All orders factorization and the Coulomb problem

Hill, Richard J.; Plestid, Ryan

doi:10.1103/physrevd.109.056006

Title: All orders factorization and the Coulomb problem

Journal Article · 07 March 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.109.056006 · OSTI ID:2320299

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University of Kentucky, Lexington, KY (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
University of Kentucky, Lexington, KY (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

In the limit of large nuclear charge, Z $$\gg$$1, or small lepton velocity, β$$\ll$$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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Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Walter Burke Institute

Grant/Contract Number:: AC02-07CH11359; SC0019095; PHY-1748958; PHY-1607611; SC0011632

OSTI ID:: 2320299

Alternate ID(s):: OSTI ID: 2007015; OSTI ID: 2479603

Report Number(s):: CALT-TH-2023-034; FERMILAB-PUB-23-454-T; arXiv:2309.15929; oai:inspirehep.net:2703878; TRN: US2406305

Journal Information:: Physical Review. D., Vol. 109, Issue 5; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Title: All orders factorization and the Coulomb problem

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