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Register a new userA formalism to assess the accuracy of nuclear-structure weak interaction effects in precision $beta$-decay studies
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Multiple high precision $beta$-decay measurements are being carried out these days on various nuclei, in search of beyond the Standard Model signatures. These measurements necessitate accurate standard model theoretical predictions to be compared with. Motivated by the experimental surge, we present a formalism for such a calculation of $beta$-decay observables, with controlled accuracy, based on a perturbative analysis of the theoretical observables related to the phenomena, including high order nuclear recoil and shape corrections. The accuracy of the corrections is analyzed by identifying a hierarchy of small parameters, related to the low momentum transfer characterizing $beta$-decays. Furthermore, we show that the sub-percent uncertainties, targeted by on-going and planned experiments, entail an accuracy of the order of 10% for the solution of the nuclear many body problem, which is well within the reach of modern nuclear theory for light to medium mass nuclei.
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The measured $ft$-values for superallowed $0^{+} to 0^{+}$ nuclear $beta$-decay can be used to obtain the value of the vector coupling constant and thus to test the unitarity of the Cabibbo-Kobayashi-Maskawa matrix. An essential requirement for this test is accurate calculations for the radiative and isospin symmetry-breaking corrections that must be applied to the experimental data. We present a new and consistent set of calculations for the nuclear-structure-dependent components of these corrections. These new results do not alter the current status of the unitarity test -- it still fails by more than two standard deviations -- but they provide calculated corrections for eleven new superallowed transitions that are likely to become accessible to precise measurements in the future. The reliability of all calculated corrections is explored and an experimental method indicated by which the structure-dependent corrections can be tested and, if necessary, improved.
We report new shell-model calculations of the isospin-symmetry-breaking correction to superallowed nuclear beta decay. The most important improvement is the inclusion of core orbitals, which are demonstrated to have a significant impact on the mismatch in the radial wave functions of the parent and daughter states. We determine which core orbitals are important to include from an examination of measured spectroscopic factors in single-nucleon pick-up reactions. We also examine the new radiative-correction calculation by Marciano and Sirlin and, by a simple reorganization, show that it is possible to preserve the conventional separation into a nucleus-independent inner radiative term and a nucleus-dependent outer term. We tabulate new values for the three theoretical corrections for twenty superallowed transitions, including the thirteen well-studied cases. With these new correction terms the corrected Ft values for the thirteen cases are statistically consistent with one another and the anomalousness of the 46V result disappears. These new calculations lead to a lower average Ft value and a higher value of Vud. The sum of squares of the top-row elements of the CKM matrix now agrees exactly with unitarity.
Neutrinoless double beta decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element associated with the given neutrinoless double-beta decay transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of the nuclear matrix element for the success of the experimental programs. This need drives the theoretical nuclear physics community to provide the most reliable calculations of the nuclear matrix elements. Among the various computational models adopted to solve the many-body nuclear problem, the shell model is widely considered as the basic framework of the microscopic description of the nucleus. Here, we review the most recent and advanced shell-model calculations of the nuclear matrix elements considering the light-neutrino-exchange channel for nuclei of experimental interest. We report the sensitivity of the theoretical calculations with respect to variations in the model spaces and the shell-model nuclear Hamiltonians.
Steven Weinbergs seminal papers from 1990-92 initiated the use of effective field theories (EFTs) for nuclei. We summarize progress, priorities, and open questions for nuclear EFT developments based on the 2019 INT program Nuclear Structure at the Crossroads.
Superallowed $0^+ to 0^+$ nuclear beta decay provides a direct measure of the weak vector coupling constant, $GV$. We survey current world data on the nine accurately determined transitions of this type, which range from the decay of $^{10}$C to that of $^{54}$Co, and demonstrate that the results confirm conservation of the weak vector current (CVC) but differ at the 98% confidence level from the unitarity condition for the Cabibbo-Kobayashi-Maskawa (CKM) matrix. We examine the reliability of the small calculated corrections that have been applied to the data, and conclude that there are no evident defects although the Coulomb correction, $delta_C$, depends sensitively on nuclear structure and thus needs to be constrained independently. The potential importance of a result in disagreement with unitarity, clearly indicates the need for further work to confirm or deny the discrepancy. We examine the options and recommend priorities for new experiments and improved calculations. Some of the required experiments depend upon the availability of intense radioactive beams. Others are possible with existing facilities.
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