A new critical survey of all half-life, decay-energy, and branching-ratio measurements related to 23 superallowed $0^{+}\to 0^{+}\beta$ decays is presented. Included are 222 individual measurements of comparable precision obtained from 174 published references. Compared with our last survey in 2015, we have added results from 28 new publications and eliminated an approximately equal number whose results have been superseded by much more precise modern data. We obtain world-average $ft$ values for each of the 21 transitions that have a complete set of data and then apply radiative and isospin-symmetry-breaking corrections to extract “corrected” $\mathcal{F}t$ values. Fifteen of these $\mathcal{F}t$ values now have a precision of $0.3\%$ or better and all take the same value within statistics, as expected from conservation of the vector current. Their average, $\overline{\mathcal{F}t}$, when combined with the muon lifetime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa matrix, $V_{\mathit{ud}}=0.97373\pm 0.00031$. This is lower than our 2015 result by one standard deviation and its uncertainty is increased by $50\%$. This is a consequence not of any shifts in the experimental data but of new calculations for the radiative corrections. The lower $V_{\mathit{ud}}$ value now leads to greater tension in the top-row test of unitarity in the CKM matrix. Updates in experimental data have independently led to a factor-of-two tighter limit being set on the possible existence of a scalar interaction. The new limit on Fierz interference is $b_F\le$ 0.0033 at the $90\%$ confidence level.

We report quantum Monte Carlo calculations of weak transitions in $A\le 10$ nuclei, based on the Norfolk two- and three-nucleon chiral interactions, and associated one- and two-body axial currents. We find that the contribution from two-body currents is at the 2–3% level, with the exception of matrix elements entering the rates of ${}^8\mathrm{Li}$, ${}^8\mathrm{B}$, and ${}^8\mathrm{He}$ $\beta$ decay. These matrix elements are suppressed in impulse approximation based on the (leading order) Gamow Teller transition operator alone; two-body currents provide a $20–30\%$ correction, which is, however, insufficient to bring theory in agreement with experimental data. For the other transitions, the agreement with the data is satisfactory, and the results exhibit a negligible to mild model dependence when different combinations of Norfolk interactions are utilized to construct the nuclear wave functions. We report a complete study of two-body weak transition densities which reveals the expected universal behavior of two-body currents at short distances throughout the range of $A=3$ to $A=10$ systems considered here.

We report on a precise measurement of the electron-antineutrino angular correlation ($a$ coefficient) in free neutron beta decay from the $a\mathrm{SPECT}$ experiment. The $a$ coefficient is inferred from the recoil energy spectrum of the protons which are detected in $4\pi$ by the $a\mathrm{SPECT}$ spectrometer using magnetic adiabatic collimation with an electrostatic filter. Data are presented from a 100-day run at the Institut Laue Langevin in 2013. The sources of systematic errors are considered and included in the final result. We obtain $a=-0.10430\left(84\right)$ which is the most precise measurement of the neutron $a$ coefficient to date. From this, the ratio of axial vector to vector coupling constants is derived giving $\left|\lambda \right|=1.2677\left(28\right)$.

The Ultracold Neutron Asymmetry (UCNA) experiment was designed to measure the $\beta$-decay asymmetry parameter, $A_0$, for free neutron decay. In the experiment, polarized ultracold neutrons are transported into a decay trap, and their $\beta$-decay electrons are detected with $\approx 4\pi$ acceptance into two detector packages which provide position and energy reconstruction. The experiment also has sensitivity to $b_n$, the Fierz interference term in the neutron $\beta$-decay rate. In this work, we determine $b_n$ from the energy dependence of $A_0$ using the data taken during the UCNA 2011–2013 run. In addition, we present the same type of analysis using the earlier 2010 $A$ dataset. Motivated by improved statistics and comparable systematic errors compared to the 2010 data-taking run, we present a new $b_n$ measurement using the weighted average of our asymmetry dataset fits, to obtain $b_n=0.066\pm 0.{041}_{\text{stat}}\pm 0.{024}_{\text{syst}}$ which corresponds to a limit of $-0.012<b_n<0.144$ at the 90% confidence level.

