Report
The Fermi function and the neutron's lifetime
| العنوان: | The Fermi function and the neutron's lifetime |
|---|---|
| المؤلفون: | Griend, Peter Vander, Cao, Zehua, Hill, Richard, Plestid, Ryan |
| سنة النشر: | 2025 |
| المجموعة: | High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory |
| مصطلحات موضوعية: | High Energy Physics - Phenomenology, Nuclear Experiment, Nuclear Theory |
| الوصف: | The traditional Fermi function ansatz for nuclear beta decay describes enhanced perturbative effects in the limit of large nuclear charge $Z$ and/or small electron velocity $\beta$. We define and compute the quantum field theory object that replaces this ansatz for neutron beta decay, where neither of these limits hold. We present a new factorization formula that applies in the limit of small electron mass, analyze the components of this formula through two loop order, and resum perturbative corrections that are enhanced by large logarithms. We apply our results to the neutron lifetime, supplying the first two-loop input to the long-distance corrections. Our result can be summarized as \begin{equation*} \tau_n \times |V_{ud}|^2\big[1+3\lambda^2\big]\big[1+\Delta_R\big] = \frac{5263.284(17)\,{\rm s}} {1 + 27.04(7)\times 10^{-3} }~, \end{equation*} with $|V_{ud}|$ the up-down quark mixing parameter, $\tau_n$ the neutron's lifetime, $\lambda$ the ratio of axial to vector charge, and $\Delta_R$ the short-distance matching correction. We find a shift in the long-distance radiative corrections compared to previous work, and discuss implications for extractions of $|V_{ud}|$ and tests of the Standard Model. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2501.17916 |
| رقم الانضمام: | edsarx.2501.17916 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |