The $Zα^2$ correction to superallowed beta decays in effective field theory and implications for $|V_{ud}|$
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915604749877248 |
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| author | Cao, Zehua Hill, Richard J. Plestid, Ryan Griend, Peter Vander |
| author_facet | Cao, Zehua Hill, Richard J. Plestid, Ryan Griend, Peter Vander |
| contents | Superallowed ($0^+\rightarrow0^+$) beta decays currently provide the most precise extraction of quark mixing in the Standard Model. Their interpretation as a measurement of $|V_{ud}|$ relies on a reliable first-principles computation of QED radiative corrections expressed as a series in $Zα$ and $α$. In this work, we provide the first model-independent result for two-loop, $O(Zα^2)$, long-distance radiative corrections where the nuclei are treated as heavy point-like particles.
We use renormalization group analysis to obtain new results at $O(Zα^3)$ for the coefficient of double-logarithms in the ratio of the maximal beta energy to the inverse nuclear size, $\Em/R^{-1}$. We use the Kinoshita-Lee-Nauenberg theorem to obtain new results at $O(Z^2α^3)$ for the coefficient of logarithms in the ratio of maximal beta energy to the electron mass, $\log(2\Em/\me)$. We identify a structure-dependent, and therefore short-distance, contribution to the traditional $Zα^2$ correction that should be revisited.. We provide the first comprehensive update to the long-distance corrections in almost forty years and comment on the impact of our findings for extractions of $|V_{ud}|$. We find that shifts in the long-distance corrections are $2.5\times$ larger than past estimates of their uncertainty, $1.5\times$ larger than the statistical uncertainty from the combined fit of superallowed decays, and about $1/2$ the size of estimated systematic error, which stems dominantly from nuclear structure effects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $Zα^2$ correction to superallowed beta decays in effective field theory and implications for $|V_{ud}|$ Cao, Zehua Hill, Richard J. Plestid, Ryan Griend, Peter Vander High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory Superallowed ($0^+\rightarrow0^+$) beta decays currently provide the most precise extraction of quark mixing in the Standard Model. Their interpretation as a measurement of $|V_{ud}|$ relies on a reliable first-principles computation of QED radiative corrections expressed as a series in $Zα$ and $α$. In this work, we provide the first model-independent result for two-loop, $O(Zα^2)$, long-distance radiative corrections where the nuclei are treated as heavy point-like particles. We use renormalization group analysis to obtain new results at $O(Zα^3)$ for the coefficient of double-logarithms in the ratio of the maximal beta energy to the inverse nuclear size, $\Em/R^{-1}$. We use the Kinoshita-Lee-Nauenberg theorem to obtain new results at $O(Z^2α^3)$ for the coefficient of logarithms in the ratio of maximal beta energy to the electron mass, $\log(2\Em/\me)$. We identify a structure-dependent, and therefore short-distance, contribution to the traditional $Zα^2$ correction that should be revisited.. We provide the first comprehensive update to the long-distance corrections in almost forty years and comment on the impact of our findings for extractions of $|V_{ud}|$. We find that shifts in the long-distance corrections are $2.5\times$ larger than past estimates of their uncertainty, $1.5\times$ larger than the statistical uncertainty from the combined fit of superallowed decays, and about $1/2$ the size of estimated systematic error, which stems dominantly from nuclear structure effects. |
| title | The $Zα^2$ correction to superallowed beta decays in effective field theory and implications for $|V_{ud}|$ |
| topic | High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2511.05446 |