New Leading Contribution to Neutrinoless Double-β Decay

Radiative Corrections to Superallowed β Decays in Effective Field Theory

The accuracy of V_{ud} determinations from superallowed β decays critically hinges on control over radiative corrections. Recently, substantial progress has been made on the single-nucleon, universal corrections, while nucleus-dependent effects, typically parametrized by a quantity δ_{NS}, are much less well constrained. Here, we lay out a program to evaluate this correction from effective field theory (EFT), highlighting the dominant terms as predicted by the EFT power counting. Moreover, we compare the results to a dispersive representation of δ_{NS} and show that the expected momentum scaling applies even in the case of low-lying intermediate states. Our EFT framework paves the way toward ab initio calculations of δ_{NS} and thereby addresses the dominant uncertainty in V_{ud}.

Ab Initio Uncertainty Quantification of Neutrinoless Double-Beta Decay in ^{76}Ge

The observation of neutrinoless double-beta (0νββ) decay would offer proof of lepton number violation, demonstrating that neutrinos are Majorana particles, while also helping us understand why there is more matter than antimatter in the Universe. If the decay is driven by the exchange of the three known light neutrinos, a discovery would, in addition, link the observed decay rate to the neutrino mass scale through a theoretical quantity known as the nuclear matrix element (NME). Accurate values of the NMEs for all nuclei considered for use in 0νββ experiments are therefore crucial for designing and interpreting those experiments. Here, we report the first comprehensive ab initio uncertainty quantification of the 0νββ-decay NME, in the key nucleus ^{76}Ge. Our method employs nuclear strong and weak interactions derived within chiral effective field theory and recently developed many-body emulators. Our result, with a conservative treatment of uncertainty, is an NME of 2.60_{-1.36}^{+1.28}, which, together with the best-existing half-life sensitivity and phase-space factor, sets an upper limit for effective neutrino mass of 187_{-62}^{+205}  meV. The result is important for designing next-generation germanium detectors aiming to cover the entire inverted hierarchy region of neutrino masses.

^{138}Ba(d,α) Study of States in ^{136}Cs: Implications for New Physics Searches with Xenon Detectors

We used the ^{138}Ba(d,α) reaction to carry out an in-depth study of states in ^{136}Cs, up to around 2.5 MeV. In this Letter, we place emphasis on hitherto unobserved states below the first 1^{+} level, which are important in the context of solar neutrino and fermionic dark matter (FDM) detection in large-scale xenon-based experiments. We identify for the first time candidate metastable states in ^{136}Cs, which would allow a real-time detection of solar neutrino and FDM events in xenon detectors, with high background suppression. Our results are also compared with shell-model calculations performed with three Hamiltonians that were previously used to evaluate the nuclear matrix element (NME) for ^{136}Xe neutrinoless double beta decay. We find that one of these Hamiltonians, which also systematically underestimates the NME compared with the others, dramatically fails to describe the observed low-energy ^{136}Cs spectrum, while the other two show reasonably good agreement.

Interplay of nuclear physics, effective field theories, phenomenology, and lattice QCD in neutrino physics

Experiments in neutrino physics cover a wide range—from deep inelastic scattering, over long base-line oscillation experiments and low-energy coherent neutrino–nucleus scattering (CEνNS), to searches for neutrinoless double β decay (0νββ)—yet in all cases a key aspect in interpreting the results concerns understanding neutrino–nucleus interactions. If the neutrino energy is sufficiently low, the required matrix elements can be constrained in a systematic way by the interplay of effective field theories, phenomenology, and lattice QCD. In these proceedings, we illustrate this strategy focusing on the CEνNS and 0νββ processes.

Ab Initio Calculation of the Contact Operator Contribution in the Standard Mechanism for Neutrinoless Double Beta Decay

Starting from chiral nuclear interactions, we evaluate the contribution of the leading-order contact transition operator to the nuclear matrix element (NME) of neutrinoless double-beta decay, assuming a light Majorana neutrino-exchange mechanism. The corresponding low-energy constant (LEC) is determined by fitting the transition amplitude of the nn→ppe^{-}e^{-} process to a recently proposed synthetic datum. We examine the dependence of the amplitude on similarity renormalization group scale and chiral expansion order of the nuclear interaction, finding that both dependences can be compensated to a large extent by readjusting the LEC. We evaluate the contribution of both the leading-order contact operator and standard long-range operator to the neutrinoless double-beta decays in the light nuclei ^{6,8}He and the candidate nucleus ^{48}Ca. Our results provide the first clear demonstration that the contact term enhances the NME in calculations with commonly used chiral two- plus three-nucleon interactions. In the case of ^{48}Ca, for example, the NME obtained with the EM(1.8/2.0) interaction is enhanced from 0.61 to 0.87(4), where the uncertainty is propagated from the synthetic datum.