As part of a continuing effort to test the unitarity of the Cabbibo-Kobayashi-Maskawa matrix, we have measured the branching ratio for the superallowed $0^{+}\to 0^{+}{\beta }^{+}$-decay transition from ${}^{26}\mathrm{Si}$ to be 0.7569(14), a result with 0.18% relative precision. With this result, the $ft$ value for the transition is now established with comparable precision to the well-known superallowed transitions currently used in the determination of $V_{ud}$. It also completes a second pair of mirror superallowed transitions, ${}^{26}\mathrm{Si}$ $\to$ ${}^{26m}\mathrm{Al}$ and ${}^{26m}\mathrm{Al}$ $\to$ ${}^{26}\mathrm{Mg}$, the ratio of whose measured $ft$ values provides a sensitive test of the method used to calculate the isospin-symmetry-breaking correction ${\delta }_C$ needed to determine $V_{ud}$. Like the previously measured ratio for the mass-38 mirror pair, the new result agrees well with the calculation based on Woods-Saxon radial wave functions and strengthens the case for rejecting the calculation that uses Hartree-Fock radial functions.

The electromagnetic responses obtained from Green's function Monte Carlo (GFMC) calculations are based on realistic treatments of nuclear interactions and currents. The main limitations of this method comes from its nonrelativistic nature and its computational cost, the latter hampering the direct evaluation of the inclusive cross sections as measured by experiments. We extend the applicability of GFMC in the quasielastic region to intermediate momentum transfers by performing the calculations in a reference frame that minimizes nucleon momenta. Additional relativistic effects in the kinematics are accounted for employing the two-fragment model. In addition, we developed a novel algorithm, based on the concept of first-kind scaling, to compute the inclusive electromagnetic cross section of ${}^4\mathrm{He}$ through an accurate and reliable interpolation of the response functions. A very good agreement is obtained between theoretical and experimental cross sections for a variety of kinematical setups. This offers a promising prospect for the data analysis of neutrino-oscillation experiments that requires an accurate description of nuclear dynamics in which relativistic effects are fully accounted for.

Background: The neutron $\beta$-decay asymmetry parameter $A_0$ defines the angular correlation between the spin of the neutron and the momentum of the emitted electron. Values for $A_0$ permit an extraction of the ratio of the weak axial-vector to vector coupling constants, $\lambda \equiv g_A/g_V$, which under assumption of the conserved vector current hypothesis ($g_V=1$) determines $g_A$. Precise values for $g_A$ are important as a benchmark for lattice QCD calculations and as a test of the standard model.

Purpose: The UCNA experiment, carried out at the Ultracold Neutron (UCN) source at the Los Alamos Neutron Science Center, was the first measurement of any neutron $\beta$-decay angular correlation performed with UCN. This article reports the most precise result for $A_0$ obtained to date from the UCNA experiment, as a result of higher statistics and reduced key systematic uncertainties, including from the neutron polarization and the characterization of the electron detector response.

Methods: UCN produced via the downscattering of moderated spallation neutrons in a solid deuterium crystal were polarized via transport through a 7 T polarizing magnet and a spin flipper, which permitted selection of either spin state. The UCN were then contained within a 3-m long cylindrical decay volume, situated along the central axis of a superconducting 1 T solenoidal spectrometer. With the neutron spins then oriented parallel or anti-parallel to the solenoidal field, an asymmetry in the numbers of emitted decay electrons detected in two electron detector packages located on both ends of the spectrometer permitted an extraction of $A_0$.

Results: The UCNA experiment reports a new 0.67% precision result for $A_0$ of $A_0=-0.12054{\left(44\right)}_{\mathrm{stat}}{\left(68\right)}_{\mathrm{syst}}$, which yields $\lambda =g_A/g_V=-1.2783\left(22\right)$. Combination with the previous UCNA result and accounting for correlated systematic uncertainties produces $A_0=-0.12015{\left(34\right)}_{\mathrm{stat}}{\left(63\right)}_{\mathrm{syst}}$ and $\lambda =g_A/g_V=-1.2772\left(20\right)$.

Conclusions: This new result for $A_0$ and $g_A/g_V$ from the UCNA experiment has provided confirmation of the shift in values for $g_A/g_V$ that has emerged in the published results from more recent experiments, which are in striking disagreement with the results from older experiments. Individual systematic corrections to the asymmetries in older experiments (published prior to 2002) were $>10$%, whereas those in the more recent ones (published after 2002) have been of the scale of $<2$%. The impact of these older results on the global average will be minimized should future measurements of $A_0$ reach the 0.1% level of precision with central values near the most recent results.

We show that electron time-of-flight can be a useful tool in $\beta$-decay spectroscopy, even in the energy range up to 700 keV relevant for neutron $\beta$ decay. As a first application, we use electron time-of-flight measurements for the precise calibration of an electron detector.

