Physics Letters B 797 (2019) 134885 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb 124 Two-neutrino double electron capture on Xe based on an effective theory and the nuclear shell model ∗ E.A. Coello Pérez a,b, , J. Menéndez c, A. Schwenk a,b,d a Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany b ExtreMe Matter Institute EMMI, Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany c Center for Nuclear Study, The University of Tokyo, Tokyo 113-0033, Japan d Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany a r t i c l e i n f o a b s t r a c t Article history: We study the two-neutrino double electron capture on 124Xe based on an effective theory (ET) and Received 22 March 2019 large-scale shell model calculations, two modern nuclear structure approaches that have been tested Received in revised form 31 July 2019 against Gamow-Teller and double-beta decay data. In the ET, the low-energy constants are fit to electron Accepted 21 August 2019 − capture and β transitions around xenon. For the nuclear shell model, we use an interaction in a large Available online 23 August 2019 configuration space that reproduces the spectroscopy of nuclei in this mass region. For the dominant Editor: J.-P. Blaizot 124 2νECEC = − × 22 transition to the Te ground state, we find half-lives T1/2 (1.3 18) 10 y for the ET and 2νECEC = − × 22 T1/2 (0.43 2.9) 10 y for the shell model. The ET uncertainty leads to a half-life almost entirely consistent with present experimental limits and largely within the reach of ongoing experiments. The shell model half-life range overlaps with the ET, but extends less beyond current limits. Our findings thus suggest that the two-neutrino double electron capture on 124Xe has a good chance to be discovered by ongoing or future experiments. In addition, we present results for the two-neutrino double electron capture to excited states of 124Te. © 2019 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction searches are increasingly active [4–10]. The planning and inter- pretation of these experiments relies on a good understanding of Second-order weak processes give rise to extremely rare decay the decay half-life, which depends on a nuclear matrix element. modes of atomic nuclei. They have been observed in about a dozen However, these are poorly known as neutrinoless ββ decay matrix- nuclei with the longest half-lives in the nuclear chart of about element calculations disagree by at least a factor two [11]. 1019 − 1021 years [1]. All these are two-neutrino double beta (ββ) Second-order weak processes with neutrino emission are ideal decays, where the emission of two electrons is accompanied by tests of neutrinoless ββ decay matrix-element calculations. The two antineutrinos. An even rarer decay can occur if no neutrinos initial and final states are common, and the transition operator is are emitted, the neutrinoless ββ decay. This process is particularly also very similar, dominated by the physics of spin and isospin. In addition to decay, a related mode is the two-neutrino double intriguing, because neutrinoless ββ decay is not allowed in the ββ electron capture (2 ECEC). Here, two K- or L-shell orbital electrons Standard Model, does not conserve lepton number, and can only ν are simultaneously captured, rather than β emitted. This mode is happen if neutrinos are their own antiparticles (Majorana parti- kinematically unfavored with respect to decay, and at present cles) [2,3]. ββ only a geochemical measurement of 130Ba [12,13], and a possible Due to its unique potential for neutrino physics, beyond the detection in 78Kr [14,15]have been claimed. Moreover, a resonant Standard Model physics, and the understanding of the matter- neutrinoless ECEC could be fulfilled in selected nuclei [16–18]. For antimatter asymmetry of the Universe, neutrinoless ββ decay both ECEC modes limits of 1021 − 1022 years have been set in var- ious isotopes [12,19–24]. 