All orders factorization and the Coulomb problem

Creators: Hill, Richard J.; Plestid, Ryan

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 $Z α / β$ 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.

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 for useful discussions, and the Neutrino Theory Network for sponsoring R. P.’s visit to University of Kentucky in 2018. R. P. thanks Benoit Assi, Florian Herren, and Robert Szafron for helpful discussions. 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. Part of this research was performed at the Kavli Institute for Theoretical Physics which is supported in part by the National Science Foundation under Grant No. NSF PHY-1748958 and at the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611. This work is supported by 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. P. acknowledges support from the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632 and the Neutrino Theory Network Program Grant under Award No. DE-AC02-07CH11359.

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PhysRevD.109.056006.pdf

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