The $Q_{\text{EC}}$ value of the superallowed ${\beta }^{+}$ emitter ${}^{42}\mathrm{Sc}$ has been measured with the JYFLTRAP Penning-trap mass spectrometer at the University of Jyväskylä to be 6426.350(53) keV. This result is at least a factor of four more precise than all previous measurements, which were also inconsistent with one another. As a byproduct we determine the excitation energy of the $7^{+}$ isomeric state in ${}^{42}\mathrm{Sc}$ to be 616.771(62) keV, which deviates by $8\sigma$ from the previous measurement.

Background: Parity-violating elastic electron-nucleon scattering at low momentum transfer allows one to access the nucleon's weak charge, the vector coupling of the $Z$-boson to the nucleon. In the Standard Model and at tree level, the weak charge of the proton is related to the weak mixing angle and accidentally suppressed, $Q_W^{p,\mathrm{tree}}=1-4{sin}^2{\theta }_W\approx 0.07$. Modern experiments aim at extracting $Q_W^p$ at $\sim 1\%$ accuracy. Similarly, parity nonconservation in atoms allows to access the weak charge of atomic nuclei.

Purpose: We consider a novel class of radiative corrections due to the exchange of two photons, with parity violation in the hadronic/nuclear system. These corrections are prone to long-range interactions and may affect the extraction of ${sin}^2{\theta }_W$ from the experimental data at the relevant level of precision.

Methods: The two-photon exchange contribution to the parity-violating electron-proton scattering amplitude is studied in the framework of forward dispersion relations. We address the general properties of the parity-violating forward Compton scattering amplitude and use relativistic chiral perturbation theory to provide the first field-theoretical proof that it obeys a superconvergence relation.

Results: We show that the significance of this new correction increases with the beam energy in parity-violating electron scattering, but the superconvergence relation protects the formal definition of the weak charge as a limit at zero-momentum transfer and zero energy. We evaluate the new correction in a hadronic model with pion loops and the $\mathrm{\Delta }\left(1232\right)$ resonance, supplemented with a high-energy contribution. For the kinematic conditions of existing and upcoming experiments we show that two-photon exchange corrections with hadronic or nuclear parity violation do not pose a problem for the interpretation of the data in terms of the weak mixing angle at the present level of accuracy.

Conclusions: Two-photon exchange in presence of hadronic or nuclear parity violation gives rise to long-range parity-violating interactions. Depending on the kinematic conditions and precision goal, this novel correction may affect the extraction of weak charges from experiments with atoms and electron scattering.

Background: Lorentz invariance is key in our understanding of nature, yet relatively few experiments have tested Lorentz invariance in weak interactions.

Purpose: Our goal is to obtain limits on Lorentz-invariance violation in weak interactions, in particular rotational invariance in $\beta$ decay.

Method: We search for a dependence of the lifetime of ${}^{20}\mathrm{Na}$ nuclei on the nuclear spin direction. Such directional dependence would be evidence for Lorentz-invariance violation in weak interactions. A difference in lifetime between nuclei that are polarized in the east and west direction is searched for. This difference is maximally sensitive to the rotation of the Earth, while the sidereal dependence is free from most systematic errors.

Results: The experiment sets a limit of $2\times {10}^{-4}$ at 90% C.L. on the amplitude of the sidereal variation of the relative lifetime differences, an improvement by a factor 15 compared to an earlier result.

Conclusions: No significant violation of Lorentz invariance is found. The result sets limits on parameters of theories describing Lorentz-invariance violation.

Research efforts ranging from studies of solid helium to searches for a neutron electric dipole moment require isotopically purified helium with a ratio of ${}^3\mathrm{He}$ to ${}^4\mathrm{He}$ at levels below that which can be measured using traditional mass spectroscopy techniques. We demonstrate an approach to such a measurement using accelerator mass spectroscopy, reaching the ${10}^{-14}$ level of sensitivity, several orders of magnitude more sensitive than other techniques. Measurements of ${}^3\mathrm{He}/{}^4\mathrm{He}$ in samples relevant to the measurement of the neutron lifetime indicate the need for substantial corrections. We also argue that there is a clear path forward to sensitivity increases of at least another order of magnitude.

We present a new measurement of the branching ratio for the decay of ${}^{14}\mathrm{O}$ to the ground state of ${}^{14}\mathrm{N}$. The experimental result, ${\lambda }_0/{\lambda }_{\mathrm{total}}=(4.934\pm 0.040(\mathrm{stat}.)\pm 0.061(\mathrm{syst}.))\times {10}^{-3}$, is significantly smaller than previous determinations of this quantity. The new measurement allows an improved determination of the partial half-life for the superallowed $0^{+}\to 0^{+}$ Fermi decay to the ${}^{14}\mathrm{N}$ first excited state, which impacts the determination of the $V_{ud}$ element of the CKM matrix. With the new measurement in place, the corrected ${}^{14}\mathrm{O}\mathcal{F}t$ value is in good agreement with the average $\mathcal{F}t$ for other superallowed $0^{+}\to 0^{+}$ Fermi decays.