124Xe is one of the most promising isotopes to observe 2νECEC * Corresponding author. due to its largest Q -value of 2857 keV [25]. Large-volume liquid- E-mail addresses: [email protected] (E.A. Coello Pérez), [email protected] (J. Menéndez), [email protected] xenon experiments primarily designed for the direct detection of (A. Schwenk). dark matter such as XMASS [26], XENON100 [27], or LUX [28]are https://doi.org/10.1016/j.physletb.2019.134885 0370-2693/© 2019 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 2 E.A. Coello Pérez et al. / Physics Letters B 797 (2019) 134885 124 126 134 (L) (1) sensitive to ECEC and ββ decays in Xe, Xe and Xe [29, † † ˜ ˜ ˜ ˜ () + CβL d ⊗ d + d ⊗ d ⊗ p ⊗ n 30]. Enriched xenon gas detectors are also very competitive [31, L 32]. Recent searches have reached a sensitivity comparable to the half-lives expected by most theoretical calculations [33,34], a con- + ..., (2) dition only paralleled in 78Kr [14]. Moreover the latest limits set where the tilde denotes well defined annihilation tensor operators, by the XMASS collaboration [35]exclude most theoretical predic- ˜ and the phonon (d, d†) and nucleon operators are tensor coupled. tions. The low-energy constants C must be fitted to data, and the ex- Calculations of 2νECEC and two-neutrino ββ decay are chal- pansion above is truncated after terms involving more than two lenging because they involve the quantum many-body prob- phonon creation or annihilation operators. The first term in Eq. (2) lem of heavy nuclei with even-even and odd-odd numbers of + neutrons and protons. The methods of choice are the quasi- couples the reference state to the lowest 11 state of the odd-odd particle random-phase approximation (QRPA) [36,37], extensively nucleus, so that Cβ can be extracted from the known log( ft) value used for 124Xe 2νECEC [38–40], and the large-scale nuclear shell of the corresponding β decay or EC: model (NSM) [41], which predicted successfully the 48Ca ββ half- κ live before its measurement [42,43]. In this mass region, shell Cβ = , (3) 128,130 2 log( ft) model studies reproduce well the ββ half-lives of Te and g A 10 136 124 Xe [44–47] and offer a prediction for Sn [48]. However no 124 = shell-model calculation exists for Xe 2νECEC. In addition to with dimensionless κ 6147 and t in seconds. The power count- ing of the ET [54–56] relates the Gamow-Teller matrix elements QRPA, the interacting boson model [49] and other more schematic + 124 from the lowest and higher 1 initial states to the common final approaches have also been applied to Xe [50–53]. + + n/2 + + 124 reference state by 0 |O |1 ∼ ( /) 0 |O |1 , where Further state-of-the-art Xe 2νECEC calculations are thus re- GT n+1 ω GT 1 ∼ 3ω is the breakdown scale of the ET. This allows us to esti- quired given the tension between theoretical predictions and ex- mate the values of C and C with consistent theoretical uncer- perimental limits. In this Letter, we calculate the corresponding β Lβ tainties. nuclear matrix elements using an effective theory (ET), introduced The 2νECEC matrix element from the ground state of the initial in Ref. [54], which describes well Gamow-Teller and two-neutrino + 128,130 nucleus to a 0 state of the final one is ββ decays of heavy nuclei, including Te. One of the advan- + + + + tages of the ET is to provide consistent theoretical uncertainties. 0 |O |1 1 |O |0 2νECEC f GT j j GT gs,i M = + , (4) Similar ETs have been used to study electromagnetic transitions D(1 )/m j j e in spherical [55,56] and deformed [57–63]nuclei. In addition, we present the first large-scale nuclear shell model calculation for + where j sums over all 1 states of the intermediate nucleus. The 124 124 + j Xe 2νECEC. We focus on transitions to the Te 0 ground gs electron mass me keeps the matrix element dimensionless, and + + + + + + state, but also consider 2νECEC to the lowest excited 0 and 2 = − +[ − 2 1 the energy denominator is D(1 j ) E(1 j ) E(0gs,i) E(0f ) states. The relation between the calculated nuclear matrix element + E(0 )]/2, neglecting the difference in electron binding energies. 2νECEC gs,i M and the 2νECEC half-life is given by + The expression for the 2νECEC to a final 2 state is similar [40], − 2 but the energy denominator appears to the third power. 2νECEC 1 = 2νECEC 4 2νECEC T1/2 G g A M , (1) Because the ET is designed to reproduce low-energy states, we calculate the 2νECEC matrix elements within the single-state dom- 2νECEC where G is a known phase-space factor [64] and g A = 1.27 inance (SSD) approximation: the axial-vector coupling constant. + + + + + 0 |O |1 1 |O |0 2νECEC f GT 1 1 GT gs,i M ≈ + , (5) 2. Effective theory D(11 )/me 124 124 which implies that only the matrix elements involving the lowest We use an ET that describes the initial Xe and final Te + 11 state contribute. The advantage is that the ET can fit these us- nuclei, both with even number of protons and neutrons, as spher- 124 ing Eq.