Towards complete leading-order predictions for neutrinoless double $\beta$ decay

Abstract

The amplitude for the neutrinoless double $\beta$ ($0\nu \beta \beta$) decay of the two-neutron system, $nn\to pp{e}^{-}{e}^{-}$, constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale $0\nu \beta \beta$ searches. Assuming that the $0\nu \beta \beta$ 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 work, we develop a method to estimate the numerical value of its coefficient in analogy to the Cottingham formula and validate the result by reproducing the charge-independence-breaking contribution to the nucleon-nucleon scattering lengths. Our central result, while derived in the $\overline{\text{MS}}$ scheme, is given in terms of the renormalized amplitude ${\mathcal{A}}_{\nu }(|\mathbf{p}|,|{\mathbf{p}}^{\prime }|)$, 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 $0\nu \beta \beta$ decay.

arXiv comment7 pages, 3 figures; journal version. See arXiv:2102.03371 for an extended version

References in corpus (68)

• An accurate nucleon-nucleon potential with charge-independence breaking
• Modern Theory of Nuclear Forces
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Chiral effective field theory and nuclear forces
• Leptogenesis
• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen
• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Neutrinoless Double-Beta Decay: Status and Prospects
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Two-pion contribution to hadronic vacuum polarization
• Theory of neutrinoless double beta decay
• Neutrino-less Double Beta Decay and Particle Physics
• Nuclear effective field theory: status and perspectives
• Ab initio calculation of the neutron-proton mass difference
• Dispersion relation for hadronic light-by-light scattering: two-pion contributions
• Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay
• Final Results of GERDA on the Search for Neutrinoless Double-$\beta$ Decay
• Three-body forces: From cold atoms to nuclei
• Nucleon-Nucleon Scattering from Effective Field Theory
• Discrepancy between experimental and theoretical $\beta$-decay rates resolved from first principles
• $0\nu \beta \beta$ and $2\nu \beta \beta$ nuclear matrix elements in the interacting boson model with isospin restoration
• Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
• $0\nu \beta \beta$ and $2\nu \beta \beta$ nuclear matrix elements, QRPA, and isospin symmetry restoration
• Dispersion relation for hadronic light-by-light scattering: theoretical foundations
• Search for Neutrinoless Double-Beta Decay with the Upgraded EXO-200 Detector
• Chiral two-body currents in nuclei: Gamow-Teller transitions and neutrinoless double-beta decay
• Improved Limit on Neutrinoless Double-Beta Decay in ${}^{130}$Te with CUORE
• Search for Zero-Neutrino Double Beta Decay in 76Ge with the Majorana Demonstrator
• A new leading contribution to neutrinoless double-beta decay
• Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Shape and pairing fluctuations effects on neutrinoless double beta decay nuclear matrix elements
• A neutrinoless double beta decay master formula from effective field theory
• Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses
• Neutrinoless double-beta decay and effective field theory
• Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Coulomb Effects in Low Energy Proton-Proton Scattering
• A renormalized approach to neutrinoless double-beta decay
• Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven
• Ab initio neutrinoless double-beta decay matrix elements for 48Ca, 76Ge, and 82Se
• Quantum Monte Carlo calculations of weak transitions in $A$=6--10 nuclei
• Nucleon Axial Radius and Muonic Hydrogen - A New Analysis and Review
• Neutrinoless double beta decay matrix elements in light nuclei
• Power Counting of Contact-Range Currents in Effective Field Theory
• Sterile neutrinos and neutrinoless double beta decay in effective field theory
• Heavy physics contributions to neutrinoless double beta decay from QCD
• Measurement of the 2$\nu \beta \beta$ decay half-life of ${}^{150}$Nd and a search for 0$\nu \beta \beta$ decay processes with the full exposure from the NEMO-3 detector
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Neutrinoless double beta decay in effective field theory: the light Majorana neutrino exchange mechanism
• The Electromagnetic Mass Differences of Pions and Kaons
• On the Corrections to Dashen's Theorem
• Quenching of nuclear matrix elements for $0\nu \beta \beta$ decay by chiral two-body currents
• Long-distance Contributions to Neutrinoless Double Beta Decay ${\pi }^{-}\to {\pi }^{+}ee$
• Shell-model calculation of neutrinoless double-$\beta$ decay of ${}^{76}$Ge
• Nucleon spin-averaged forward virtual Compton tensor at large $Q^2$
• The path from lattice QCD to the short-distance contribution to $0\nu \beta \beta$ decay with a light Majorana neutrino
• Ab initio benchmarks of neutrinoless double beta decay in light nuclei with a chiral Hamiltonian
• Light-Neutrino Exchange and Long-Distance Contributions to $0\nu 2\beta$ Decays: An Exploratory Study on $\pi \pi \to ee$
• The Long and Short of Nuclear Effective Field Theory Expansions
• Charge independence breaking and charge symmetry breaking in the nucleon-nucleon interaction from effective field theory
• On the mass difference between proton and neutron
• Finite-volume formalism in the $2\stackrel{H_I+H_I}{\to }2$ transition: an application to the lattice QCD calculation of double beta decays
• Lattice QCD Inputs for Nuclear Double Beta Decay
• Sum rule for the Compton amplitude and implications for the proton-neutron mass difference
• Isospin splittings in the decuplet baryon spectrum from dynamical QCD+QED
• First data from the CUPID-Mo neutrinoless double beta decay experiment

