The finite-size correction to $β$-decay plays an important role in determining the expected antineutrino spectra from reactors at a level that is important for the reactor-neutrino anomaly. Here we express the leading-order finite-size correction to allowed $β$-decay in terms of Zemach moments. We calculate the Zemach moments within a Hartree-Fock model using a Skyrme-like energy density functional. We find that the Zemach moments are increased relative to predictions based on the simple assumption of identical uniform nuclear-charge and weak-transition densities. However, for allowed ground-state to ground-state transitions in medium and heavy nuclei, the detailed nuclear structure calculations do not change the finite-size corrections significantly from the simple model predictions, and are only 10-15% larger than the latter even though the densities differ significantly.
We review the status of ab initio calculations of allowed beta decays (both Fermi and Gamow-Teller), within the framework of the valence-space in-medium similarity renormalization group approach.
Several searches for Beyond Standard Model physics rely on an accurate and highly precise theoretical description of the allowed $β$ spectrum. Following recent theoretical advances, a C++ implementation of an analytical description of the allowed beta spectrum shape was constructed. It implements all known corrections required to give a theoretical description accurate to a few parts in $10^4$. The remaining nuclear structure-sensitive input can optionally be calculated in an extreme single-particle approximation with a variety of nuclear potentials, or obtained through an interface with more …
We study the influence of the Coulomb force on the Fermi beta-decays in nuclei. This work is composed of two main parts. In the first part, we calculate the Coulomb corrections to super-allowed beta decay. We use the notion of the isovector monopole state and the self-consistent charge-exchange Random Phase Approximation to compute the correction. In the second part of this work, we examine the influence of the anti-analog state on isospin mixing in the isobaric analog state and the correction to the beta-decay Fermi transition.
We propose formulas of the nuclear beta-decay rate that are useful in a practical calculation. The decay rate is determined by the product of the lepton and hadron current densities. A widely used formula relies upon the fact that the low-energy lepton wave functions in a nucleus can be well approximated by a constant and linear to the radius for the $s$-wave and $p$-wave wave functions, respectively. We find, however, the deviation from such a simple approximation is evident for heavy nuclei with large $Z$ by numerically solving the Dirac equation. In our proposed formulas, the neutrino wave …
Addendum to: QRPA uncertainties and their correlations in the analysis of neutrinoless double beta decay
在以前的文章[Phys. Rev. D 79，053001（2009）]中，我们在准粒子无规相位近似（QRPA）中估计了与无中微子双β衰变（0 nu β β）的核矩阵元（NME）相关的不确定性。这种估计包括最近对NME的独立计算，因此仍然可以提供核模型不确定性的公平代表。在这种情况下，我们比较了Ge-76中0 nu β β衰变的声明与最近在Ge-136和其他核中的负结果，并推断了在90% C. L.时允许或排除的寿命范围。我们还强调了一些问题，应加以解决，以适当地比较和结合来自不同的0 nu β β衰变候选核的结果。
Validation of the effective conversion method in the reactor antineutrino flux calculation is examined using the \textit{ab initio} calculation of the electron and antineutrino spectra from the state-of-the-art nuclear database. It turns out that neglecting the shape variation of beta decay branches between the allowed and forbidden transitions would induce significant bias in the total inverse-beta-decay yields and energy spectral distributions. We propose a new realization of the conversion method with both the allowed and forbidden virtual branches, and apply it to both the \textit{simulate…
We quantify the extent to which future experiments will test the existence of neutrinoless double-beta decay mediated by light neutrinos with inverted-ordered masses. While it remains difficult to compare measurements performed with different isotopes, we find that future searches will fully test the inverted ordering scenario, as a global, multi-isotope endeavor. They will also test other possible mechanisms driving the decay, including a large uncharted region of the allowed parameter space assuming that neutrino masses follow the normal ordering.
