All orders factorization and the Coulomb problem

Richard J. Hill; Ryan Plestid

doi:10.1103/PhysRevD.109.056006

All orders factorization and the Coulomb problem

Richard J. Hill, Ryan Plestid

Physics And Astronomy

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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 language	English
Article number	056006
Journal	Physical Review D
Volume	109
Issue number	5
DOIs	https://doi.org/10.1103/PhysRevD.109.056006
State	Published - 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 "https://creativecommons.org/licenses/by/4.0/"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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10.1103/PhysRevD.109.056006

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AB - 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.

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All orders factorization and the Coulomb problem

Abstract

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