Cited by in corpus (47)

• Toward the discovery of matter creation with neutrinoless double-beta decay
• A Next-Generation Liquid Xenon Observatory for Dark Matter and Neutrino Physics
• Kaon electromagnetic form factors in dispersion theory
• 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
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Impact of the leading-order short-range nuclear matrix element on the neutrinoless double-beta decay of medium-mass and heavy nuclei
• Ab initio uncertainty quantification of neutrinoless double-beta decay in ${}^{76}$Ge
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Towards Precise and Accurate Calculations of Neutrinoless Double-Beta Decay: Project Scoping Workshop Report
• Unraveling the $0\nu \beta \beta$ Decay Mechanisms
• Neutrinoless $\beta \beta$-decay nuclear matrix elements from two-neutrino $\beta \beta$-decay data
• Neutrinoless double-beta decay: combining quantum Monte Carlo and the nuclear shell model with the generalized contact formalism
• Leptonic anomalous magnetic moments in $\nu$SMEFT
• Large-$N_c$ analysis of two-nucleon neutrinoless double beta decay and charge-independence-breaking contact terms
• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Radiative corrections to superallowed $\beta$ decays in effective field theory
• 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
• On the Extraction of Low-energy Constants of Single- and Double-$\beta$ Decays from Lattice QCD: A Sensitivity Analysis
• Testing the Inverted Neutrino Mass Ordering with Neutrinoless Double-Beta Decay
• Width effects of broad new resonances in loop observables and application to $(g-2{)}_{\mu }$
• $\nu$DoBe -- A Python Tool for Neutrinoless Double Beta Decay
• Sterile neutrinos with non-standard interactions in $\beta$- and $0\nu \beta \beta$-decay experiments
• Neutrinoless double beta decay in Left-Right symmetric model with double seesaw mechanism
• Correlations Between Neutrinoless Double-Beta, Double Gamow-Teller and Double-Magnetic Decays in the pnQRPA Framework
• Neutrinoless double beta decay rates in the presence of light sterile neutrinos
• What Can Possibly Go Wrong?
• Recent progress in the electroweak structure of light nuclei using quantum Monte Carlo methods
• Beta Decay in Medium-Mass Nuclei with the In-Medium Similarity Renormalization Group
• Lattice QCD calculation of light sterile neutrino contribution in $0\nu 2\beta$ decay
• Neutrinoless Double Beta Decay Sensitivity of the XLZD Rare Event Observatory
• Relativistic model-free prediction for neutrinoless double beta decay at leading order
• Contact operators in renormalization of attractive singular potentials
• Uncovering a chirally suppressed mechanism of $0\nu \beta \beta$ decay with LHC searches
• Impact of nuclear matrix element calculations for current and future neutrinoless double beta decay searches
• Two-neutrino $\beta \beta$ decay of ${}^{136}$Xe to the first excited $0^{+}$ state in ${}^{136}$Ba
• Confronting the low-scale seesaw and leptogenesis with neutrinoless double beta decay
• Inference of neutrino nature and Majorana CP phases from $0\nu \beta \beta$ decays with inverted mass ordering
• Perturbative renormalization of chiral nuclear forces at subleading order in 3S1-3D1 channel
• Workshop summary -- Kaons@CERN 2023
• Neutrinoless double-beta decay in a finite volume from relativistic effective field theory
• Scalarful double beta decay
• Dark matter scattering off ${}^4$He in chiral effective field theory
• Scalar-induced Neutrinoless Double Beta Decay in $SU(5)$
• Impact of dim-6 $\nu$SMEFT operators on low-scale leptogenesis
• Canadian Contributions to the Search for Neutrinoless Double Beta Decay