results of these calculations for 100 Mo. Clearly, a precision high-statistics study of single-electron energy distributions can discriminate between the SSD and HSD models. So far, NEMO3 (20) is the only experiment with the sensitivity to carry out such a study (Section 6.3).

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4. EXPERIMENTAL METHODS Experimental approaches to double-β decay search can be broadly subdivided into two categories: direct (counter) experiments and indirect assays. In a direct experiment, the two electrons emitted during a decay are directly observed by a particle detector (e.g., a scintillator or a semiconductor). The detection therefore occurs in real time, and the energy, time, and (in some cases) angular distributions of the electrons are recorded. Indirect assays focus on identifying and counting an excess of daughter isotopes in a material containing the parent isotopes that can undergo double-β decay. Although indirect experiments have historically been the first to detect the process, they do not distinguish between the two-neutrino and zero-neutrino modes of the decay. The main focus of the current double-β research is therefore on direct experimental methods. Nevertheless, as discussed below in Section 7, comparison between indirect and direct experiments may yield interesting information about some fundamental aspects of physics.

4.1. Indirect Methods The geochemical method is based on analyzing an ancient mineral containing a double-β isotope with the aim of extracting and counting the number of daughter atoms of the double-β transition accumulated over long geological times. In 1950, Inghram & Reynolds (21) made the first positive observation of the double-β decay with this method; the isotope was 130 Te. Since then, numerous experiments have been performed with this and other isotopes (e.g., 130 Te, 82 Se, 130 Ba, and 100 Mo). In most cases, the daughter isotope is a gas (e.g., 130 Te→130 Xe), which allows one to heat the sample in a furnace, efficiently extract the accumulated daughter nuclei, and subsequently analyze the isotopic ratios in a mass spectrometer. The age of the samples ranges from 106 to >109 years and is estimated by use of, for example, potassium–argon and uranium–xenon methods. A key systematic uncertainty in the geochemical experiments is the question of gas retention in the mineral. Gas retention is estimated by looking at other isotopes, such as 132 Xe accumulated from the spontaneous fission of 238 U traces in the parent mineral. Also, an age estimate based on the uranium–xenon method may already include a correction for xenon retention in the mineral for 512

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the 130 Te→130 Xe transition. Geochemical experiments must contend with possible backgrounds from neutron spallation reactions due to exposure of the sample to cosmic muons, which depends on the geological history of the mineral and how long it was on the surface. Trapped xenon inside the sample is another potential source of background, which is estimated by looking at different isotope ratios and modeling xenon isotope production by cosmic rays. The idea of radiochemical experiments is based on the detection of radioactive daughters of the double-β decay. This method has been successfully used to detect the 238 U→238 Pu transition (22). Plutonium has been isolated from a uranyl nitrate sample, purified, and placed into lowbackground α particle counters for the observation of 5.51-MeV α particles from 238 Pu, allowing one to measure the amount of 238 Pu. The main backgrounds come from (a) traces of 241 Am and 222 Rn, which produce α particles of similar energies, and (b) the fallout of 238 Pu from atmospheric tests and satellites.

4.2. Direct Methods Current experimental efforts are focusing on the direct detection of two electrons emitted in the double-β decay. There are several criteria that an ideal 2νββ experiment must satisfy. Unsurprisingly, it is virtually impossible to satisfy all of them, so one must strike a compromise. To explore the most significant criteria, let us examine a generic formula for the two-neutrino half-life sensitivity. If the effect is positively identified, then the half-life is calculated according to ε· M ·a 2ν = N A ln 2 t, T 1/2 W · N obs where NA is Avogadro’s number, ε is the detection efficiency, a is the isotopic abundance in the source of the mass M, W is the molar mass of the source, N obs is the number of events attributed to 2νββ (above all possible backgrounds), and t is the time of measurement. In the absence of the 2νββ signal, a lower limit can be placed on the half-life of the process:  M ·t ε·a 2ν , T 1/2 > N A ln 2 W · kCL N bkg · E where N bkg is a background index, namely the number of background events normalized to energy unit, source mass, and measurement time (e.g., in kg−1 keV−1 year−1 ); E is the energy interval over which 2νββ is searched; and kCL is the number of standard deviations corresponding to a given confidence level (e.g., 1.64 σ for 90% CL). The above formulae refer to a simple counting experiment and the Gaussian approximation of the background fluctuation. A much better approach is to apply a maximum-likelihood analysis to the two-electron spectrum, making use of the spectral shape to boost the sensitivity of the experiment. This approach is especially applicable for the 2νββ mode, which has a continuum of electron energies. Nevertheless, this simplistic formula highlights key parameters that need to be optimized in a double-β experiment. An ideal experiment will therefore have: 1. A good source strength, which is determined by its mass M and the abundance of the doubleβ isotope. The latter means that in most cases enrichment would be necessary (a notable exception is 130 Te, due to its high natural isotopic abundance). 2. A low-background index. This is arguably the most important and certainly the most challenging aspect of a 2νββ experiment; it is discussed in more detail in Section 5. Using ultralow-background materials, preventing radon diffusion inside the detector, going underground in a low-background environment and using detector technologies for active background suppression (e.g., explicit identification of the two-electron topology) are some techniques that experimenters employ to improve the signal-to-background ratio. www.annualreviews.org • Two-Neutrino Double-Beta Decay

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3. High detection efficiency of two electrons. 4. Good energy resolution. Note, however, that this requirement is less critical for 2νββ detection compared with 0νββ due to the continuous spectrum of the electron’s energy sum in the 2νββ decay. The strategies employed to detect double-β decay can be broadly subdivided into two main categories: calorimeters and topological detectors. Each category is described below.

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4.2.1. Calorimeter detectors. Calorimeters are the most common type of detector, and in most cases, such detectors are made of the source material itself. Examples include semiconductor detectors [high-purity germanium (HPGe), cadmium–zinc–tellurite (CdZnTe)], low-temperature bolometers, scintillators, and liquid–noble gas detectors. The main observable in this type of detector is the energy deposited by two electrons, hence the name calorimeters. The source = detector approach gives these instruments high detection efficiency and compactness. They often offer excellent energy resolution, especially in the case of HPGe detectors and bolometers. The disadvantage of this approach is the limited information provided by the energy-only readout. In the absence of particle identification and two-electron signature reconstruction, 2νββ searches in these experiments rely mainly on background mitigation through careful material selection and several layers of protection against external backgrounds. Modern versions of the calorimetertype detectors, however, have some particle-identification capabilities that allow them to reduce the background. For example, a pulse-shape analysis of HPGe detector data helps discriminate between ionization events with multiple interactions inside the detector (γ particles) and events with single-site energy deposition (electrons) (23). Although the single-site event selection reduces the detection efficiency for the signal double-β events, the overall result is an improved signal-tobackground ratio. 4.2.2. Topological detectors. The other category of detectors comprises those in which the double-β source and the detector are separated. The double-β isotope, often in the form of a thin foil, is surrounded by a suite of detectors that can reconstruct the full topology of the double-β event. The ability to unambiguously identify electrons and reconstruct their individual tracks, as well as the angle between them, represents a powerful tool to use for background suppression. The main disadvantages of these detectors are their relatively larger size, their lower detection efficiency, and their modest energy resolution. However, due to the continuous nature of the twoelectron energy spectrum, these problems are usually well compensated for by their event-by-event background-suppression capabilities. The topology reconstruction provides a better signal-tobackground ratio for the 2νββ decay than does the energy resolution. Consequently, topological detectors generally perform better for 2νββ detection, as discussed in Section 6. There is also an intermediate category of detector technologies that attempt to combine key features of the above-described two approaches. Examples include high-pressure gaseous timeprojection chambers (TPCs) filled with xenon (which could be enriched in 136 Xe) and pixelated CdZnTe detectors. Although the source and detector in these technologies are the same, electron tracks can be reconstructed and electrons can be discriminated against α and γ particles and sometimes positrons. Nevertheless, the angular information obtained by these detectors is very limited, and individual electron energies, as a rule, cannot be measured.

