Double-$\beta$ Decay Matrix Elements from Lattice Quantum Chromodynamics

Abstract

A lattice quantum chromodynamics (LQCD) calculation of the nuclear matrix element relevant to the $nn\to ppee{\overline{\nu }}_e{\overline{\nu }}_e$ transition is described in detail, expanding on the results presented in Ref. [1]. This matrix element, which involves two insertions of the weak axial current, is an important input for phenomenological determinations of double-$\beta$ decay rates of nuclei. From this exploratory study, performed using unphysical values of the quark masses, the long-distance deuteron-pole contribution to the matrix element is separated from shorter-distance hadronic contributions. This polarizability, which is only accessible in double-weak processes, cannot be constrained from single-$\beta$ decay of nuclei, and is found to be smaller than the long-distance contributions in this calculation, but non-negligible. In this work, technical aspects of the LQCD calculations, and of the relevant formalism in the pionless effective field theory, are described. Further calculations of the isotensor axial polarizability, in particular near and at the physical values of the light-quark masses, are required for precise determinations of both two-neutrino and neutrinoless double-$\beta$ decay rates in heavy nuclei.

30 pages, 9 figures

References in corpus (17)

• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Phase space factors for double-$\beta$ decay
• Ab initio calculation of the neutron-proton mass difference
• Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry
• Precise half-life values for two neutrino double beta decay
• Up, down, and strange nucleon axial form factors from lattice QCD
• Magnetic moments of light nuclei from lattice quantum chromodynamics
• Extracting Nucleon Magnetic Moments and Electric Polarizabilities from Lattice QCD in Background Electric Fields
• On the Feynman-Hellmann Theorem in Quantum Field Theory and the Calculation of Matrix Elements
• Electromagnetic and spin polarisabilities in lattice QCD
• The isotensor axial polarisability and lattice QCD input for nuclear double-$\beta$ decay phenomenology
• Exploratory Lattice QCD Study of the Rare Kaon Decay $K^{+}\to {\pi }^{+}\nu \bar{\nu }$
• A Feynman-Hellmann approach to the spin structure of hadrons
• Neutrinoless double beta decay and chiral $SU(3)$
• Two-Particle Elastic Scattering in a Finite Volume Including QED
• Sea contributions to the electric polarizability of the hadrons

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