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arXiv · 2309.15929

All orders factorization and the Coulomb problem

Richard J. Hill·Ryan Plestid
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Abstract

In the limit of large nuclear charge, $Z\gg 1$, or small lepton velocity, $\beta \ll 1$, Coulomb corrections to nuclear beta decay and related processes are enhanced as $Z\alpha/\beta$ and become large or even non-perturbative (with $\alpha$ 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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Richard J. Hill, Ryan Plestid. 2023-09-27. All orders factorization and the Coulomb problem. https://doi.org/10.1103/physrevd.109.056006

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