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

Abstract

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.

arXiv comment6 pages, 4 figures and 1 table. supplementary material included. version to be published

References in corpus (54)

• Evidence for oscillation of atmospheric neutrinos
• First Results from KamLAND: Evidence for Reactor Anti-Neutrino Disappearance
• Observation of electron-antineutrino disappearance at Daya Bay
• Measurement of the rate of nu_e + d --> p + p + e^- interactions produced by 8B solar neutrinos at the Sudbury Neutrino Observatory
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• Quantum Monte Carlo methods for nuclear physics
• Improved nuclear matter calculations from chiral low-momentum interactions
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Coupled-cluster computations of atomic nuclei
• Tables of E2 Transition Probabilities from the first $2^{+}$ States in Even-Even Nuclei
• Phase space factors for double-$\beta$ decay
• From low-momentum interactions to nuclear structure
• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay
• Recent developments in no-core shell-model calculations
• Energy density functional study of nuclear matrix elements for neutrinoless $\beta \beta$ decay
• Anatomy of nuclear matrix elements for neutrinoless double-beta decay
• Discrepancy between experimental and theoretical $\beta$-decay rates resolved from first principles
• Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation
• $0\nu \beta \beta$ and $2\nu \beta \beta$ nuclear matrix elements, QRPA, and isospin symmetry restoration
• Lattice simulations for few- and many-body systems
• A nucleus-dependent valence-space approach to nuclear structure
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Chiral two-body currents in nuclei: Gamow-Teller transitions and neutrinoless double-beta decay
• Saturation with chiral interactions and consequences for finite nuclei
• Triaxial Angular Momentum Projection and Configuration Mixing calculations with the Gogny force
• Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions
• Configuration mixing of angular-momentum and particle-number projected triaxial HFB states using the Skyrme energy density functional
• A new leading contribution to neutrinoless double-beta decay
• Shape and pairing fluctuations effects on neutrinoless double beta decay nuclear matrix elements
• Systematic study of nuclear matrix elements in neutrinoless double-beta decay with a beyond mean-field covariant density functional theory
• Low-momentum interaction in few-nucleon systems
• Particle-Number Restoration within the Energy Density Functional Formalism
• The Magnus expansion and the in-medium similarity renormalization group
• Structure of ${}^{78}$Ni from first principles computations
• Towards an ab initio covariant density functional for nuclear structure
• Symmetry-guided large-scale shell-model theory
• Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
• New Calculations for Phase Space Factors Involved in Double Beta Decay
• Quantum Monte Carlo Methods in Nuclear Physics: Recent Advances
• The calculation of the neutrinoless double-beta decay matrix element within the realistic shell model
• Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - II. Numerical implementation at second order with a two-nucleon interaction
• Large-scale shell-model analysis of the neutrinoless $\beta \beta$ decay of ${}^{48}$Ca
• Ab initio electromagnetic observables with the in-medium similarity renormalization group
• Neutrinoless double beta decay matrix elements in light nuclei
• In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei
• Generator-coordinate reference states for spectra and $0\nu \beta \beta$ decay in the in-medium similarity renormalization group
• Neutrinoless double beta decay in effective field theory: the light Majorana neutrino exchange mechanism
• Improved description of the $2\nu \beta \beta$-decay and a possibility to determine the effective axial-vector coupling constant
• Proton-Neutron Pairing Amplitude as a Generator Coordinate for Double-Beta Decay
• Neutrinoless double-beta decay matrix elements in large shell-model spaces with the generator-coordinate method
• Quenching of nuclear matrix elements for $0\nu \beta \beta$ decay by chiral two-body currents
• Testing the importance of collective correlations in neutrinoless $\beta \beta$ decay
• Nuclear Structure from the In-Medium Similarity Renormalization Group

Cited by in corpus (105)

• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Toward the discovery of matter creation with neutrinoless double-beta decay
• A Next-Generation Liquid Xenon Observatory for Dark Matter and Neutrino Physics
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Symmetry restoration in mean-field approaches
• Analysis of Light Neutrino Exchange and Short-Range Mechanisms in $0\nu \beta \beta$ Decay
• Ab initio neutrinoless double-beta decay matrix elements for 48Ca, 76Ge, and 82Se
• Coupled-cluster calculations of neutrinoless double-beta decay in ${}^{48}$Ca
• Self-consistent Green's function theory for atomic nuclei
• Towards grounding nuclear physics in QCD
• Opportunities for Fundamental Physics Research with Radioactive Molecules
• Towards complete leading-order predictions for neutrinoless double $\beta$ decay
• Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT
• Ab initio calculation of the contact operator contribution in the standard mechanism for neutrinoless double beta decay
• Determining the leading-order contact term in neutrinoless double $\mathbf{\beta }$ decay
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Nuclear Dynamics and Reactions in the Ab Initio Symmetry-Adapted Framework
• Impact of the leading-order short-range nuclear matrix element on the neutrinoless double-beta decay of medium-mass and heavy nuclei
• The time-dependent generator coordinate method in nuclear physics
• Gamow-Teller strength in ${}^{48}$Ca and ${}^{78}$Ni with the charge-exchange subtracted second random-phase approximation
• Combining the in-medium similarity renormalization group with the density matrix renormalization group: Shell structure and information entropy
• Ab initio uncertainty quantification of neutrinoless double-beta decay in ${}^{76}$Ge
• Shell-model calculation of ${}^{100}$Mo double-$\beta$ decay
• In-medium $k$-body reduction of $n$-body operators
• Towards Precise and Accurate Calculations of Neutrinoless Double-Beta Decay: Project Scoping Workshop Report
• Variational approach with the superposition of the symmetry-restored quasi-particle vacua for nuclear shell-model calculations
• The path from lattice QCD to the short-distance contribution to $0\nu \beta \beta$ decay with a light Majorana neutrino
• Unraveling the $0\nu \beta \beta$ Decay Mechanisms
• Ab initio benchmarks of neutrinoless double beta decay in light nuclei with a chiral Hamiltonian
• Neutrinoless $\beta \beta$-decay nuclear matrix elements from two-neutrino $\beta \beta$-decay data
• Natural orbitals for many-body expansion methods
• Neutrinoless double-beta decay: combining quantum Monte Carlo and the nuclear shell model with the generalized contact formalism
• Moving away from singly-magic nuclei with Gorkov Green's function theory
• A new and practical formulation for overlaps of Bogoliubov vacua
• Multiscale physics of atomic nuclei from first principles
• Symmetry-projected variational calculations with the numerical suite TAURUS I. Variation after particle-number projection
• Electromagnetic Properties of Indium Isotopes Elucidate the Doubly Magic Character of ${}^{100}$Sn
• A Statistical Analysis for the Neutrinoless Double-Beta Decay Matrix element of 48Ca
• Ab initio studies of double Gamow-Teller transition and its correlation with neutrinoless double beta decay
• $\gamma \gamma$ decay as a probe of neutrinoless $\beta \beta$ decay nuclear matrix elements
• Ab initio computations of strongly deformed nuclei around ${}^{80}$Zr
• Zero- and finite-temperature electromagnetic strength distributions in closed- and open-shell nuclei from first principles
• Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $sd$-shell
• Testing the Inverted Neutrino Mass Ordering with Neutrinoless Double-Beta Decay
• Neutrinoless double-beta decay from an effective field theory for heavy nuclei
• Ab initio calculation of muon capture on ${}^{24}$Mg
• Benchmark neutrinoless double-beta decay matrix elements in a light nucleus
• Predicting the neutrinoless double-beta decay matrix element of ${}^{136}$Xe using a statistical approach
• Benchmarking ${}^{136}$Xe Neutrinoless $\beta \beta$ Decay Matrix Element Calculations with the ${}^{138}\mathrm{Ba}(p,t)$ Reaction
• Application of efficient generator-coordinate subspace-selection algorithm to neutrinoless double-$\beta$ decay
• Global calculation of two-neutrino double-$\beta$ decay within the finite amplitude method in nuclear density functional theory
