Electroweak nuclear radii constrain the isospin breaking correction to $V_{ud}$

Abstract

We lay out a novel formalism to connect the isospin-symmetry breaking correction to the rates of superallowed nuclear beta decays, ${\delta }_{\text{C}}$, to the isospin-breaking sensitive combinations of electroweak nuclear radii that can be accessed experimentally. We individuate transitions in the superallowed decay chart where a measurement of the neutron skin of a stable daughter even at a moderate precision could already help discriminating between models used to compute ${\delta }_{\text{C}}$. We review the existing experimental situation and make connection to the existing and future experimental programs.

Version to appear on PLB. Some typos (e.g. the expansion formula of ${\bar{f}}_{+}(t)$) are corrected and a new section on experimental feasibility is included

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Cited by in corpus (18)

• Scrutinizing CKM unitarity with a new measurement of the $K_{\mu 3}/K_{\mu 2}$ branching fraction
• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Dispersive formalism for the nuclear structure correction ${\delta }_{\mathrm{NS}}$ to the $\beta$ decay rate
• Radiative corrections to superallowed $\beta$ decays in effective field theory
• Superallowed nuclear beta decays and precision tests of the Standard Model
• Model-independent determination of nuclear weak form factors and implications for Standard Model precision tests
• Data-driven reevaluation of $ft$-values in superallowed $\beta$ decays
• Nuclear charge radius of ${}^{26m}$Al and its implication for V${}_{ud}$ in the quark-mixing matrix
• New quantification of symmetry energy from neutron skin thicknesses of ${}^{48}$Ca and ${}^{208}$Pb
• Towards $ab$-$initio$ nuclear theory calculations of ${\delta }_{\mathrm{C}}$
• Critical evaluation of reference charge radii and applications in mirror nuclei
• Opportunities and open questions in modern $\beta$ decay
• Simultaneous Extraction of the Weak Radius and the Weak Mixing Angle from Parity-Violating Electron Scattering on ${}^{12}\mathrm{C}$
• Cabibbo-Kobayashi-Maskawa unitarity deficit reduction via finite nuclear size
• Exploring Isospin Symmetry Breaking in Exotic Nuclei: High-Precision Mass Measurement of 23Si and Shell-Model Calculations of T = 5/2 Nuclei
• Cabibbo angle anomalies and a global fit to vector-like quarks
• The Role of Ab Initio Beta-Decay Calculations in Light Nuclei for Probes of Physics Beyond the Standard Model
• Complete one-loop QED corrections to $D_s^{+}$ leptonic decays and impact on the CKM unitarity test