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All orders factorization and the Coulomb problem
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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.
Forward citations
Cited by 2 Pith papers
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$2\nu\beta\beta$ Spectrum in Chiral Effective Field Theory
Chiral EFT corrections to the 2νββ electron spectrum from weak magnetism and pion exchange appear at next-to-leading order and must be included in searches for new physics.
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