Eur. Phys. J. D (2025) 79: 28
https://doi.org/10.1140/epjd/s10053-025-00964-5

Regular Article - Atomic Physics

Laboratory constraint on the electric charge of the neutron and the neutrino

¹ Fakultät für Physik, Ludwig-Maximilians-Universität, 80799, Munich, Germany
² Max-Planck-Institut für Quantenoptik, 85748, Garching, Germany

^a savely.karshenboim@mpq.mpg.de

Received: 9 December 2024
Accepted: 21 January 2025
Published online: 2 April 2025

Abstract

We revisit constraints on the value of the electric charge of the neutron and the neutrinos as well as on the electric-charge proton–electron difference $e_p+e_e$. We consider phenomenological constraints based on laboratory study of the electrical neutrality of would-be neutral subatomic, atomic, and molecular species under assumption of the conservation of the electric charge in the $\beta$ decay that relates the values of $e_p+e_e,e_n,e_{\nu }$. Some of constraints published previously utilized an additional assumption $e_{\nu }=0$, which we do not. We dismiss a cosmological constraint at the level of ${10}^{-35}e$ utilized by Particle Data Group (PDG) in their Review of particle properties Workman et al. (Particle Data Group) (Prog Theor Exp Phys 2022:083C01, 2022) as a controversial one which makes the laboratory constraints on $e_{\nu }$ dominant. The phenomenological constraints from the available data of laboratory experiments are obtained as $e_p+e_e=(0.2\pm 2.6)\times {10}^{-21}e$, $e_n=(-0.4\pm 1.1)\times {10}^{-21}e$, and $e_{\nu }=(0.6\pm 3.2)\times {10}^{-21}e$. The ones on $e_p+e_e$ and $e_n$ are at the same level as the related constraints of PDG but somewhat different because of releasing the value of $e_{\nu }$. Our $e_{\nu }$ constraint is several orders of magnitude weaker than the controversial cosmological result dominated in the PDG constraint, but several orders of magnitude stronger than the other individual $e_{\nu }$ constraints considered by PDG. We also consider consistency of the phenomenological constraints and the Standard Model (SM). The SM ignores the mass term of the neutrinos and cannot describe the neutrino oscillations which makes it not a complete theory but a part of it. We demonstrate that the condition of the cancellation of the triangle anomalies within the complete theory does not disagree with the phenomenological constraints since different extensions of the SM may produce different additional contributions to the anomalies. A choice of the extension fixes the way how those contributions are organized. In particular, we consider a minimal extension of the SM, where leptons ($\nu ,e$) are treated the same ways as quarks, which sets $e_p+e_e=0$ and allows for numerical strengthening the constraint on $e_n$ and $e_{\nu }$, which is $e_n=-e_{\nu }=(-0.4\pm 1.0)\times {10}^{-21}e$.