Lattice QCD Inputs for Nuclear Double Beta Decay

Abstract

Second order beta-decay processes with and without neutrinos in the final state are key probes of nuclear physics and of the nature of neutrinos. Neutrinoful double-beta decay is the rarest Standard Model process that has been observed and provides a unique test of the understanding of weak nuclear interactions. Observation of neutrinoless double-beta decay would reveal that neutrinos are Majorana fermions and that lepton number conservation is violated in nature. While significant progress has been made in phenomenological approaches to understanding these processes, establishing a connection between these processes and the physics of the Standard Model and beyond is a critical task as it will provide input into the design and interpretation of future experiments. The strong-interaction contributions to double-beta decay processes are non-perturbative and can only be addressed systematically through a combination of lattice Quantum Chromoodynamics (LQCD) and nuclear many-body calculations. In this review, current efforts to establish the LQCD connection are discussed for both neutrinoful and neutrinoless double-beta decay. LQCD calculations of the hadronic contributions to the neutrinoful process $nn\to pp{e}^{-}{e}^{-}{\bar{\nu }}_e{\bar{\nu }}_e$ and to various neutrinoless pionic transitions are reviewed, and the connections of these calculations to the phenomenology of double-beta decay through the use of effective field theory (EFTs) is highlighted. At present, LQCD calculations are limited to small nuclear systems, and to pionic subsystems, and require matching to appropriate EFTs to have direct phenomenological impact. However, these calculations have already revealed qualitatively that there are terms in the EFTs that can only be constrained from double-beta decay processes themselves or using inputs from LQCD. Future prospects for direct calculations in larger nuclei are also discussed.

53 pages, 17 figures

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• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Towards Precise and Accurate Calculations of Neutrinoless Double-Beta Decay: Project Scoping Workshop Report
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• On the Extraction of Low-energy Constants of Single- and Double-$\beta$ Decays from Lattice QCD: A Sensitivity Analysis
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• Lattice QCD calculation of light sterile neutrino contribution in $0\nu 2\beta$ decay
• Relativistic model-free prediction for neutrinoless double beta decay at leading order
• Electroweak Currents from Chiral Effective Field Theory
• Feynman--Hellmann approach to transition matrix elements and quasi-degenerate energy states
• Neutrinoless double-beta decay in a finite volume from relativistic effective field theory
• Pathfinding Quantum Simulations of Neutrinoless Double-Beta Decay
• Advances in modeling nuclear matrix elements of neutrinoless double beta decay
• Status and Perspectives of Neutrino Physics