All orders factorization and the Coulomb problem

Richard J. Hill, Ryan Plestid

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In the limit of large nuclear charge, Z≫1, or small lepton velocity, β≪1, Coulomb corrections to nuclear beta decay and related processes are enhanced as Zα/β and become large or even nonperturbative (with α the QED fine structure constant). We provide a constructive demonstration of factorization to all orders in perturbation theory for these processes and compute the all-orders hard and soft functions appearing in the factorization formula. We clarify the relationship between effective field theory amplitudes and historical treatments of beta decay in terms of a Fermi function.

Original languageEnglish
Article number056006
JournalPhysical Review D
Issue number5
StatePublished - Mar 1 2024

Bibliographical note

Publisher Copyright:
© 2024 authors. Published by the American Physical Society. 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. Funded by SCOAP3.

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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