4.3. Isotope Enrichment As mentioned above, enrichment is often a strong requirement for successful detection of 2νββ. Also, it often contributes significantly to experimental costs. The most advanced and by far the 514

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least expensive enrichment technology is gas centrifugation, which was originally developed for the separation of 235 U. The main requirement for the application of this technology to the separation of a particular isotope is the presence of a stable hexafluoride gaseous compound for the element in question (e.g., MoF6 ). This compound is fed to a centrifuge spinning at high speed, providing centripetal force acting on the molecules of the gas and causing the heavier molecules to move closer to the outside wall and the lighter ones to remain closer to the center. Also, a thermal gradient is established along a vertical axis of the centrifuge column, providing convection currents that move the lighter molecules to the top of the column and leave the heavier ones at the bottom. To reach large enrichment fractions (90–99%), multiple cascades of individual centrifuge stages are used. The double-β isotopes that can be enriched by this method are 100 Mo, 82 Se, 76 Ge, 116 Cd, 130 Te, and 124 Sn. In all cases, large enrichment fractions (>90%) have been demonstrated. The limitations in the choice of isotopes, as well as the large infrastructures required for gas centrifuge separation, led to the development of enrichment technologies based on high-power lasers. In this method, a laser is tuned to a specific wavelength that preferentially excites and ionizes only one isotope of the material. The ions can then be collected through the application of an electric field. The material has to be prepared in a special form of atomic vapors, hence the name of the method: atomic vapor laser isotope separation. Currently, several laboratories are researching the possibility of enriching substantial quantities of interesting high-Qββ isotopes, namely 48 Ca, 150 Nd, and 96 Zr, which cannot be enriched with conventional gas centrifuge technologies due to the absence of stable hexafluoride compounds. Another example of a laser separation method is molecular laser isotope separation. Again, this method is applied to a hexafluoride gaseous compound and was developed as an alternative to the gas centrifugal separation of 235 U. In this technique, an IR laser is directed into a UF6 gas, exciting the molecules containing the 235 U isotope. A second laser frees one fluorine atom to leave UF5 , which is then precipitated out of the gas. Finally, there exist older, more traditional ways of electromagnetically separating isotopes, so-called calutrons. Although this method has the advantage of being applicable to almost any isotope, only small amounts thereof (grams) can be produced at a reasonable price. Nevertheless, this technology was used to produce isotopes for 2νββ research, for which modest quantities can be sufficient.

5. BACKGROUNDS Due to the exceptionally long lifetimes of the double-β decay nuclei, the main challenge faced by experimentalists can be summarized in a short statement: Its observation depends crucially on background reduction. The diversity of the sources that could mimic double-β decay is especially striking in the two-neutrino mode due to the continuous energy spectrum of the decay electrons, ranging from zero to the Qββ value of the decay. There are three main categories of backgrounds, each of which is discussed below.

5.1. Natural α, β, and γ Radioactivity Natural α, β, and γ radioactivity is the most common and most problematic background for 2νββ. All materials contain traces of long-lived 238 U and 232 Th, which produce many α, β, and γ particles that, depending on the detector, can mimic a double-β event in different ways. Due to the short range of α and β particles, the external background, defined as originating outside the detector volume, can come only from γ radiation. γ -Rays interact with detector materials via the photoelectric effect, Compton scattering, or pair production. Depending on the material’s properties (e.g., Z, density), different spectra may be observed in the detector. Typically, these www.annualreviews.org • Two-Neutrino Double-Beta Decay

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103

40K

Open lid

102

Counts

208 TI

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Closed lid

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1 500

1,000

1,500

2,000

2,500

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Energy (keV) Figure 6 A background spectrum of a high-purity germanium detector at the Boulby underground laboratory (United Kingdom). The lid of the passive shielding is shown both open (black) and closed (red ). Two prominent γ lines of 40 K and 208 Tl are highlighted.

spectra produce a continuum with possible peaks if the detector contains a high-Z material (Figure 6). α Particles in natural decay chains typically have higher energies than those released in double-β decays. However, surface contamination with radioactive isotopes can produce so-called degraded αs, which lose part of their energy in a passive material of the detector (e.g., detector support or frame elements), thereby producing a continuum energy distribution that extends to double-β relevant energies. Electrons from β decays in radioactive chains (or produced indirectly by γ interactions, described above) are the most likely candidates to mimic a double-β event. The importance of these three types of radioactivity depends on the detector technology in question. Pure calorimeters cannot distinguish between different particle types and are sensitive only to the energy deposited. Their usually good energy resolution (e.g., that of HPGe and bolometers) does not have a strong discriminating power due to the continuum nature of the 2νββ spectrum. They have to rely on very pure materials and on efficient passive and active shielding surrounding the detector. Some particle identification can significantly improve the background situation because α and γ particle energy deposits can be rejected with a certain degree of efficiency. The trade-off is in the overall efficiency of the detector, but in the case of 2νββ, it is a price worth paying. Tracking detectors that can reconstruct the vertex and tracks of the electrons emitted in the decay are the most sensitive way of detecting the two-neutrino process, as was demonstrated by NEMO3 (see Section 6.3). In this case, only events containing two electron tracks, such as Moller ¨ scattering or internal conversion electrons accompanying an electron emitted from a simple β decay, can mimic the 2νββ signal. Although the background energy spectrum depends on a particular detector type, the common feature is an exponentially dropping spectrum characterized by a significant drop after the 2,614-keV line of 208 Tl from the 232 Th chain. This drop is often referred to as a natural-radioactivity cutoff (Figure 6). Therefore, the use of isotopes with higher Qββ values leads to a better signal-to-background ratio. 516

