Dispersive formalism for the nuclear structure correction ${\delta }_{\mathrm{NS}}$ to the $\beta$ decay rate

Abstract

We analyze the axial $\gamma W$-box diagram for $I(J^P)=1(0^{+})$ nuclei and provide a dispersion representation of the nuclear-structure correction ${\delta }_{\text{NS}}$ including its energy-dependent part. We also summarize useful isospin rotation formula and representations in nuclear theory that could facilitate the calculation of the parity-odd nuclear structure function $F_3(\nu ,Q^2)$. They provide a rigorous theory framework for the future, high-precision calculation of the nuclear structure correction ${\delta }_{\text{NS}}$ necessary for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ud}|$ from superallowed nuclear $\beta$ decays.

Version accepted by Physical Review C

References in corpus (25)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• Test of lepton universality using $B^{+}\to K^{+}{\ell }^{+}{\ell }^{-}$ decays
• Superallowed 0+ to 0+ nuclear beta decays: A new survey with precision tests of the conserved vector current hypothesis and the standard model
• Search for lepton-universality violation in $B^{+}\to K^{+}{\ell }^{+}{\ell }^{-}$ decays
• Muon g-2: Review of Theory and Experiment
• An improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi beta decay
• Measurement of the Weak Axial-Vector Coupling Constant in the Decay of Free Neutrons Using a Pulsed Cold Neutron Beam
• Isospin corrections for superallowed Fermi beta decay in self-consistent relativistic random phase approximation approaches
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• Inclusive neutrino scattering off deuteron from threshold to GeV energies
• First-principles calculation of electroweak box diagrams from lattice QCD
• Isospin-symmetry-breaking corrections to superallowed Fermi beta decay: Formalism and schematic models
• Coulomb corrections to superallowed beta decay in nuclei
• Microscopic calculations of isospin-breaking corrections to superallowed beta-decay
• Pion-induced radiative corrections to neutron beta-decay
• Dispersion relation analysis of the radiative corrections to $g_A$ in the neutron $\beta$-decay
• Parameterization of the statistical rate function for select superallowed transitions
• Complete theory of radiative corrections to $K_{\ell 3}$ decays and the $V_{us}$ update
• Electroweak nuclear radii constrain the isospin breaking correction to $V_{ud}$
• Radiative corrections to semileptonic beta decays: Progress and challenges
• Lattice QCD Determination of $g_A$
• A New Theory Framework for the Electroweak Radiative Corrections in $K_{l3}$ Decays
• Nucleon-Nucleon Short-Ranged Correlations, $\beta$ Decay and the Unitarity of the CKM Matrix
• $K_{\ell 3}$ form factors at the physical point: Toward the continuum limit
• Electron Mass Singularities in Semileptonic Kaon Decays

Cited by in corpus (11)

• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Radiative corrections to superallowed $\beta$ decays in effective field theory
• An $\text{ab initio}$ strategy for taming nuclear-structure dependence of $V_{ud}$ extractions: the ${}^{10}\mathrm{C}\to {}^{10}\mathrm{B}$ superallowed transition
• Superallowed nuclear beta decays and precision tests of the Standard Model
• Data-driven reevaluation of $ft$-values in superallowed $\beta$ decays
• Towards $ab$-$initio$ nuclear theory calculations of ${\delta }_{\mathrm{C}}$
• Opportunities and open questions in modern $\beta$ decay
• Quantum Monte Carlo calculations of magnetic form factors in light nuclei
• Magnetic structure of $A\le 10$ nuclei using the Norfolk nuclear models with quantum Monte Carlo methods
• The Role of Ab Initio Beta-Decay Calculations in Light Nuclei for Probes of Physics Beyond the Standard Model
• Pion $\beta$ decay and $\tau \to \pi \pi {\nu }_{\tau }$ beyond leading logarithms