High precision analytical description of the allowed $\beta$ spectrum shape

Abstract

A fully analytical description of the allowed $\beta$ spectrum shape is given in view of ongoing and planned measurements. Its study forms an invaluable tool in the search for physics beyond the standard electroweak model and the weak magnetism recoil term. Contributions stemming from finite size corrections, mass effects, and radiative corrections are reviewed. A particular focus is placed on atomic and chemical effects, where the existing description is extended and analytically provided. The effects of QCD-induced recoil terms are discussed, and cross-checks were performed for different theoretical formalisms. Special attention was given to a comparison of the treatment of nuclear structure effects in different formalisms. Corrections were derived for both Fermi and Gamow-Teller transitions, and methods of analytical evaluation thoroughly discussed. In its integrated form, calculated $f$ values were in agreement with the most precise numerical results within the aimed for precision. We stress the need for an accurate evaluation of weak magnetism contributions, and note the possible significance of the oft-neglected induced pseudoscalar interaction. Together with improved atomic corrections, we then present an analytical description of the allowed $\beta$ spectrum shape accurate to a few parts in $10^{-4}$ down to 1\,keV for low to medium $Z$ nuclei, thereby extending the work by previous authors by nearly an order of magnitude.

arXiv commentAccepted for Reviews of Modern Physics

References in corpus (52)

• Nuclear ground-state masses and deformations: FRDM(2012)
• Improved Predictions of Reactor Antineutrino Spectra
• Quantum Monte Carlo methods for nuclear physics
• Quantum Monte Carlo Calculations of Light Nuclei
• Superallowed 0+ to 0+ nuclear beta decays: A new survey with precision tests of the conserved vector current hypothesis and the standard model
• Tests of the standard electroweak model in beta decay
• Probing Novel Scalar and Tensor Interactions from (Ultra)Cold Neutrons to the LHC
• Improved Calculation of Electroweak Radiative Corrections and the Value of V_ud
• Superallowed 0+ --> 0+ nuclear beta decays: 2014 critical survey, with precise results for Vud and CKM unitarity
• The effective g_A in the pf-shell
• An improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi beta decay
• Superallowed nuclear beta decays: A critical survey with tests of CVC and the standard model
• Beta Decays and Non-Standard Interactions in the LHC Era
• Precision Measurements and CKM Unitarity
• Calculated corrections to superallowed Fermi beta decay: New evaluation of the nuclear-structure-dependent terms
• Non-standard Charged Current Interactions: beta decays versus the LHC
• Low Energy Precision Test of Supersymmetry
• Quantum Monte Carlo calculations of spectroscopic overlaps in $A\le 7$ nuclei
• Induced pseudoscalar coupling of the proton weak interaction
• Ft values of the T = 1/2 mirror beta transitions
• Low Energy Tests of the Weak Interaction
• Comparative tests of isospin-symmetry-breaking corrections to superallowed 0+-to-0+ nuclear beta decay
• Isospin breaking in the nucleon mass and the sensitivity of beta decays to new physics
• Measurement of the Beta-Neutrino Correlation of Sodium-21 using Shakeoff Electrons
• Neutron Beta-Decay as Laboratory for Test of Standard Model
• Radiative Corrections in Precision Electroweak Physics: a Historical Perspective
• Symmetry violations in nuclear and neutron $\beta$ decay
• Lorentz violation in neutron and allowed nuclear beta decay
• Statistical analysis of beta decays and the effective value of g_A in the proton-neutron quasiparticle random-phase approximation framework
• Radiative Correction to the anti-nu_e (nu_e) Spectrum in beta-Decay
• Parameterization of the statistical rate function for select superallowed transitions
• Second Class Current in QCD Sum Rules
• Beta asymmetry parameter in the decay of 114In
• Renormalization of the weak hadronic current in the nuclear medium
• Tensor interaction constraints from beta decay recoil spin asymmetry of trapped atoms
• Precision Measurement of the Radiative $\mathrm{B}$ Decay of the Free Neutron
• Precision measurements of the ${}^{60}$Co $\beta$-asymmetry parameter in search for tensor currents in weak interactions
• Hylleraas-configuration-interaction analysis of the low-lying states in the three-electron Li atom and Be+ ion
• A new analysis of 14O beta decay: branching ratios and CVC consistency
• A T-odd Momentum Correlation in Radiative β-Decay
• An Investigation into the 113-Cd Beta Decay Spectrum using a CdZnTe Array
• Radiative Beta Decay for Studies of CP Violation
• Measurement of the $\beta$-asymmetry parameter of ${}^{67}$Cu in search for tensor type currents in the weak interaction
• Test of the Conserved Vector Current Hypothesis by beta-ray Angular Distribution Measurement in the Mass-8 System
• Electron shakeoff following the ?+ decay of trapped 35Ar+ ions
• Precision measurements with LPCTrap at GANIL
• Nuclear Charge Density Distributions from Elastic Electron Scattering Data
• Atomic excitations during the nuclear ß- decay in light atoms
• Radiative tritium beta-decay and the neutrino mass
• Measurement of the Shape Factor for the Beta Decay of ${}^{14}$O
• Mean-field description of nuclear charge density distributions.
• Accurate CI and Hylleraas-CI wave functions for the atomic effects in the whole-atom-nuclear beta-decay of the Li atom

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