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Due to stringent radiopurity requirements, all double-β experiments perform extensive screening campaigns to select materials that contain only minute traces of long-lived radioactive contaminants. A typical requirement for 238 U and 232 Th contamination is <0.1 ppb (or lower) for materials in the detector’s fiducial volumes. HPGe detectors, mass spectrometry, and neutron-activation analysis are used in these studies. Radon is a particularly troublesome background for all rare event searches. It is a noble gas that is present in both decay chains (222 Rn in 238 U and 220 Rn in 232 Th). 222 Rn is especially dangerous due to its relatively long half-life of 3.8 days, which allows the gas to escape from rock and materials containing traces of 238 U and diffuse into the detector. The permeability of a given material to radon depends on its diffusion coefficient and is an important factor in designing the detector, especially its seals. 220 Rn from the 232 Th chain is usually less problematic due to its shorter halflife of 55.6 s. However, outgasing of the materials inside the detector gives rise to backgrounds originating from progenies of both isotopes. Usually the most dangerous isotopes are 214 Bi and 208 Tl due to the high Qββ values of their decays (3.27 MeV and 4.99 MeV, respectively), although for 2νββ other isotopes contribute to the background too. Delayed coincidences can be exploited to mitigate these backgrounds. Specifically, the 214 Bi β decay is followed by an α decay of 214 Po with a half-life of 164 μs. Detection of the prompt electron and a delayed α event represents a powerful tool for this background rejection. Similarly, the 212 Bi→212 Po delayed coincidence can be detected in the 232 Th–220 Rn chain. However, in this case the half-life of 212 Po is much shorter (300 ns), so a detector with adequate time resolution is required.

5.2. Neutrons from Natural Radioactivity Spontaneous fission of 238 U produces neutrons with an average kinetic energy of ∼2 MeV. Also, natural-radioactivity neutrons are produced by (α,n) reactions on light elements. The main mechanism by which these neutrons can generate a background to 2νββ is through thermalization and subsequent capture of thermal neutrons by nuclei and γ emission. The emitted γ -rays then interact with the detector and its surroundings, producing the background. The background event rate from neutron capture is typically much lower than that from α, β, and γ natural radioactivity in the 2νββ energy range. It usually produces a flat energy spectrum and therefore becomes more significant at higher energies, so it is more of a concern for 0νββ searches.

5.3. Cosmic Muons An underground laboratory is a must for modern double-β decay experiments. At sea level, the muon flux is approximately 1 min−1 cm−2 and will overwhelm any detector searching for rare events. Figure 7 shows an attenuation of the cosmic-muon flux as a function of overburden depth, measured in meters water equivalent (mwe). An underground laboratory such as Gran Sasso provides an ∼106 -fold reduction in cosmic-muon flux. Very high energy muons (∼10–100 TeV) can still reach an underground experimental site and produce electromagnetic showers and high-energy neutrons that are difficult to shield against. However, the background rate from such a source is much lower than that from natural radioactivity and does not pose a significant problem for 2νββ searches for an overburden greater than 1,000 mwe.

5.4. Shielding for Double-Beta Experiments Although an underground environment provides sufficient shielding against cosmic muons, it does not protect the detector from natural radioactivity. A multilayer shielding arrangement is www.annualreviews.org • Two-Neutrino Double-Beta Decay

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Muon flux (m–2 sr–1 year–1)

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Equivalent vertical depth (meters water equivalent) Figure 7 Cosmic muon flux attenuation in underground laboratories. The solid line is a parameterization of the total muon flux as a function of the vertical depth with a flat overburden (24).

often used in a low-background double-β experiment. The first two layers around the detector provide shielding against external γ -rays. The external layer has a high-Z material (ideally lead, but iron is often used for large detectors to reduce cost) to maximize γ absorption, along with an internal layer made of copper. Copper is used because of its intrinsic radiopurity; it provides shielding against the lead/iron shielding itself. The third layer serves as shielding against neutrons and contains a low-Z material to moderate fast neutrons; it often contains dopants (e.g., borated polyethylene) that have a high cross section for thermal neutron capture. The γ -rays produced as a result of (n,γ ) reactions in the neutron shielding are then absorbed by the γ shielding. The experimental setup is sometimes surrounded by active shielding (e.g., scintillator planes read out by photomultiplier tubes) to tag cosmic muons and other external background events (from neutrons or γ -rays). Active shielding might be especially important for shallow underground laboratories; it can also be used to reject internal detector events coinciding with hits in the active shielding. The volume around the detector is usually flushed with air purified from radon (or gaseous nitrogen from cylinders). The use of purified air is an efficient and often necessary way of reducing radon concentration outside the detector and, therefore, its diffusion into the fiducial volume.

6. EXPERIMENTAL RESULTS The 2νββ half-life has been measured for 12 isotopes by use of different experimental techniques. Table 2 compiles the most accurate positive results. Below, we review several landmark measurements in greater detail.

6.1. First Observations The first experiment to detect the double-β decay was carried out in 1948 by Fireman (25). A foil containing 124 Sn was surrounded by Geiger counters, and the event rate was compared with the background obtained by measuring a blank foil that did not contain the double-β candidate. 518

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Table 2 Main positive results for 2νββ to the ground state Isotope

Experiment (type)

48 Ca

Hoover Dam (TPC) TGV (planar HPGe) NEMO3 (track calorimeter)

Reference(s) 35 36 34

19 (4.2+3.3 −1.3 ) × 10 (4.4 ± 0.64) × 1019

IGEX (HPGe) Heidelberg–Moscow (HPGe) GERDA (HPGe)

(1.45 ± 0.15) × 1021 21 [1.74 ± 0.01 (stat.)+0.18 −0.16 (syst.)] × 10

48 49 28

82 Se

Geochemistry NEMO3 (track calorimeter)

(1.3 ± 0.05) × 1020 [0.96 ± 0.03 (stat.) ± 0.1 (syst.)] × 1020

50 51

96 Zr

Geochemistry Geochemistry NEMO3 (track calorimeter)

(3.9 ± 0.9) × 1019 (0.94 ± 0.32) × 1019 [2.35 ± 0.14 (stat.) ± 0.16 (syst.)] × 1019

52 53 54

100 Mo

Geochemistry Hoover Dam (TPC) DBA (liquid argon TPC) NEMO3 (track calorimeter)

(2.1 ± 0.3) × 1018 18 [6.82+0.38 −0.53 (stat.) ± 0.68 (syst.)] × 10 [7.2 ± 1.1 (stat.) ± 1.8 (syst.)] × 1018 [7.17 ± 0.01 (stat.) ± 0.54 (syst.)] × 1018

55 56 57 34

116 Cd

Solotvina (scintillator) NEMO3 (track calorimeter)

19 [2.9 ± 0.06 (stat.)+0.4 −0.3 (syst.)] × 10 (2.88 ± 0.17) × 1019

37 34

128 Te

76 Ge

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T1/2 (2ν) (years) 19 [4.3+2.4 −1.1 (stat.) ± 1.4 (syst.)] × 10