Background: A major goal of nuclear theory is to understand the strong interaction in nuclei as it manifests itself in terms of two- and many-body forces among the nuclear constituents, the protons and neutrons, and the interactions of these constituents with external electroweak probes via one- and many-body currents.

Purpose: The objective of the present work is to calculate the quasielastic electroweak response functions in light nuclei within the realistic dynamical framework outlined above. These response functions determine the inclusive cross section as function of the lepton momentum and energy transfers.

Methods: Their ab initio calculation is a very challenging quantum many-body problem, since it requires summation over the entire excitation spectrum of the nucleus and inclusion in the electroweak currents of one- and many-body terms. Green's functions Monte Carlo methods allow one to circumvent both difficulties by computing the response in imaginary time (the so-called Euclidean response) and hence summing implicitly over the bound and continuum states of the nucleus, and by implementing specific algorithms designed to deal with the complicated spin-isospin structure of nuclear many-body operators.

Results: Theoretical predictions for ${}^4\mathrm{He}$ and ${}^{12}\mathrm{C}$, confirmed by experiment in the electromagnetic case, show that two-body currents generate excess transverse strength from threshold to the quasielastic to the dip region and beyond.

Conclusions: These results challenge the conventional picture of quasielastic inclusive scattering as being largely dominated by single-nucleon knockout processes.

The $\beta$ decay of molecular tritium currently provides the highest sensitivity in laboratory-based neutrino mass measurements. The upcoming Karlsruhe Tritium Neutrino (KATRIN) experiment will improve the sensitivity to 0.2 eV, making a percent-level quantitative understanding of molecular effects essential. The modern theoretical calculations available for neutrino mass experiments agree with spectroscopic data. Moreover, when neutrino mass experiments performed in the 1980s with gaseous tritium are reevaluated using these modern calculations, the extracted neutrino mass squared values are consistent with zero instead of being significantly negative. However, the calculated molecular final-state branching ratios are in conflict with dissociation experiments performed in the 1950s. We reexamine the theory of the final-state spectrum of molecular-tritium decay and its effect on the determination of the neutrino mass, with an emphasis on the role of the vibrational- and rotational-state distribution in the ground electronic state. General features can be reproduced quantitatively from considerations of kinematics and zero-point motion. We summarize the status of validation efforts and suggest means for resolving the apparent discrepancy in dissociation rates.

A new critical survey is presented of all half-life, decay-energy, and branching-ratio measurements related to 20 superallowed $0^{+}\to 0^{+}\beta$ decays. Included are 222 individual measurements of comparable precision obtained from 177 published references. Compared with our last review in 2008, we have added results from 24 new publications and eliminated 9 references, the results from which having been superseded by much more precise modern data. We obtain world-average $ft$ values for each of the 18 transitions that have a complete set of data, then apply radiative and isospin-symmetry-breaking corrections to extract “corrected” $\mathcal{F}t$ values. Fourteen of these $\mathcal{F}t$ values now have a precision of order 0.1% or better. In the process of obtaining these results we carefully evaluate the available calculations of the isospin-symmetry-breaking corrections by testing the extent to which they lead to $\mathcal{F}t$ values consistent with conservation of the vector current. Only one set of calculations satisfactorily meets this condition. The resultant average $\mathcal{F}t$ value, when combined with the muon lifetime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa matrix, $V_{ud}=0.97417\pm 0.00021.$ The unitarity test on the top row of the matrix becomes $|V_{ud}{|}^2+|V_{us}{|}^2+{\left|V_{ub}\right|}^2=0.99978\pm 0.00055$ if the Particle Data Group (PDG) recommended value for $V_{us}$ is used. However, recent lattice QCD calculations, not included yet in the PDG evaluation, have introduced some inconsistency into kaon-decay measurements of $V_{us}$ and $V_{us}/V_{ud}.$ We examine the impact of these new results on the unitarity test and conclude that there is no evidence of any statistically significant violation of unitarity. Finally, from the $\mathcal{F}t$-value data we also set limits on the possible existence of scalar interactions.

Time reversal invariance violating (TRIV) effects in neutron transmission through a nuclear target are discussed. We demonstrate the existence of a class of experiments that are free from false asymmetries. We discuss the enhancement of TRIV effects for neutron energies corresponding to $p$-wave resonances in the compound nuclear system. We analyze a model experiment and show that such tests can have a discovery potential of ${10}^2–{10}^4$ compared to current limits.

