Long-distance Contributions to Neutrinoless Double Beta Decay ${\pi }^{-}\to {\pi }^{+}ee$

Abstract

Neutrinoless double beta decay, if detected, would prove that neutrinos are Majorana fermions and provide the direct evidence for lepton number violation. If such decay would exist in nature, then ${\pi }^{-}{\pi }^{-}\to ee$ and ${\pi }^{-}\to {\pi }^{+}ee$ (or equivalently ${\pi }^{-}{e}^{+}\to {\pi }^{+}{e}^{-}$) are the two simplest processes accessible via first-principle lattice QCD calculations. In this work, we calculate the long-distance contributions to the ${\pi }^{-}\to {\pi }^{+}ee$ transition amplitude using four ensembles at the physical pion mass with various volumes and lattice spacings. We adopt the infinite-volume reconstruction method to control the finite-volume effects arising from the (almost) massless neutrino. Providing the lattice QCD inputs for chiral perturbation theory, we obtain the low energy constant $g_{\nu }^{\pi \pi }(m_{\rho })=-10.89(28{)}_{\text{stat}}(74{)}_{\text{sys}}$, which is close to $g_{\nu }^{\pi \pi }(m_{\rho })=-11.96(31{)}_{\text{stat}}$ determined from the crossed-channel ${\pi }^{-}{\pi }^{-}\to ee$ decay.

arXiv comment19 pages, 6 figures

References in corpus (27)

• Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Results on neutrinoless double beta decay of 76Ge from GERDA Phase I
• Ab initio calculation of the neutron-proton mass difference
• Search for Majorana neutrinos with the first two years of EXO-200 data
• Limit on Neutrinoless ββ Decay of Xe-136 from the First Phase of KamLAND-Zen and Comparison with the Positive Claim in Ge-76
• Domain wall QCD with physical quark masses
• Current Status and Future Prospects of the SNO+ Experiment
• First Results from CUORE: A Search for Lepton Number Violation via $0\nu \beta \beta$ Decay of ${}^{130}$Te
• Improved limit on neutrinoless double beta decay of ${}^{76}$Ge from GERDA Phase II
• Background free search for neutrinoless double beta decay with GERDA Phase II
• Search for Neutrinoless Double-Beta Decay with the Upgraded EXO-200 Detector
• Search for Zero-Neutrino Double Beta Decay in 76Ge with the Majorana Demonstrator
• A new leading contribution to neutrinoless double-beta decay
• QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons
• A neutrinoless double beta decay master formula from effective field theory
• Covariant approximation averaging
• First Result on the Neutrinoless Double Beta Decay of ${}^{82}$Se with CUPID-0
• Finite-Volume Electromagnetic Corrections to the Masses of Mesons, Baryons and Nuclei
• Heavy physics contributions to neutrinoless double beta decay from QCD
• Neutrinoless double beta decay in effective field theory: the light Majorana neutrino exchange mechanism
• Double-$\beta$ Decay Matrix Elements from Lattice Quantum Chromodynamics
• The isotensor axial polarisability and lattice QCD input for nuclear double-$\beta$ decay phenomenology
• Renormalization Group Evolution of Dimension-seven Operators in Standard Model Effective Field Theory and Relevant Phenomenology
• Light-Neutrino Exchange and Long-Distance Contributions to $0\nu 2\beta$ Decays: An Exploratory Study on $\pi \pi \to ee$
• Initial Results from the MAJORANA DEMONSTRATOR
• Multi-Grid Lanczos

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• Towards Precise and Accurate Calculations of Neutrinoless Double-Beta Decay: Project Scoping Workshop Report
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• The path from lattice QCD to the short-distance contribution to $0\nu \beta \beta$ decay with a light Majorana neutrino
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• 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 Calculation of the Pion Mass Splitting
• On the Extraction of Low-energy Constants of Single- and Double-$\beta$ Decays from Lattice QCD: A Sensitivity Analysis
• Two-neutrino double-beta decay in pionless effective field theory from a Euclidean finite-volume correlation function
• First-principle calculation of ${\eta }_c\to 2\gamma$ decay width from lattice QCD
• Finite-volume effects in long-distance processes with massless leptonic propagators
• Neutrinoless $\beta \beta$ decay nuclear matrix elements complete up to N${}^2$LO in heavy nuclei
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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
• Radiative corrections to leptonic decays using infinite-volume reconstruction
• Neutrinoless Double Beta Decay from Lattice QCD: The Short-Distance ${\pi }^{-}\to {\pi }^{+}{e}^{-}{e}^{-}$ Amplitude
• Investigating nuclear beta decay using lattice quantum Monte Carlo approach
• Neutrinoless double-beta decay in a finite volume from relativistic effective field theory
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