21 1.84+0.14 −0.10 × 10

Geochemistry

∼2.2 × 1024 , (7.7 ± 0.4) × 1024

58, 59

130 Te

Geochemistry MiBETA (bolometer) NEMO3 (track calorimeter)

∼0.8 × (2.7 ± 0.1) × 20 [6.1 ± 1.4 (stat.)+2.9 −3.5 (syst.)] × 10 [7.0 ± 0.9 (stat.) ± 1.1 (syst.)] × 1020

58, 59 60 61

136 Xe

EXO-200 (LXe TPC) KamLAND–Zen

[2.11 ± 0.04 (stat.) ± 0.21 (syst.)] × 1021 [2.38 ± 0.02 (stat.) ± 0.14 (syst.)] × 1021

150 Nd

Hoover Dam (TPC) NEMO3 (track calorimeter)

238 U 130 BaECEC

(2ν)

1021 ,

1021

38 39

18 [6.75+0.37 −0.42 (stat.) ± 0.68 (syst.)] × 10

56 62

18 [9.11+0.25 −0.22 (stat.) ± 0.63 (syst.)] × 10

Radiochemistry

(2.0 ± 0.6) × 1021

22

Geochemistry

(2.2 ± 0.5) ×

45

1021

Abbreviations: EC, electron capture; HPGe, high-purity germanium; TPC, time-projection chamber.

Because there was no statistically significant excess between the two measurements, a lower bound on the half-life was deduced: T1/2 > 3 × 1015 years. The first positive observation of 2νββ was made in a 1950 geochemical experiment by Inghram & Reynolds (21). They performed an isotopic analysis of xenon extracted from a sample of tellurium ore (Bi2 Te3 ), which was ∼1.5 × 109 years old. An observed excess of 130 Xe led to a half-life estimate of the 130 Te double-β decay of 1.4 × 1021 years. Although this result was met with skepticism, the observation held its ground and was subsequently confirmed by other geochemical measurements. It took almost 40 years for 2νββ to be detected in a direct counter experiment. This experiment was performed by the Moe group from the University of California at Irvine (26). The source R film that formed a central electrode was 14 g of 97%-enriched 82 Se deposited on a thin Mylar of a TPC. The TPC was placed in a magnetic field of 700 G, and the kinematical characteristics of the electrons emitted in the decay were measured. The detector was surrounded by a passive lead shield and placed in a laboratory in the university’s basement to reduce the cosmic-muon background. Only 36 double-β candidate events were observed, but they allowed the group to 20 years. This measurement had a profound effect and measure the half-life to be 1.1+0.8 −0.3 × 10 www.annualreviews.org • Two-Neutrino Double-Beta Decay

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triggered the observation of 2νββ processes in other experiments. Within a few years, the effect had been observed in several other isotopes.

6.2. 76 Ge

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The availability of enriched 76 Ge crystals for HPGe detectors gave the double-β field of study a significant boost. The excellent energy resolution of HPGe detectors is less important for studies of a broad spectrum of 2νββ. However, the intrinsic purity of germanium crystals, necessary for the operation of HPGe semiconductor detectors, is generally accompanied by very low levels of radioactive contaminants. The first observation of 2νββ in 76 Ge (27) yielded a half-life of (0.9 ± 0.1) × 1021 years. Subsequently, two groups made more accurate measurements: the Heidelberg–Moscow (HM) experiment at Gran Sasso and the IGEX experiment at Canfranc (Table 2). The detectors had a low background index and were among the most sensitive double-β decay experiments in the 1990s. Recently, the GERDA experiment published its measurement of the 76 Ge half-life (28). The first phase of this experiment, currently under way at Gran Sasso, uses HPGe crystals recovered from the HM and IGEX experiments. The half-life measured by GERDA is slightly higher than the previous value from the HM and IGEX experiments: 1.84 × 1021 years versus (1.45–1.74) × 1021 years. However, the results are consistent within the quoted systematic errors.

6.3. NEMO3 Results Some of the most remarkable 2νββ results have come from a series of NEMO experiments. The NEMO detectors topologically reconstructed the final-state particles in the decay, collecting the most comprehensive information about the process, including individual electron energies and their trajectories and the times and vertices of the events. The NEMO2 detector (29), which was built as a prototype for the NEMO3 experiment, provided measurements of the 2νββ half-lives for 100 Mo (30), 116 Cd (31), 82 Se (32), and 96 Zr (33). In the case of 96 Zr, NEMO2 made the first observation of its 2νββ decay in a direct experiment. The NEMO2 technology was perfected and scaled up in the NEMO3 experiment. NEMO3 studied seven double-β isotopes simultaneously: 100 Mo, 82 Se, 116 Cd, 130 Te, 150 Nd, 96 Zr, and 48 Ca. In all cases, the most accurate half-life measurements were obtained, and in some cases, these were the first direct measurements. The NEMO3 detector (20) operated at the Modane underground laboratory from February 2003 to January 2011 (Figure 8). The detector is a cylinder (∼5 × 2.5 m) that can hold up to ∼10 kg of enriched isotopes in the form of thin (30–60 mg cm−2 thick) foils surrounded by a tracker and a calorimeter. The tracking volume contains ∼6,180 open octagonal drift cells operated in Geiger mode. The tracker is enclosed by 1,940 polystyrene scintillator blocks coupled to lowradioactivity photomultiplier tubes through light guides that make up the calorimeter. A solenoid surrounding the detector generated a 25-G magnetic field parallel to the Geiger cells to identify the charge of the particle. Different particle types were reconstructed with high efficiency by use of the available tracking, charge, energy, and timing information; thus, two electron events emitted from a vertex in the foil were the only background to the double-β decay. This method led to an unusually high signal-to-background ratio and, consequently, to the most precise measurements of the two-neutrino half-lives. The most remarkable example is 100 Mo, the main isotope of NEMO3, which made up ∼7 kg of the total isotope mass. The two-electron energy spectrum and the angular distribution between two electrons are shown in Figure 9. With the total background at the percent level, the half-life was measured with a negligible statistical error: 7.17 ± 0.01 (stat.) ± 0.54 (syst.) × 1018 years (34). Table 2 presents this and other results 520

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a

b Neutron and γ shielding (borated water, wood, and pure iron)

Calorimeter block

1,341 keV

ββ source foil 1,535 keV Magnetic coil

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Calorimeter block

Calorimeter detector = 1,940 plastic scintillator blocks coupled to low radioactive photomultiplier tubes

Tracking volume = 6,180 drift cells working in Geiger mode in helium + alcohol gas mixture

Figure 8 (a) The NEMO3 detector with its shielding. (b) NEMO3 event display with a double-β candidate event. Two electron-like tracks are emitted from a single vertex in the source foil, are bent in the magnetic field, and deposit energy in two calorimeter blocks. Reproduced courtesy of the NEMO3 Collaboration.

obtained with NEMO3. Interestingly, out of the nine most accurate half-life measurements of 2νββ transitions to the ground state performed to date in direct counter experiments and presented in Table 2, seven were obtained with NEMO3. NEMO3 also studied double-β transitions to excited states (Section 6.6) and used its highstatistics data to probe the SSD mechanism for the 100 Mo 2νββ transition (Section 3). Preliminary results indicate that the SSD model is valid, but the final conclusions have yet to be published.

