The neutron is one of the most neutral particles in nature. But if you add a special parameter to the laws of physics, called the theta term Standard Model, a tiny charge imbalance appears inside the neutron. One edge becomes slightly positive, the other slightly negative. This imbalance is called the electric dipole moment.
Measuring it directly is nearly impossible: it requires fantastic precision. The authors of the study devised a workaround. They placed the neutron in a constant electric field and watched how its energy changed. According to the theorem by Richard Feynman and Hans Bethe (also known as the Feynman–Hellmann theorem), this energy shift is directly related to the sought-after imbalance. But instead of calculating the charge over the entire volume, the physicists took samples at a single time slice, as if taking a snapshot of the charge cloud. This drastically reduced statistical noise.
One problem remained: the standard way of isolating the neutron from the sea of quantum fluctuations mixed in extra excited states. To clean up the signal, the authors constructed the ground state of a deformed neutron using a non-Hermitian eigenvalue problem. It's like tuning a radio to a clear frequency, cutting out interference. As a result, consistent numbers were obtained for different ways of describing the neutron: [formula]$d_n$=-0.0050(4)^\text{stat}(8)^\text{sys}\,\bar{\theta}\,e\,\text{fm}[/formula].
This result is an important step toward understanding why there is so little antimatter in our universe. If the imbalance were slightly larger, matter and antimatter would have annihilated completely, and we wouldn't exist.
as written by the authors arXiv:2607.10606
We present the calculation of the neutron electric dipole moment (nEDM) $$d_n$$ using 2+1 flavor domain wall fermion ensembles with fixed lattice spacing $$a\approx 0.11\,\text{fm}$$ and pion masses of 340, 420, and 576 MeV. We show that the neutron electric dipole moment can be extracted from the energy shift induced by a static uniform external background electric field in the presence of the CP-violating QCD theta-term, $$\bar\theta Q_{top}$$. Motivated by the Feynman-Hellmann theorem, we employ sampling of the topological charge $$q_\text{top}(t)$$ on a single time-slice rather than the global topological charge $$Q_\text{top}=\int q_\text{top}(t) \, dt$$, which dramatically improves the statistical precision of the $$\theta$$-induced nEDM. Key to our method is to calculate the forward matrix element of the topological charge density in the nucleon deformed by a background electric field. We find that calculation with the traditional positive parity-projected nucleon operator is subject to large excited-state contamination. To remove the contamination, we construct the ground state of the deformed nucleon by solving a non-Hermitian generalized eigenvalue problem. With this approach, we find consistent values for the nEDM when using different nucleon interpolating operators, regardless of whether they are covariant or non-covariant under chiral transformations. Finally, after extrapolating to the physical point, we obtain $$d_n=-0.0050(4)^\text{stat}(8)^\text{sys}\bar{\theta}$$ $$e$$ fm, where the systematic uncertainty includes excited-state effects estimated as variation with the Euclidean-time fits and the dependence on the strength of the electric field applied to the neutron. Conventional systematic errors like discretization, finite-volume, and chiral extrapolation effects will be addressed in future work.
The neutron's electric dipole moment is so small that if you scaled the neutron up to the size of the Earth, the charge imbalance would be smaller than the thickness of a human hair.
In Stanisław Lem's novel Solaris, the ocean could control quantum states — much like physicists manipulate neutrons to catch traces of symmetry violation.