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.

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

References in corpus (9)

• The five-loop beta function of Yang-Mills theory with fermions
• CP Violation and Neutrino Oscillations
• Origin of the Large Perturbative Corrections to Higgs Production at Hadron Colliders
• The Mu2e Experiment
• Dispersion relation analysis of the radiative corrections to $g_A$ in the neutron $\beta$-decay
• Long-Baseline Neutrino Experiments
• Superallowed nuclear beta decays and precision tests of the Standard Model
• All orders factorization and the Coulomb problem
• Precision half-life measurement of the \boldmath${\beta }^{+}$ decay of \tsups{37}K

Cited by in corpus (4)

• 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