The Fermi function and the neutron's lifetime

Peter Vander Griend; Zehua Cao; Richard J. Hill; Ryan Plestid

doi:10.1016/j.physletb.2025.139678

The Fermi function and the neutron's lifetime

Peter Vander Griend
, Zehua Cao
, Richard J. Hill
, Ryan Plestid

Physics And Astronomy

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 τ_n×|V_ud|²[1+3λ²][1+Δ_R]=[Formula presented], with |V_ud| the up-down quark mixing parameter, τ_n the neutron's lifetime, λ the ratio of axial to vector charge, and Δ_R 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 |V_ud| and tests of the Standard Model.

Original language	English
Article number	139678
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	868
DOIs	https://doi.org/10.1016/j.physletb.2025.139678
State	Published - Sep 2025

Bibliographical note

Publisher Copyright:
© 2025 The Author(s)

Funding

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 .

Funders	Funder number
Kavli Institute for Theoretical Physics, University of California, Santa Barbara
Universities Space Research Association
Office of Science Programs
The George Washington University
National Science Foundation Arctic Social Science Program	PHY-1748958, DEAC02-07CH11359
U.S. Department of Energy	DE-FG02-00ER41132
Walter Burke Institute for Theoretical Physics	DE-SC0019095
Institute for High Energy Physics	DE-SC0011632
Fermi Forward Discovery Group, LLC	DE-AC02-06CH11357, 89243024CSC000002

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.physletb.2025.139678

Cite this

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title = "The Fermi function and the neutron's lifetime",

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]=[Formula presented], 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.",

author = "\{Vander Griend\}, Peter and Zehua Cao and Hill, \{Richard J.\} and Ryan Plestid",

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doi = "10.1016/j.physletb.2025.139678",

language = "English",

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T1 - The Fermi function and the neutron's lifetime

AU - Vander Griend, Peter

AU - Cao, Zehua

AU - Hill, Richard J.

AU - Plestid, Ryan

PY - 2025/9

Y1 - 2025/9

N2 - 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]=[Formula presented], 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.

AB - 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]=[Formula presented], 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.

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JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

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ER -

The Fermi function and the neutron's lifetime

Abstract

Bibliographical note

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ASJC Scopus subject areas

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