Bound-state decay of a charged scalar particle in an external Coulomb field
Abstract
We determine the decay rate Γ of a scalar particle bound to a light nucleus, numerically and analytically. As a model system, we consider a negatively charged kaon in the ground state of a hydrogen-like ion decaying into charged and neutral scalar pions, K-→ π-π0. All particles are assumed point-like; the nucleus is infinitely heavy. The partial wave expansion converges slowly, as in a recent analysis of the bound-muon decay. To overcome this difficulty, we introduce a subtraction method: the free π- contribution is evaluated separately, while the partial-wave sum is used only for the Coulomb distortion. The ratio of bound-to-free decay rates, Γ/Γ0, is found for light nuclei, 1≤ Z≤ 10. The numerical calculation is complemented by a diagrammatic small-αZ expansion. We find $ Γ/Γ_0 = 1-(αZ)^2/2 + 17(αZ)^4/24 +\mathcal{O}((αZ)^5)$, in agreement with the all-orders numerical calculation at low Z.
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BibTeX
@misc{czarnecki2026boundstate,
title = {{Bound-state decay of a charged scalar particle in an external Coulomb field}},
author = {Andrzej Czarnecki and Artem O. Davydov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37651},
eprint = {2609.37651},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37651},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bound-state decay of a charged scalar particle in an external Coulomb field
AU - Andrzej Czarnecki
AU - Artem O. Davydov
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37651
UR - https://arxiv.org/abs/2609.37651
AB - We determine the decay rate Γ of a scalar particle bound to a light nucleus, numerically and analytically. As a model system, we consider a negatively charged kaon in the ground state of a hydrogen-like ion decaying into charged and neutral scalar pions, K^-→ π^-π^0. All particles are assumed point-like; the nucleus is infinitely heavy. The partial wave expansion converges slowly, as in a recent analysis of the bound-muon decay. To overcome this difficulty, we introduce a subtraction method: the free π^- contribution is evaluated separately, while the partial-wave sum is used only for the Coulomb distortion. The ratio of bound-to-free decay rates, Γ/Γ_0, is found for light nuclei, 1≤ Z≤ 10. The numerical calculation is complemented by a diagrammatic small-αZ expansion. We find $ Γ/Γ_0 = 1-(αZ)^2/2 + 17(αZ)^4/24 +\mathcal{O}((αZ)^5)$, in agreement with the all-orders numerical calculation at low Z.
ER -