In 1976, Gerard 't Hooft noticed that the vacuum of a gauge theory is not as simple as it seems: it possesses a topological structure that manifests itself in a nonzero topological susceptibility. This quantity, a measure of the vacuum's sensitivity to topological field configurations, requires the existence of a pseudoscalar state, a particle with zero spin and negative parity. In quantum chromodynamics, the η′ meson plays this role, but for the electroweak sector of the Standard Model, the question remained open.

Recent works have postulated the existence of ηW as a new light state, but its physical nature was not established. The authors of the new paper approach the problem from an unexpected angle: they use the perspective of a three-form gauge field, in which the topological susceptibility is equivalent to the presence of a massive pseudoscalar degree of freedom. Then they construct the 't Hooft operator, a four-fermion interaction that violates baryon number, and show that after the Higgs mechanism and QCD confinement, this operator corresponds to a QED-bound state of a proton and an electron, that is, a hydrogen atom.

The result is striking: the pseudoscalar state requires no new physics. It is a CP-odd superposition of the ground states of hydrogen and antihydrogen: ηW = -i/√2 ($Ψ_H$ - $Ψ_{anti}$-H). The CP-even partner $φ_H$ is also defined. In the renormalizable Standard Model, baryon number minus lepton number is conserved, so transitions that change B+L by four units are forbidden, and hydrogen–antihydrogen oscillations are absent. However, in extensions with B+L violation, operators that induce such oscillations arise. Then ηW and $φ_H$ become energy eigenstates, and atomic physics gains direct access to the topological sector.

The work differs radically from neighboring studies, which either introduce new particles or treat ηW as an electroweak meson state. Here, for the first time, a concrete infrared realization in the form of an atomic system is proposed. The topological "ghost," long a mathematical abstraction, takes on flesh in the most ordinary atom. This opens a new channel for testing fundamental symmetries without high energies: precision spectroscopy of hydrogen could become a window into physics beyond the Standard Model.

Future prospects include a precise calculation of the matrix element ⟨0|OW|$η_H$⟩ in effective field theory, which would quantitatively link the mass of the three-form field to atomic parameters. Also promising is the estimation of hydrogen–antihydrogen oscillation amplitudes in specific models with B+L violation and the revision of existing constraints. If such oscillations are detected, they would point to processes that violate baryon number, which are necessary for generating the matter–antimatter asymmetry in the Universe. Thus, the humble hydrogen atom could become the key to one of cosmology's greatest mysteries.