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 · 06 March 2024 · Physical Review. D.

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

Hill, Richard J.;

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 $Z α / β$ 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. Published by the American Physical Society 2024

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

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

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

OSTI ID:: 2320299

Report Number(s):: CALT-TH-2023-034; FERMILAB-PUB-23-454-T; arXiv:2309.15929; 056006

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

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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