6.4. 48 Ca and 116 Cd Although the NEMO3 and HPGe experiments have dominated precision measurements of 2νββ lifetimes, other experimental techniques have been used to independently observe this rare process. For example, 2νββ of 48 Ca was first observed in an experiment that used a TPC placed in a tunnel in the Hoover Dam (35). A total of 42.2 g of finely powdered CaCO3 enriched to 19 years. Despite the 76% in 48 Ca were used to obtain a half-life of 4.3+2.4 −1.1 (stat.) ± 1.4(syst.) × 10 large errors, this value was the first evidence that a shell-model calculation of the 48 Ca NME can provide a result in the right range. Another result came from the TGV experiment (36), located in the Modane underground laboratory. This experiment used several planar HPGe detectors with a source made of a mixture of CaCO3 powder and polyvinyl formal (a polymer made from polyvinyl alcohol by reaction with formaldehyde) sandwiched between them. Natural calcium sources were interleaved with 78%-enriched sources to subtract the background associated with the calcium material. The result (Table 2) is consistent with both the shell model and other measurements. An accurate measurement of the 2νββ half-life of 116 Cd was obtained by an experiment performed in the Solotvina underground laboratory (37). This study used four CdWO4 scintillating www.annualreviews.org • Two-Neutrino Double-Beta Decay

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NEMO3 Data ββ 100Mo Total background

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NEMO3 Data ββ 100Mo Total background

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20,000 20,000 10,000 0 0

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1

1.5

2

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3

3.5

0 –1

–0.5

0

0.5

1

cos(Θ)

Figure 9 NEMO3 100 Mo spectra after 28 kg year−1 exposure. (a) Energy sum of two electrons. (b) Cosine of the angle between two electrons. Preliminary results reproduced courtesy of the NEMO3 Collaboration.

crystals with a total mass of 330 g, enriched in 116 Cd to 83%. The enriched crystals were surrounded by an active shield made of natural CdWO4 crystals and plastic scintillator. An elaborate model was used to accurately characterize the background. After 12,649 h of data collection, the 19 half-life of 116 Cd was measured to be 2.9 ± 0.06(stat.)+0.4 −0.3 (syst.) × 10 years; this value agrees well with that obtained by NEMO3 (Table 2).

6.5. 136 Xe The isotope of 136 Xe has always attracted great interest due to its relative ease of enrichment and the possibility of building a TPC-like detector combining elements of topological reconstruction of the double-β signature with certain advantages of the source = detector technology. Consequently, several searches were performed, but until recently, no signal was observed, resulting in strong lower bounds on T1/2 2ν (136 Xe). It became clear that 2νββ of 136 Xe is likely to have the longest lifetime of the main double-β candidates. Recently, however, the 2νββ decay of 136 Xe was positively identified by two independent experiments that employed very different technologies, EXO-200 and KamLAND–Zen, and the 2νββ half-life was measured with good precision. The EXO-200 detector (38) is a TPC that uses liquid xenon as both the source of the decays and the detection medium. The chamber contains 175 kg of liquid xenon enriched to 80.6% in 136 Xe. An important feature of the EXO-200 detector is the readout of ionization and scintillation signals in the liquid xenon, which improves the energy resolution and further suppresses backgrounds. The ability of the TPC to reconstruct energy depositions in space was used to remove interactions at the edges of the detector. To reduce this background, the fiducial volume was defined within the central part of the detector containing 63 kg of enriched xenon, which represented ∼45% of the total amount of isotope in the detector. The range of ∼MeV electrons in liquid xenon is very short (∼1 mm), whereas γ -rays are likely to scatter more than once and survive several energy

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depositions. This detector’s ability to distinguish between single-cluster (electron-like) events and multicluster (γ -like) events is an additional way to suppress backgrounds. The simultaneouslikelihood fit to the single- and multicluster events revealed a strong signal from 2νββ (3,886 events during a 752.66-h run), and the half-life was measured to be 2.11 ± 0.04 (stat.) ± 0.21 (syst.) × 1021 years (38). The KamLAND–Zen experiment (39) exploits the success of large liquid-scintillator detectors in achieving ultralow backgrounds, as has been demonstrated by the Borexino and KamLAND experiments. The double-β source and detector are 13 tons of xenon-loaded liquid scintillator (Xe-LS) hosted in a 3.08-m-diameter spherical inner balloon. The balloon containing the Xe-LS is surrounded by 1 kton of outer liquid scintillator that acts as an active shield against external γ particles and neutrons and detects internal background radiation in the Xe-LS. The xenon loading fraction in the Xe-LS is 2.5%; the xenon is enriched to 91%, yielding a total of 296 kg of 136 Xe. Candidate double-β events are selected as single energy deposits; vertices within a fiducial volume inside the Xe-LS correspond to 129 kg of 136 Xe. The events with detected muons, delayed coincidences (e–α from 214 Bi→214 Po and 212 Bi→212 Po), and multiple-site energy depositions (characteristic for γ interaction) are removed on the basis of timing information obtained from the photomultiplier tubes. Interestingly, a significant contribution to the backgrounds may arise from the contamination of the inner balloon with isotopes originating from the fallout of the Fukushima-I reactor accident in March 2011. For 2νββ searches, the most relevant isotope is 134 Cs, whereas for zero-neutrino searches, it appears to be 110m Ag (where the superscript m means metastable). Although the backgrounds are significant in the zero-neutrino energy window (2.2–3.0 MeV), in the two-neutrino window (0.4–2.2 MeV) the signal from 136 Xe 2νββ dominates over backgrounds, resulting in an accurate half-life measurement of 2.38 ± 0.02 (stat.) ± 0.14 (syst.) × 1021 years (39). Note that the EXO-200 and KamLAND–Zen results for T1/2 2ν (136 Xe) are consistent with one another and that both are significantly lower than the limit of >1022 years (90% CL) reported in Reference 40.

