Field Theory of the Fermi Function

Creators: Hill, Richard J.; Plestid, Ryan

Abstract

The Fermi function 𝐹⁡(𝑍,𝐸) accounts for QED corrections to beta decays that are enhanced at either small electron velocity 𝛽 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 𝜋 enhancements with renormalization-group methods. Our results are important for tests of fundamental physics with precision beta decay and related processes.

Copyright and License

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Funding

Funded by SCOAP³.

Acknowledgement

We thank Susan Gardner and Oleksandr Tomalak for useful discussions regarding radiative corrections for beta decays, and Peter Vander Griend for collaboration on Ref. [44]. R. P. thanks the Institute for Nuclear Theory at the University of Washington for its kind hospitality and stimulating research environment during program INT 23-1B. This research was supported in part by the INT’s U.S. Department of Energy Grant No. DE-FG02-00ER41132. This work was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0019095. Fermilab is operated by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy. R. P. is supported by the Neutrino Theory Network under Award No. DEAC02-07CHI11359, the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the Walter Burke Institute for Theoretical Physics. R. J. H. gratefully acknowledges support from the Institute for Advanced Study, where a part of this work was completed.

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PhysRevLett.133.021803.pdf

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