Precision measurements in allowed nuclear beta decays and neutron decay are reviewed and analyzed both within the Standard Model and looking for new physics. The analysis incorporates the most recent experimental and theoretical developments. The results are interpreted in terms of Wilson coefficients describing the effective interactions between leptons and nucleons (or quarks) that are responsible for beta decay. New global fits are performed incorporating a comprehensive list of precision measurements in neutron decay, superallowed $0^+\rightarrow 0^+$ transitions, and other nuclear decays …
$Q_β$ represents one of the most important factors characterizing unstable nuclei, as it can lead to a better understanding of nuclei behavior and the origin of heavy atoms. Recently, machine learning methods have been shown to be a powerful tool to increase accuracy in the prediction of diverse atomic properties such as energies, atomic charges, volumes, among others. Nonetheless, these methods are often used as a black box not allowing unraveling insights into the phenomena under analysis. Here, the state-of-the-art precision of the $β$-decay energy on experimental data is outperformed by me…
We present the first chiral effective theory derivation of the neutrinoless double beta-decay $nn\rightarrow pp$ potential induced by light Majorana neutrino exchange. The effective-field-theory framework has allowed us to identify and parameterize short- and long-range contributions previously missed in the literature. These contributions can not be absorbed into parameterizations of the single nucleon form factors. Starting from the quark and gluon level, we perform the matching onto chiral effective field theory and subsequently onto the nuclear potential. To derive the nuclear potential me…
Pion beta decay, $π^+\to π^0 e^+ν(γ)$, provides a theoretically clean $\pm 0.3\%$ determination of the CKM matrix element $V_{\text{ud}}$. That value falls short of super-allowed nuclear beta decays where an order of magnitude better precision already exists. We advocate a new strategy for utilizing pion beta decay, based on its role in determining ${V_{\text{us}} / V_{\text{ud}}}$ via the ratio $R_V=Γ\left(K\to πl ν(γ)\right)/Γ\left(π^+\to π^0 e^+ν(γ)\right)$. $R_V$ measures $ { f_+^K(0) |V_{\text{us}}| / f_+^π(0) |V_{\text{ud}}| }$ and is insensitive to the Fermi constant and some radiative …
The universal radiative corrections common to neutron and super-allowed nuclear beta decays (also known as ``inner'' corrections) are revisited in light of a recent dispersion relation study that found $+2.467(22)\%$, i.e.~about $2.4σ$ larger than the previous evaluation. For comparison, we consider several alternative computational methods. All employ an updated perturbative QCD four-loop Bjorken sum rule (BjSR) defined QCD coupling supplemented with a nucleon form factor based Born amplitude to estimate axial-vector induced hadronic contributions. In addition, we now include hadronic contrib…
Global Ab initio Neutrino Mass Limits from Neutrinoless Double-Beta Decay
TRIUMF；University of British Columbia（不列颠哥伦比亚大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心有限公司）；Massachusetts Institute of Technology（麻省理工学院）；McGill University（麦吉尔大学）
The determinations of the Cabibbo angle from kaon, pion, $D$ and tau decays disagree with the one from super-allowed beta decays. The resulting $\approx 3\,σ$ deficit in first row (but also first column) CKM unitarity is known as the Cabibbo angle anomaly (CAA). Determining $V_{ud}$ from beta decays requires knowledge of the Fermi constant $G_F$, usually extracted from muon decay. However, because new physics might also affect muon decay, and thus the determination of the Fermi constant, an interesting interplay with the global electroweak fit arises where $G_F$ is a crucial input. In these pr…
We investigate neutrinoless double beta decay ($0νββ$) in the presence of sterile neutrinos with Majorana mass terms. These gauge-singlet fields are allowed to interact with Standard-Model (SM) fields via renormalizable Yukawa couplings as well as higher-dimensional gauge-invariant operators up to dimension seven in the Standard Model Effective Field Theory extended with sterile neutrinos. At the GeV scale, we use Chiral effective field theory involving sterile neutrinos to connect the operators at the level of quarks and gluons to hadronic interactions involving pions and nucleons. This allow…
An overview of modern experiments on the search for neutrinoless double decay is presented. The obtained limits on the effective mass of the Majorana neutrino $\langle m_ν \rangle$ are discussed taking into account the uncertainties in the value of the nuclear matrix elements (NMEs) and the value of the axial-vector constant $g_A$. Predictions for the values of $\langle m_ν \rangle$ from the results of oscillation experiments and modern cosmological data are presented. The possibilities of the next generation experiments with sensitivity to $\langle m_ν \rangle$ at the level of $\sim$ 10-50 me…