Background: Double-$\beta$ decay is a rare nuclear process in which two neutrons in the nucleus are converted to two protons with the emission of two electrons and two electron antineutrinos.

Purpose: We measured the half-life of the two-neutrino double-$\beta$ decay of ${}^{150}\mathrm{Nd}$ to excited final states of ${}^{150}\mathrm{Sm}$ by detecting the deexcitation $\gamma$ rays of the daughter nucleus.

Method: This study yields the first detection of the coincidence $\gamma$ rays from the $0{}_1^{+}$ excited state of ${}^{150}\mathrm{Sm}$. These $\gamma$ rays have energies of 333.97 and 406.52 keV and are emitted in coincidence through a $0_1^{+}\to 2_1^{+}\to 0_{\mathrm{gs}}^{+}$ transition.

Results: The enriched ${\mathrm{Nd}}_2{\mathrm{O}}_3$ sample consisted of 40.13 g ${}^{150}\mathrm{Nd}$ and was observed for 642.8 days at the Kimballton Underground Research Facility, producing 21.6 net events in the region of interest. This count rate gives a half-life of $T_{1/2}=[1.{07}_{-0.25}^{+0.45}\left(\mathrm{stat}\right)\pm 0.07\left(\mathrm{syst}\right)]\times {10}^{20}$ yr. The effective nuclear matrix element was found to be $0.0465{}_{-0.0054}^{+0.0098}$. Finally, lower limits were obtained for decays to higher excited final states.

Conclusions: Our half-life measurement agrees within uncertainties with another recent measurement in which no coincidence was employed. Our nuclear matrix element calculation may have an impact on a recent neutrinoless double-$\beta$ decay nuclear matrix element calculation which implies that the decay to the first excited state in ${}^{150}\mathrm{Sm}$ is favored over that to the ground state.

Background: Precision measurements at low energy search for physics beyond the standard model in a way complementary to searches for new particles at colliders. In the weak sector the most general $\beta$-decay Hamiltonian contains, besides vector and axial-vector terms, also scalar, tensor, and pseudoscalar terms. Current limits on the scalar and tensor coupling constants from neutron and nuclear $\beta$ decay are on the level of several percent.

Purpose: Extracting new information on tensor coupling constants by measuring the $\beta$-asymmetry parameter in the pure Gamow-Teller decay of ${}^{67}\mathrm{Cu}$, thereby testing the V-A structure of the weak interaction.

Method: An iron sample foil into which the radioactive nuclei were implanted was cooled down to mK temperatures in a ${}^3\mathrm{He}{\text{−}}^4\mathrm{He}$ dilution refrigerator. An external magnetic field of 0.1 T, in combination with the internal hyperfine magnetic field, oriented the nuclei. The anisotropic $\beta$ radiation was observed with planar high-purity germanium detectors operating at a temperature of about 10 K. An on-line measurement of the $\beta$ asymmetry of ${}^{68}\mathrm{Cu}$ was performed as well for normalization purposes. Systematic effects were investigated using geant4 simulations.

Results: The experimental value, $\tilde{A}=0.587\left(14\right)$, is in agreement with the standard model value of 0.5991(2) and is interpreted in terms of physics beyond the standard model. The limits obtained on possible tensor-type charged currents in the weak interaction Hamiltonian are $-0.045<(C_T+C_T^{\prime })/C_A<0.159$ (90% C.L.).

Conclusions: The obtained limits are comparable to limits from other correlation measurements in nuclear $\beta$ decay and contribute to further constraining tensor coupling constants.

The half-life of ${}^{37}\mathrm{K}$ has been measured to be $1.23651\left(94\right)\mathrm{s}$, a value nearly an order of magnitude more precise than the best previously reported. The ${\beta }^{+}$ decay of ${}^{37}\mathrm{K}$ occurs mainly via a superallowed branch to the ground state of its $T=1/2$ mirror, ${}^{37}\mathrm{Ar}$. This transition has been used recently, together with similar transitions from four other nuclei, as a method for determining $V_{ud}$, but the precision of its $ft$ value was limited by the relatively large half-life uncertainty. Our result corrects that situation. Another motivation for improving the $ft$ value was to determine the standard-model prediction for the $\beta$-decay correlation parameters, which will be compared to those currently being measured by the TRINAT Collaboration at TRIUMF. The new $ft$ value, $4605\left(8\right)\mathrm{s}$, is now limited in precision by the $97.99\left(14\right)\%$ ground-state branching ratio.