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Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
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abstract
Radiative corrections are essential for an accurate determination of $V_{ud}$ from superallowed $\beta$ decays. In view of recent progress in the single-nucleon sector, the uncertainty is dominated by the theoretical description of nucleus-dependent effects, limiting the precision that can currently be achieved for $V_{ud}$. In this work, we provide a detailed account of the electroweak corrections to superallowed $\beta$ decays in effective field theory (EFT), including the power counting, potential and ultrasoft contributions, and factorization in the decay rate. We present a first numerical evaluation of the dominant corrections in light nuclei based on Quantum Monte Carlo methods, confirming the expectations from the EFT power counting. Finally, we discuss strategies how to extract from data the low-energy constants that parameterize short-distance contributions and whose values are not predicted by the EFT. Combined with advances in ab-initio nuclear-structure calculations, this EFT framework allows one to systematically address the dominant uncertainty in $V_{ud}$, as illustrated in detail for the $^{14}$O $\to$ $^{14}$N transition.
Forward citations
Cited by 4 Pith papers
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The first quantum Monte Carlo evaluation of the nuclear-structure-dependent radiative correction in carbon-10 confirms the NCSM dispersion result, with the residual uncertainty set by two undetermined low-energy constants.
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Recent Progress in Ab-Initio Nuclear Theory for Precision Physics Searches in Muonic Atoms and Superallowed $\beta$ Decays
Ab initio nuclear theory for two-photon exchange in muonic atoms and the γW box in superallowed β decays shares one hadronic tensor, with recent light-nuclei results impacting charge radii, the helium isotope shift, and Vud.
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Future directions in nuclear $\beta$ decay at FRIB and beyond
A community white paper summarizing the current state and future directions of nuclear beta-decay studies at FRIB, with no new quantitative result.
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