• Variation after projection calculations for high-spin states
• Neutrinoless double beta decay rates in the presence of light sterile neutrinos
• Present Status of Nuclear Shell-Model Calculations of Neutrinoless Double-Beta Decay Matrix Elements
• Recent progress in the electroweak structure of light nuclei using quantum Monte Carlo methods
• Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation
• Neutrinoless $\beta \beta$ decay nuclear matrix elements complete up to N${}^2$LO in heavy nuclei
• Beta Decay in Medium-Mass Nuclei with the In-Medium Similarity Renormalization Group
• Ab initio computations from ${}^{78}$Ni towards ${}^{70}$Ca along neutron number $N=50$
• Demonstration of the Rodeo Algorithm on a Quantum Computer
• Lattice Effective Field Theory Simulations of Nuclei
• Relativistic model-free prediction for neutrinoless double beta decay at leading order
• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• Multireference covariant density-functional theory for the low-lying states of odd-mass nuclei
• NMEs for $0\nu \beta \beta (0^{+}\to 2^{+})$ of two-nucleon mechanism for ${}^{76}$Ge
• Impact of correlations on nuclear binding energies
• Impact of isovector pairing fluctuation on neutrinoless double-beta decay in multi-reference covariant density functional theory
• 16O electroweak response functions from first principles
• A brief account of Steven Weinberg's legacy in ab initio many-body theory
• Ab initio nuclear shape coexistence and emergence of island of inversion around $N=20$
• Structure and dynamics of open-shell nuclei from spherical coupled-cluster theory
• Symmetry-projected variational calculations with the numerical suite TAURUS II. Configuration mixing of symmetry-projected reference states
• Estimation of nuclear matrix elements of double-$\beta$ decay from shell model and quasiparticle random-phase approximation
• Quantum-number projected generator coordinate method for ${}^{21}$Ne with a chiral two-nucleon-plus-three-nucleon interaction
• Nuclear matrix elements of neutrinoless double-beta decay in covariant density functional theory with different mechanisms
• Nuclear Schiff Moments and CP Violation
• Generator coordinate method for nuclear octupole excitations: status and perspectives
• Radiative and exchange corrections for two-neutrino double-beta decay
• Symmetry restoration methods
• Confronting the low-scale seesaw and leptogenesis with neutrinoless double beta decay
• Global Framework for Emulation of Nuclear Calculations
• Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model
• Evidence of a higher nodal band $\alpha$+${}^{44}$Ca cluster state in fusion reactions and $\alpha$ clustering in ${}^{48}$Ti
• Modewise Johnson-Lindenstrauss Embeddings for Nuclear Many-Body Theory
• Effective field theories for collective excitations of atomic nuclei
• Observation of long-range collective flow in OO and NeNe collisions and implications for nuclear structure studies
• NuLattice: Ab initio computations of atomic nuclei on lattices
• Advances in modeling nuclear matrix elements of neutrinoless double beta decay
• Toward scalable quantum computations of atomic nuclei
• Pathfinding Quantum Simulations of Neutrinoless Double-Beta Decay
• $\alpha$ + ${}^{92}$Zr cluster structure in ${}^{96}$Mo
• Neutrinoless $\beta \beta$ decay in the interacting boson model based on the nuclear energy density functionals
• Benchmarking nuclear matrix elements of $0\nu \beta \beta$ decay with high-energy nuclear collisions
• Two-neutrino $\beta \beta$ decay to excited states at next-to-leading order
• Singular Value Decomposition and Similarity Renormalization Group Evolution of Nuclear Interactions
• Mean-field approximation on steroids: exact description of the deuteron
• Controlled Gate Networks: Theory and Application to Eigenvalue Estimation
• Canadian Contributions to the Search for Neutrinoless Double Beta Decay
• In-Medium Similarity Renormalization Group at Finite Temperature
• Quantum State Preparation with Resolution Refinement
• Benchmarking projected generator coordinate method for nuclear Gamow-Teller transitions
• Ab initio study in the island of inversion within the two-major-shell valence space
• Ab initio short-range nuclear matrix elements for neutrinoless double-beta decay
• The lepton-number-violating pion decay and the type-I seesaw mechanism in chiral perturbation theory