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.
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.