The Fermi function and the neutron's lifetime
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1.
University of Kentucky
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2.
Fermilab
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3.
California Institute of Technology
Abstract
The traditional Fermi function ansatz for nuclear beta decay describes enhanced perturbative effects in the limit of large nuclear charge Z and/or small electron velocity β. We define and compute the quantum field theory object that replaces this ansatz for neutron beta decay, where neither of these limits hold. We present a new factorization formula that applies in the limit of small electron mass, analyze the components of this formula through two loop order, and resum perturbative corrections that are enhanced by large logarithms. We apply our results to the neutron lifetime, supplying the first two-loop input to the long-distance corrections. Our result can be summarized as τn × | Vud |² [1 + 3λ²] [1 + ΔR] = 5263.284 (17) s / 1 + 27.04 (7) × 10 ⁻³, with | Vud | the up-down quark mixing parameter, τn the neutron's lifetime, λ the ratio of axial to vector charge, and ΔR the short-distance matching correction. We find a shift in the long-distance radiative corrections compared to previous work, and discuss implications for extractions of | Vud | and tests of the Standard Model.
Copyright and License
© 2025 The Author(s). Published by Elsevier B.V. Funded by SCOAP³. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Acknowledgement
We thank Vincenzo Cirigliano and Bradley Filippone for helpful discussions. We thank Susan Gardner, Martin Hoferichter, and Andreas Kronfeld for comments on the manuscript. PVG acknowledges support from the Visiting Scholars Program Award of the Universities Research Association. RP thanks the Institute for Nuclear Theory at the University of Washington for its kind hospitality and stimulating research environment during program INT 23-1b. This research was supported in part by the INT's U.S. Department of Energy grant No. DE-FG02-00ER41132. Part of the research of RP was performed at the Kavli Institute for Theoretical Physics which is supported by the National Science Foundation under Grant No. NSF PHY-1748958. RP is supported by the Neutrino Theory Network under Award Number DEAC02-07CH11359, the U.S. Department of Energy, Office of Science, Office of High Energy Physics under Award Number DE-SC0011632, and by the Walter Burke Institute for Theoretical Physics. This work was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award DE-SC0019095. This work was produced by Fermi Forward Discovery Group, LLC under Contract No. 89243024CSC000002 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. RJH gratefully acknowledges support from the HEP Theory Group at Argonne National Laboratory, where a part of this work was completed. Argonne is operated under Contract No. DE-AC02-06CH11357.
Supplemental Material
In this supplementary material, we present our calculation of the recoil and radiative recoil corrections given in Table 1 of the paper.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2501.17916 (arXiv)
- Is supplemented by
- Supplemental Material: https://ars.els-cdn.com/content/image/1-s2.0-S0370269325004393-mmc1.pdf (URL)
Funding
- Universities Research Association
- United States Department of Energy
- DE-FG02-00ER41132
- National Science Foundation
- PHY-1748958
- United States Department of Energy
- DEAC02-07CH11359
- United States Department of Energy
- DE-SC0011632
- California Institute of Technology
- Walter Burke Institute for Theoretical Physics -
- United States Department of Energy
- DE-SC0019095
- Fermilab Accelerator Complex
- 89243024CSC000002
- United States Department of Energy
- DE-AC02-06CH11357
- SCOAP3
Dates
- Accepted
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2025-06-20
- Available
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2025-06-26Available online
- Available
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2025-07-07Version of record