The renormalization-group running of neutrino mixing is undetectable
Abstract
Quantum corrections make the parameters of a theory depend on an arbitrary renormalization scale, μ. The renormalization-group (RG) running of neutrino masses and mixing is a standard tool to relate models defined at a high mass scale to measured values. A growing body of work holds that the running is also directly observable: a neutrino produced or detected at momentum transfer Q would carry the mixing matrix evaluated at μ= Q. Proposed signatures include flavor change at zero distance from the source, shifts in the measured CP-violation phase, and an anomalous flavor composition of high-energy astrophysical neutrinos. We show that this premise is incorrect. The mixing is a property of the neutrino itself, fixed by its self-energy on the mass shell, not by the process that produces or detects it. Setting μ= Q is legitimate, but then large logarithms in the self-energy undo the running; the premise incorrectly drops them. Hence, apart from small vertex and box corrections, every experiment measures the same mixing: the running is undetectable. We illustrate this in the Minimal Supersymmetric Standard Model, two seesaw models, and the Standard Model effective field theory. Independently, short-baseline data already limit the change of any one mixing angle between pion decay and detection at Q of a few GeV to below 0.7∘--2.4∘.
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BibTeX
@misc{barenboim2026renormalizationgroup,
title = {{The renormalization-group running of neutrino mixing is undetectable}},
author = {Gabriela Barenboim and Mauricio Bustamante and Qinrui Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28744},
eprint = {2610.28744},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28744},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The renormalization-group running of neutrino mixing is undetectable
AU - Gabriela Barenboim
AU - Mauricio Bustamante
AU - Qinrui Liu
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28744
UR - https://arxiv.org/abs/2610.28744
AB - Quantum corrections make the parameters of a theory depend on an arbitrary renormalization scale, μ. The renormalization-group (RG) running of neutrino masses and mixing is a standard tool to relate models defined at a high mass scale to measured values. A growing body of work holds that the running is also directly observable: a neutrino produced or detected at momentum transfer Q would carry the mixing matrix evaluated at μ= Q. Proposed signatures include flavor change at zero distance from the source, shifts in the measured CP-violation phase, and an anomalous flavor composition of high-energy astrophysical neutrinos. We show that this premise is incorrect. The mixing is a property of the neutrino itself, fixed by its self-energy on the mass shell, not by the process that produces or detects it. Setting μ= Q is legitimate, but then large logarithms in the self-energy undo the running; the premise incorrectly drops them. Hence, apart from small vertex and box corrections, every experiment measures the same mixing: the running is undetectable. We illustrate this in the Minimal Supersymmetric Standard Model, two seesaw models, and the Standard Model effective field theory. Independently, short-baseline data already limit the change of any one mixing angle between pion decay and detection at Q of a few GeV to below 0.7^∘--2.4^∘.
ER -