6.6. Transitions to Excited States + Double-β decay can also proceed to 0+ 1 and 21 excited states of the daughter nucleus. Figure 5 de100 picts such a decay for Mo. Apart from the canonical ground-state decay where Qββ = 3,034 keV, excited-state transitions can occur. The decay to the 0+ 1 state proceeds with the simultaneous emission of two electrons and two γ -rays with energies of 590 keV and 540 keV. There is also a possibility of decay to the 2+ 1 state, which would be accompanied by the emission of a single 540-keV γ -ray. However, this possibility is much less likely on account of angular momentum suppression. Due to the smaller transition energies, the probability of double-β decay to excited states is substantially suppressed compared with the ground-state decay, making it much more difficult to observe. However, the excited-state transitions offer important additional information about the process. For example, in the framework of QRPA models the behavior of the g p p parameter (see Section 3) is completely different for transitions to ground and excited states (11, 41). The decay to excited states can therefore probe different aspects of the calculation method, thereby providing complementary input to NME models. With expected half-lives for excited-state transitions on the order of 1020 to 1022 years, and following significant improvements in detector technology and background suppression, the positive detection of this process has become a real possibility. The authors of Reference 42 showed that one can use HPGe detectors to detect 2νββ to excited states by exploiting their fine energy resolution for γ -rays and looking for deexcitation

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+ Table 3 Best current results for 2νββ to 0+ 1 and 21 excited states; corresponding theoretical

predictions Excited state, Qββ X

Isotope 48 Ca 76 Ge

82 Se

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96 Zr

100 Mo

0+ 1 , 1,275 keV 2+ 1 , 3,289 keV

Experimental half-life (years)

Theoretical half-life (years)

>1.5 × 1020 (63) >1.8 × 1020 (63)

N/A 1.7 × 1024 (68)

0+ 1 , 917 keV

>6.2 × 1021 (64)

2+ 1 , 1,480 keV

>1.1 × 1021 (65)

(7.5–310) × 1021 (41, 66) 4.5 × 1021 (67) 5.8 × 1028 (68) (7.8–10) × 1025 (41, 66)

0+ 1 , 1,506 keV 2+ 1 , 2,219 keV

>3.0 × 1021 (69) >1.4 × 1021 (69)

(1.5–3.3) × 1021 (41, 66) (2.8–3,300) × 1023 (41, 66)

0+ 1 , 2,203 keV

>6.8 × 1019 (70)

2+ 1 , 2,572 keV

>7.9 × 1019 (70)

(2.4–2.7) × 1021 (41, 66) 3.8 × 1021 (67) 2.3 × 1025 (68) (3.8–4.8) × 1021 (41, 66)

0+ 1 , 1,904 keV

20 6.1+1.8 −1.1 × 10 (43)

20 (9.3+2.8 −1.7 ± 1.4) × 10 (71)

1.6 × 1021 (74) 2.1 × 1021 (67)

20 (6.0+1.9 −1.1 ± 0.6) × 10 (72, 73)

2+ 1,

2,495 keV

20 (5.7+1.3 −0.9 ± 0.8) × 10 (44) 21 >1.6 × 10 (43)

0+ 1 , 1,048 keV

>2.0 × 1021 (75)

2+ 1 , 1,512 keV

>2.3 × 1021 (75)

130 Te

0+ 1 , 735 keV 2+ 1 , 1,993 keV

>2.3 × 1021 (76) >2.8 × 1021 (77)

150 Nd

0+ 1 , 2,627 keV

+0.27 [1.33+0.36 −0.23 (stat)−0.13 (syst)] × 1020 (78) >2.2 × 1020 (78)

116 Cd

2+ 1 , 3,034 keV

1.2 × 1025 (68) 3.4 × 1022 (67) 1.1 1.1 3.4 1.1

× × × ×

1022 (41, 66) 1021 (67) 1026 (68) 1024 (41, 66)

(5.1–14) × 1022 (41, 66, 76) 6.9 × 1026 (68) (3–27) × 1022 (41, 66) N/A N/A

Limits are given at 90% CL. Other than the NEMO3 results for 100 Mo (44), the results were obtained with HPGe (high-purity germanium) detectors.

γ particles from the decay. This decay was first observed in 100 Mo (0+ 1 state) (43) and was later independently confirmed by several other experiments. Table 3 compiles the current best results obtained from excited-state decay searches in different nuclei, along with theoretical predictions for the half-lives of these processes. There are two 100 Mo and 150 Nd. For the rest of the listed isotopes positive measurements for the 0+ 1 transitions in + and for 21 transitions, lower limits have been set for the corresponding half-lives. In some cases, these limits contest existing theoretical models, but most of the results have not yet reached the sensitivity needed to confirm or refute theoretical predictions. The results presented in Table 3 were obtained mainly with HPGe detectors. An important exception is the NEMO3 result for 100 Mo (44), in which the power of the topological event reconstruction was used to observe, for the first time, all the final-state particles of the excitedstate decay: two electrons and two γ -rays. 524

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Table 4 Weighted average values of the 2νββ half-lives; corresponding nuclear matrix element (NME) valuesa Isotope

82 Se 96 Zr

(2.35 ± 0.21) × 1019 (54)

100 Mo

(7.1 ± 0.4) ×

1018

5.9+0.8 −0.6

(79)

76 Ge

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100 Mo

(0+ 1)

|M2ν |exp

Average/best half-life (years) 19 4.4+0.6 −0.5 × 10 (79) +0.14 1.84−0.10 × 1021 (28) (0.92 ± 0.07) × 1020

48 Ca

× 1020

0.0236 ± 0.0015 0.0655+0.0019 −0.0024

0.0509+0.0021 −0.0018

(79)

0.0455+0.0022 −0.0019 0.1139+0.0034 −0.0031

(79)

0.0995+0.0055 −0.0061 0.0654+0.0025 −0.0022

116 Cd

(2.8 ± 0.2) × 1019 (79)

128 Te 130 Te 136 Xe

(2.30 ± 0.12) × 1021b

0.0107 ± 0.0003

150 Nd

(9.11 ± 0.68) ×

0.0339+0.0013 −0.0012

150 Nd

(0+ 1)

a b

(79)

(7.0 ± 1.4) ×

1020

(61)

1.33+0.45 −0.26

× 1020

(2.0 ± 0.6) ×

238 U 130 Ba,

(1.9 ± 0.4) ×

1024

ECEC (2ν)

1018

0.0271+0.0034 −0.0025 0.0189+0.0022 −0.0016

(62)

0.0257+0.0030 −0.0035

(79)

1021

0.1143+0.0223 −0.0141

(79)

0.105+0.014 −0.010

(2.2 ± 0.5) × 1021 (79)

The single-state dominance model is used for the NMEs of 96 Zr, 100 Mo, 116 Cd, and 128 Te. For 136 Xe the weighted average value from References 38 and 39 is used. Abbreviation: EC, electron capture.

6.7. Two-Neutrino ECEC, ECβ + , and β + β + Transitions As mentioned above, ECEC, ECβ + , and β + β + transitions are suppressed compared with β − β − decay due to their smaller phase-space factors. So far, none of these processes have been observed in a direct experiment. The only positive indication has come from a geochemical experiment with 130 Ba (Table 2) (45). Due to its larger phase space, the ECEC mode is most likely to be observed first. A signature of the two-neutrino ECEC process in a direct experiment is the emission of two (or more) X-rays, which occurs following the capture of orbital electrons. The detectors used for these searches, such as semiconductor detectors, should therefore have good energy resolution and be sensitive to low energies. The observation of the two-neutrino mode of this decay is an important input to NME calculations, which can probe aspects of the models that are different from those addressed by the β − β − decay. Experimental results for these transitions for some of the most promising isotopes can be found in References 46 and 47.