Coupled-Cluster Calculations of Neutrinoless Double-β Decay in ^{48}Ca

We use coupled-cluster theory and nuclear interactions from chiral effective field theory to compute the nuclear matrix element for the neutrinoless double-β decay of ^{48}Ca. Benchmarks with the no-core shell model in several light nuclei inform us about the accuracy of our approach. For ^{48}Ca we find a relatively small matrix element. We also compute the nuclear matrix element for the two-neutrino double-β decay of ^{48}Ca with a quenching factor deduced from two-body currents in recent ab initio calculation of the Ikeda sum rule in ^{48}Ca [Gysbers et al., Nat. Phys. 15, 428 (2019)NPAHAX1745-247310.1038/s41567-019-0450-7].

Toward Complete Leading-Order Predictions for Neutrinoless Double β Decay

The amplitude for the neutrinoless double β (0νββ) decay of the two-neutron system nn→ppe^{-}e^{-} constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale 0νββ searches. Assuming that the 0νββ process is mediated by a light-Majorana-neutrino exchange, a systematic analysis in chiral effective field theory shows that already at leading order a contact operator is required to ensure renormalizability. In this Letter, we develop a method to estimate the numerical value of its coefficient (in analogy to the Cottingham formula for electromagnetic contributions to hadron masses) and validate the result by reproducing the charge-independence-breaking contribution to the nucleon-nucleon scattering lengths. Our central result, while derived in dimensional regularization, is given in terms of the renormalized amplitude A_{ν}(|p|,|p^{'}|), matching to which will allow one to determine the contact-term contribution in regularization schemes employed in nuclear-structure calculations. Our results thus greatly reduce a crucial uncertainty in the interpretation of searches for 0νββ decay.

Left-Right Symmetry and Leading Contributions to Neutrinoless Double Beta Decay

We study the impact of the mixing (LR mixing) between the standard model W boson and its hypothetical, heavier right-handed parter W_{R} on the neutrinoless double beta decay (0νββ decay) rate. Our study is done in the minimal left-right symmetric model assuming a type-II dominance scenario with charge conjugation as the left-right symmetry. We then show that the 0νββ decay rate may be dominated by the contribution proportional to this LR mixing, which at the hadronic level induces the leading-order contribution to the interaction between two pions and two charged leptons. The resulting long-range pion exchange contribution can significantly enhance the decay rate compared to previously considered short-range contributions. Finally, we find that even if future cosmological experiments rule out the inverted hierarchy for neutrino masses, there are still good prospects for a positive signal in the next generation of 0νββ decay experiments.

Path from Lattice QCD to the Short-Distance Contribution to 0νββ Decay with a Light Majorana Neutrino

Neutrinoless double-β (0νββ) decay of certain atomic isotopes, if observed, will have significant implications for physics of neutrinos and models of physics beyond the standard model. In the simplest scenario, if the mass of the light neutrino of the standard model has a Majorana component, it can mediate the decay. Systematic theoretical studies of the decay rate in this scenario, through effective field theories matched to ab initio nuclear many-body calculations, are needed to draw conclusions about the hierarchy of neutrino masses, and to plan the design of future experiments. However, a recently identified short-distance contribution at leading order in the effective field theory amplitude of the subprocess nn→pp(ee) remains unknown, and only lattice quantum chromodynamics (QCD) can directly and reliably determine the associated low-energy constant. While the numerical computations of the correlation function for this process are underway with lattice QCD, the connection to the physical amplitude, and hence this short-distance contribution, is missing. A complete framework that enables this complex matching is developed in this Letter. The complications arising from the Euclidean and finite-volume nature of the corresponding correlation function are fully resolved, and the value of the formalism is demonstrated through a simple example. The result of this work, therefore, fills the gap between first-principles studies of the nn→pp(ee) amplitude from lattice QCD and those from effective field theory, and can be readily employed in the ongoing lattice-QCD studies of this process.

Ab Initio Neutrinoless Double-Beta Decay Matrix Elements for ^{48}Ca, ^{76}Ge, and ^{82}Se

We calculate basis-space converged neutrinoless ββ-decay nuclear matrix elements for the lightest candidates: ^{48}Ca, ^{76}Ge, and ^{82}Se. Starting from initial two- and three-nucleon forces, we apply the ab initio in-medium similarity renormalization group to construct valence-space Hamiltonians and consistently transformed ββ-decay operators. We find that the tensor component is non-negligible in ^{76}Ge and ^{82}Se, and the resulting nuclear matrix elements are overall 25%-45% smaller than those obtained from the phenomenological shell model. While a final matrix element with uncertainties still requires substantial developments, this work nevertheless opens a path toward a true first-principles calculation of neutrinoless ββ decay in all nuclei relevant for ongoing large-scale searches.

Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ^{48}Ca

Working with Hamiltonians from chiral effective field theory, we develop a novel framework for describing arbitrary deformed medium-mass nuclei by combining the in-medium similarity renormalization group with the generator coordinate method. The approach leverages the ability of the first method to capture dynamic correlations and the second to include collective correlations without violating symmetries. We use our scheme to compute the matrix element that governs the neutrinoless double beta decay of ^{48}Ca to ^{48}Ti, and find it to have the value 0.61, near or below the predictions of most phenomenological methods. The result opens the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as ^{76}Ge, ^{130}Te, and ^{136}Xe.

Improved Limit on Neutrinoless Double-Beta Decay in ^{130} Te with CUORE

We report new results from the search for neutrinoless double-beta decay in ^{130} Te with the CUORE detector. This search benefits from a fourfold increase in exposure, lower trigger thresholds, and analysis improvements relative to our previous results. We observe a background of (1.38±0.07)×10^{-2}  counts/(keV kg yr)) in the 0νββ decay region of interest and, with a total exposure of 372.5 kg yr, we attain a median exclusion sensitivity of 1.7×10^{25}  yr. We find no evidence for 0νββ decay and set a 90% credibility interval Bayesian lower limit of 3.2×10^{25}  yr on the ^{130} Te half-life for this process. In the hypothesis that 0νββ decay is mediated by light Majorana neutrinos, this results in an upper limit on the effective Majorana mass of 75-350 meV, depending on the nuclear matrix elements used.

Precision Analysis of the ^{136}Xe Two-Neutrino ββ Spectrum in KamLAND-Zen and Its Impact on the Quenching of Nuclear Matrix Elements

We present a precision analysis of the ^{136}Xe two-neutrino ββ electron spectrum above 0.8 MeV, based on high-statistics data obtained with the KamLAND-Zen experiment. An improved formalism for the two-neutrino ββ rate allows us to measure the ratio of the leading and subleading 2νββ nuclear matrix elements (NMEs), ξ_{31}^{2ν}=-0.26_{-0.25}^{+0.31}. Theoretical predictions from the nuclear shell model and the majority of the quasiparticle random-phase approximation (QRPA) calculations are consistent with the experimental limit. However, part of the ξ_{31}^{2ν} range allowed by the QRPA is excluded by the present measurement at the 90% confidence level. Our analysis reveals that predicted ξ_{31}^{2ν} values are sensitive to the quenching of NMEs and the competing contributions from low- and high-energy states in the intermediate nucleus. Because these aspects are also at play in neutrinoless ββ decay, ξ_{31}^{2ν} provides new insights toward reliable neutrinoless ββ NMEs.

Light-Neutrino Exchange and Long-Distance Contributions to 0ν2β Decays: An Exploratory Study on ππ→ee

We present an exploratory lattice QCD calculation of the neutrinoless double beta decay ππ→ee. Under the mechanism of light-neutrino exchange, the decay amplitude involves significant long-distance contributions. The calculation reported here, with pion masses m_{π}=420 and 140 MeV, demonstrates that the decay amplitude can be computed from first principles using lattice methods. At unphysical and physical pion masses, we obtain that amplitudes are 24% and 9% smaller than the predication from leading order chiral perturbation theory. Our findings provide the lattice QCD inputs and constraints for effective field theory. A follow-on calculation with fully controlled systematic errors will be possible with adequate computational resources.

Heavy Physics Contributions to Neutrinoless Double Beta Decay from QCD

Observation of neutrinoless double beta decay, a lepton number violating process that has been proposed to clarify the nature of neutrino masses, has spawned an enormous world-wide experimental effort. Relating nuclear decay rates to high-energy, beyond the standard model (BSM) physics requires detailed knowledge of nonperturbative QCD effects. Using lattice QCD, we compute the necessary matrix elements of short-range operators, which arise due to heavy BSM mediators, that contribute to this decay via the leading order π^{-}→π^{+} exchange diagrams. Utilizing our result and taking advantage of effective field theory methods will allow for model-independent calculations of the relevant two-nucleon decay, which may then be used as input for nuclear many-body calculations of the relevant experimental decays. Contributions from short-range operators may prove to be equally important to, or even more important than, those from long-range Majorana neutrino exchange.