Field Theory of the Fermi Function

Abstract

The Fermi function $F(Z,E)$ accounts for QED corrections to beta decays that are enhanced at either small electron velocity $\beta$ or large nuclear charge $Z$. For precision applications, the Fermi function must be combined with other radiative corrections and with scale- and scheme-dependent hadronic matrix elements. We formulate the Fermi function as a field theory object and present a new factorization formula for QED radiative corrections to beta decays. We provide new results for the anomalous dimension of the corresponding effective operator complete through three loops, and resum perturbative logarithms and $\pi$-enhancements with renormalization group methods. Our results are important for tests of fundamental physics with precision beta decay and related processes.

arXiv commentNew supplemental material discussing factorization, impact on CKM unitarity, and real radiation. Matches journal

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• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Radiative corrections to superallowed $\beta$ decays in effective field theory
• Unique forbidden beta decays at zero momentum transfer
• Pion $\beta$ decay and $\tau \to \pi \pi {\nu }_{\tau }$ beyond leading logarithms