7. DISCUSSION Table 4 presents the weighted average values for positive half-life measurements of the 2νββ transitions (both ground and excited states). For 76 Ge, 96 Zr, 130 Te, and 150 Nd, the most accurate measurements to date are used. For 136 Xe, the average of the two recent results from References 38 and 39 is given; the averaging is performed according to Reference 79. For the remaining isotopes, recommended values of the half-lives are taken from Reference 79.

7.1. Experimental Nuclear Matrix Elements By use of the formula for  2ν (Section 2.2), the corresponding experimental values of the NMEs have been calculated. The phase-space factors for β − β − processes presented in Table 4 are taken www.annualreviews.org • Two-Neutrino Double-Beta Decay

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from recent calculations (4) that benefit from the improved electron wave functions and other updates. Note that we include the axial-vector coupling constant gA in the phase-space factor G2ν , so we effectively use (G2ν gA 4 ) for the phase-space factors. Doing so makes it easier to directly compare these values with phase-space factors reported earlier (11) and traditionally used for NME calculations. The phase-space factor for the ECEC in 130 Ba is taken from Reference 11. The experimental matrix elements M 2ν reported in Table 4 are dimensionless values of |(me c 2 )M 2ν |. To convert them into MeV−1 units, which are sometimes used in the literature, one has to divide them by the electron rest mass. The SSD model is used to determine |M 2ν |exp of 96 Zr, 100 Mo, 116 Cd, and 128 Te (Section 3).

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7.2. Time Variation of the Fermi Coupling Constant and Two-Neutrino Double-Beta Rates It has been suggested (80) that the observed differences between the 2νββ half-life measurements from geochemical and direct experiments can be used to study possible variation of the Fermi coupling constant (GF ). In fact, there is a systematic dependence of the measured half-life value on the age of the mineral used in geochemical experiments. For example, relatively young (<108 -yearold) minerals containing the isotopes of 82 Se, 128 Te, and 130 Te exhibit shorter half-lives than those of their older (≥109 -year-old) counterparts (80). Similarly, direct experiments, which measure the present-day rate of 2νββ, yield smaller half-life values. Table 2 shows that the difference is ∼3 σ for 82 Se and that the difference for 130 Te is even larger. The most natural explanation for this effect is a systematic error due to gas-retention uncertainties in the mineral. In all three cases, the daughter isotope is a gas (82 Kr for 82 Se and 128,130 Xe for 128,130 Te). The older the sample is, the more likely it is to lose the gas over its long geological history. However, by looking at isotope ratios and using the uranium–xenon dating technique, researchers have taken these effects into account. Thus, provided that systematic effects are kept under control, by comparing past 2νββ rates obtained in geochemical experiments with present-day rates characterized by direct experiments, one can probe possible variations of GF over a time span of ∼109 years. 2νββ provides a more reliable test of GF variation than similar single-β decay studies because it is a second-order process and, therefore, its probability is proportional to G4F . Thus, a change in GF is not compensated for by a similar change in other fundamental constants and can in principle be observed. Some authors have proposed (80) performing further experiments, especially with nuclei for which the daughter isotope is not a gas. A particularly appealing example is the 100 Mo→100 Ru transition, for which accurate measurements are available from direct experiments. There is one geochemical measurement of the 100 Mo half-life (55). However, this result has not been cross-checked with other samples and has not undergone the same scrutiny as results with, for example, 130 Te. A systematic geochemical survey of the 2νββ of 100 Mo and other isotopes is therefore desirable.

8. CONCLUSION AND OUTLOOK Double-β decay addresses several fundamental and important questions in modern particle and nuclear physics. Its neutrinoless version provides the only practical means to test for lepton number violation, the nature and absolute value of neutrino mass, and many other aspects of physics beyond the Standard Model. 2νββ, the subject of this review, is allowed in the Standard Model and is also of fundamental importance both in its own right and for helping to understand and interpret results obtained in 0νββ experiments. NMEs responsible for double-β transitions are extremely difficult to evaluate, and existing calculations are rather model dependent. 2νββ offers the unique opportunity to test these models experimentally. Due to their sensitivity to the nuclear structure of the intermediate nucleus, 526

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the two-neutrino NMEs provide an excellent test bench for tuning the existing nuclear models, even if there exists no direct link between zero-neutrino and two-neutrino NME calculations. Moreover, 2νββ is the ultimate Standard Model background to the zero-neutrino mode, and its full characterization is important to quantify this background and interpret any observed New Physics signal in 0νββ. Experimental searches for double-β decay have a long history, and there is a rich experimental program employing a wealth of different detection techniques. Very low backgrounds are necessary for the detection of 2νββ. The detectors that have been developed to search for this process have pushed ultralow-background technologies to the limit. These technologies have found applications in other areas such as dark matter, solar neutrino studies, and environmental science. So far, 2νββ has been positively identified and its rate measured in 12 nuclei. For three of them—128 Te, 130 Ba (ECEC), and 238 U—only indirect (geo- and radiochemical) measurements are available. For the remaining nine nuclei, direct (counter) measurements, including transitions to excited states of the daughter nucleus for the isotopes of 100 Mo and 150 Nd, have been performed. It is our opinion that a positive observation of 2νββ is a necessary (although not sufficient) condition for a successful 0νββ experiment. However, only a few technologies have managed to measure 2νββ directly. Detectors that can reconstruct, at least to some degree, the event topology and particle identities have a clear advantage over pure calorimeters in searches for 2νββ, as demonstrated by the first direct detection of 2νββ in 82 Se (26) and by the NEMO3 results (34). Several 2νββ measurements remain to be performed. In the near future, NEMO3 will release its final results on the validity of the SSD model for 100 Mo and will attempt to perform this analysis for 116 Cd. In the more distant future, experiments will need to address the questions of the SSD model and to measure transitions to excited states in other isotopes. Another important measurement that has yet to be made is that of the two-neutrino ECEC transition in a direct experiment. More generally, precision measurements of different two-neutrino processes will help further constrain NME calculations and fully characterize the shape of two-neutrino distributions so that we may better understand the Standard Model background for 0νββ searches. Several double-β experiments are in different stages of construction, planning, and research and development. Some of them may be able to address the future challenges of 2νββ detection, described above. The experiments with the best chance of success will be those that can accommodate different isotopes in the detectors and employ technologies that reconstruct individual energies and topologies of the final states, such as SuperNEMO (81). There is also a possibility of exploring New Physics with 2νββ through comparison between the two-neutrino rates in precision measurements from direct and geochemical observations of the decay. There exist other exotic possibilities that are not covered in this review, such as probing the bosonic (symmetric) fraction of the neutrino wave function with 2νββ (82). Nearly 80 years after having first been suggested by Goeppert-Mayer, and after more than 60 years of experimental research, 2νββ still represents a research program with many important questions waiting to be answered.

DISCLOSURE STATEMENT The author is not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.

ACKNOWLEDGMENTS The author’s research activities are supported by the UK Science and Technology Facilities Council and the Higher Education Funding Council for England. The author thanks his www.annualreviews.org • Two-Neutrino Double-Beta Decay

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NEMO3 and SuperNEMO collaborators. Special thanks go to Alexander Barabash for readˇ ing this manuscript and providing valuable remarks, to Fedor Simkovic for discussions on nuclear matrix elements, and to Vladimir Tretyak for his help with providing theoretical double-β decay spectra. LITERATURE CITED

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Contents

Annual Review of Nuclear and Particle Science Volume 63, 2013

Wolfgang K.H. Panofsky: Scientist and Arms-Control Expert Vera G. Luth ¨ pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp1 Recent Results in Bottomonium C. Patrignani, T.K. Pedlar, and J.L. Rosner p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p21 The LSND and MiniBooNE Oscillation Searches at High m2 Janet M. Conrad, William C. Louis, and Michael H. Shaevitz p p p p p p p p p p p p p p p p p p p p p p p p p p p45 Axions: Theory and Cosmological Role Masahiro Kawasaki and Kazunori Nakayama p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p69 Time-Dependent Density Functional Theory and the Real-Time Dynamics of Fermi Superfluids Aurel Bulgac p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p97 Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions Ulrich Heinz and Raimond Snellings p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 123 The Supernova in the Pinwheel Galaxy Daniel Kasen and Peter E. Nugent p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 153 Muonic Hydrogen and the Proton Radius Puzzle Randolf Pohl, Ronald Gilman, Gerald A. Miller, and Krzysztof Pachucki p p p p p p p p p p p p p p 175 Rare Decays and CP Violation in the Bs System Guennadi Borissov, Robert Fleischer, and Marie-H´el`ene Schune p p p p p p p p p p p p p p p p p p p p p p p p 205 Low-Energy Measurements of the Weak Mixing Angle K.S. Kumar, Sonny Mantry, W.J. Marciano, and P.A. Souder p p p p p p p p p p p p p p p p p p p p p p p p p 237 Status and New Ideas Regarding Liquid Argon Detectors Alberto Marchionni p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 269 Progress in the Determination of the Partonic Structure of the Proton Stefano Forte and Graeme Watt p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 291 Photodetectors in Particle Physics Experiments Peter Kriˇzan and Samo Korpar p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 329

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Naturalness and the Status of Supersymmetry Jonathan L. Feng p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 351 Search for Superheavy Nuclei J.H. Hamilton, S. Hofmann, and Y.T. Oganessian p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 383 Low-Energy e + e − Hadronic Annihilation Cross Sections Michel Davier p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 407 The Legacy of the Tevatron in the Area of Accelerator Science Stephen D. Holmes and Vladimir D. Shiltsev p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 435

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The Tevatron Collider Physics Legacy Paul D. Grannis and Melvyn J. Shochet p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 467 Two-Neutrino Double-Beta Decay Ruben Saakyan p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 503 Charged Lepton Flavor–Violation Experiments S. Mihara, J.P. Miller, P. Paradisi, and G. Piredda p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p 531 Index Cumulative Index of Contributing Authors, Volumes 54–63 p p p p p p p p p p p p p p p p p p p p p p p p p p p 553 Errata An online log of corrections to Annual Review of Nuclear and Particle Science articles may be found at http://nucl.annualreviews.org/errata.shtml

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Annual Reviews It’s about time. Your time. It’s time well spent.

New From Annual Reviews:

Annual Review of Statistics and Its Application Volume 1 • Online January 2014 • http://statistics.annualreviews.org

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Editor: Stephen E. Fienberg, Carnegie Mellon University

Associate Editors: Nancy Reid, University of Toronto Stephen M. Stigler, University of Chicago The Annual Review of Statistics and Its Application aims to inform statisticians and quantitative methodologists, as well as all scientists and users of statistics about major methodological advances and the computational tools that allow for their implementation. It will include developments in the field of statistics, including theoretical statistical underpinnings of new methodology, as well as developments in specific application domains such as biostatistics and bioinformatics, economics, machine learning, psychology, sociology, and aspects of the physical sciences.

Complimentary online access to the first volume will be available until January 2015. table of contents:

• What Is Statistics? Stephen E. Fienberg • A Systematic Statistical Approach to Evaluating Evidence from Observational Studies, David Madigan, Paul E. Stang, Jesse A. Berlin, Martijn Schuemie, J. Marc Overhage, Marc A. Suchard, Bill Dumouchel, Abraham G. Hartzema, Patrick B. Ryan

• High-Dimensional Statistics with a View Toward Applications in Biology, Peter Bühlmann, Markus Kalisch, Lukas Meier • Next-Generation Statistical Genetics: Modeling, Penalization, and Optimization in High-Dimensional Data, Kenneth Lange, Jeanette C. Papp, Janet S. Sinsheimer, Eric M. Sobel

• The Role of Statistics in the Discovery of a Higgs Boson, David A. van Dyk

• Breaking Bad: Two Decades of Life-Course Data Analysis in Criminology, Developmental Psychology, and Beyond, Elena A. Erosheva, Ross L. Matsueda, Donatello Telesca

• Brain Imaging Analysis, F. DuBois Bowman

• Event History Analysis, Niels Keiding

• Statistics and Climate, Peter Guttorp

• Statistical Evaluation of Forensic DNA Profile Evidence, Christopher D. Steele, David J. Balding

• Climate Simulators and Climate Projections, Jonathan Rougier, Michael Goldstein • Probabilistic Forecasting, Tilmann Gneiting, Matthias Katzfuss • Bayesian Computational Tools, Christian P. Robert • Bayesian Computation Via Markov Chain Monte Carlo, Radu V. Craiu, Jeffrey S. Rosenthal • Build, Compute, Critique, Repeat: Data Analysis with Latent Variable Models, David M. Blei • Structured Regularizers for High-Dimensional Problems: Statistical and Computational Issues, Martin J. Wainwright

• Using League Table Rankings in Public Policy Formation: Statistical Issues, Harvey Goldstein • Statistical Ecology, Ruth King • Estimating the Number of Species in Microbial Diversity Studies, John Bunge, Amy Willis, Fiona Walsh • Dynamic Treatment Regimes, Bibhas Chakraborty, Susan A. Murphy • Statistics and Related Topics in Single-Molecule Biophysics, Hong Qian, S.C. Kou • Statistics and Quantitative Risk Management for Banking and Insurance, Paul Embrechts, Marius Hofert

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