The most stringent limit on the electric dipole moment (EDM) of any diamagnetic atom, ∣d(199Hg)∣<7.4×10−30 e⋅|d(^{199}\mathrm{Hg})|<7.4\times10^{-30}\ e\cdotcm, cannot currently be translated into unambiguous knowledge of nucleon-level charge-parity (CPCP) violation. The bottleneck is threefold: independent nuclear-structure calculations of the 199^{199}Hg Schiff moment — the radially weighted nuclear moment that escapes electron screening and transmits nuclear CPCP violation to the atom — disagree by up to three orders of magnitude and even in sign for the isovector CPCP-odd pion-nucleon coupling gˉ1\bar g_1; the atomic conversion factor is consolidated only at the 10–25% level; and the dominant experimental systematic, high-voltage-correlated mechanical motion of the vapor cells in residual magnetic-field gradients, is bounded but not eliminated. The problem asks for a controlled-uncertainty determination of the 199^{199}Hg Schiff-moment coefficients with respect to the CPCP-odd pion-nucleon couplings gˉ0,1,2\bar g_{0,1,2} and the nucleon EDMs, consolidation of the atomic conversion factor, and demonstrated suppression of the motion systematic, so that the standing bound and its next-generation improvements yield quantitative limits on θˉQCD\bar\theta_{\rm QCD}, gˉ0,1,2\bar g_{0,1,2}, the nucleon EDMs, and light-quark chromo-EDMs, each carrying the single-source assumption as at present. A 2025 review documents the persisting theory disagreement; the ab initio program, first demonstrated on 129^{129}Xe in 2026, has not yet reached 199^{199}Hg; and no newer measurement supersedes the 2016 result, so the problem is open.

Background

A permanent electric dipole moment (EDM) of a particle, nucleus, atom, or molecule is a vector expectation value aligned with the spin; because it singles out a direction along an axial vector, any nonzero EDM of a non-degenerate state violates time-reversal symmetry TT and hence, by the CPTCPT theorem, CPCP symmetry. The two known sources of CPCP violation in the Standard Model — the CKM quark-mixing phase, whose EDM contribution is far below experimental reach, and the QCD vacuum angle θˉQCD\bar\theta_{\rm QCD}, measured to be unnaturally small (the strong-CPCP problem) — are insufficient for the matter–antimatter asymmetry of the universe, so EDM searches are a leading probe of new physics. The most sensitive probes of CPCP violation inside the nucleus are diamagnetic atoms — atoms with zero electronic angular momentum such as 199^{199}Hg, whose atomic EDM is generated entirely by nuclear CPCP violation.

In such an atom the bare nuclear EDM is screened by the electron cloud: to leading order the electrons rearrange so that the nucleus feels no net internal electric field. The leading nuclear moment that escapes this screening is the Schiff moment SS, a radially weighted remnant of the PP- and TT-violating nuclear charge distribution. The observable atomic EDM is proportional to it, datom=αSd_{\rm atom}=\alpha S, with an atomic-structure coefficient α\alpha computed by relativistic many-body theory; for 199^{199}Hg the average of several calculations gives α≃−2.4×10−17 e⋅\alpha\simeq-2.4\times10^{-17}\ e\cdotcm per e fm3e\,{\rm fm}^3.

The Schiff moment itself is induced by CPCP-violating nuclear forces. The standard parameterization uses the P,TP,T-odd pion-nucleon couplings gˉ0\bar g_0, gˉ1\bar g_1, gˉ2\bar g_2 — the isoscalar, isovector, and isotensor components of a CPCP-violating pion-exchange nucleon-nucleon interaction — with S=a0gˉ0+a1gˉ1+a2gˉ2S=a_0\bar g_0+a_1\bar g_1+a_2\bar g_2; alternatively SS is induced by the neutron and proton EDMs, dnd_n and dpd_p. Moving up in energy, gˉ0\bar g_0 is fixed by θˉQCD\bar\theta_{\rm QCD} and gˉ1\bar g_1 by the difference of the up- and down-quark chromo-EDMs (the CPCP-violating color dipole moments of the quarks), so an EDM limit propagates to fundamental parameters — provided both the atomic and the nuclear coefficients are known.

The University of Washington 199^{199}Hg experiment stacks vapor cells of optically spin-polarized 199^{199}Hg in a common magnetic field, reverses a high voltage (HV, ±10\pm10 kV) applied across the cells, and searches for an electric-field-correlated shift of the Larmor precession frequency measured by Faraday rotation. The 2016 run set ∣dHg∣<7.4×10−30 e⋅|d_{\rm Hg}|<7.4\times10^{-30}\ e\cdotcm (95% C.L.), still the most stringent limit on any diamagnetic atom. Its systematic budget is dominated by HV-correlated mechanical motion of the cells and vessel in residual magnetic-field gradients: a displacement as small as 2 nm in the lab-fixed axial gradient produces a frequency shift with exactly the reversal symmetries of an EDM; the experiment bounded this channel to 1.26×10−30 e⋅1.26\times10^{-30}\ e\cdotcm of the 1.48×10−30 e⋅1.48\times10^{-30}\ e\cdotcm total systematic by comparing runs with large and small motion signals.

On the theory side the interpretation is stuck. The atomic coefficient is now computed consistently at the 10–25% level by several relativistic many-body methods. But the nuclear coefficients aia_i of 199^{199}Hg — computed with the random-phase approximation (RPA, the linear response of the nuclear mean field), Skyrme density-functional theory (a self-consistent mean-field method whose spin-dependent, time-odd coupling constants are weakly constrained), and the interacting shell model (diagonalization in a truncated valence orbital space) — disagree by up to three orders of magnitude for a0a_0 and in sign for a1a_1. The physical reason is that 199^{199}Hg is soft (its nuclear shape deforms at very low energy cost) and possibly triaxial (with three unequal principal axes), with a near-degenerate second 1/2−1/2^- excited state whose Schiff moment is strongly quenched and whose admixture into other methods' ground states is suspected but unverified. Ab initio methods — nuclear-structure calculations built from chiral effective-field-theory interactions with systematically improvable truncations, such as the in-medium similarity renormalization group (IMSRG), which decouples a valence space from the full many-body problem through a continuous unitary transformation — are regarded as the route to a controlled answer; the first ab initio Schiff moment was achieved for 129^{129}Xe in 2026, but not yet for 199^{199}Hg.

The question left open by the 2016 measurement is what the 199^{199}Hg EDM limit actually constrains. Closing the interpretation gap — chiefly a controlled-uncertainty Schiff moment of 199^{199}Hg — and suppressing the motion systematic are jointly what is needed to turn the strongest diamagnetic-atom EDM bound, or its next generation, into unambiguous nucleon-level CPCP-violation limits.

Problem Statement

Make the 199^{199}Hg EDM limit unambiguous, in both its theoretical interpretation and its experimental reach. Concretely: (1) determine the nuclear Schiff moment of 199^{199}Hg — the coefficients a0a_0, a1a_1, a2a_2 (in e fm3e\,{\rm fm}^3) in S=a0gˉ0+a1gˉ1+a2gˉ2S=a_0\bar g_0+a_1\bar g_1+a_2\bar g_2, and the coefficients of the neutron and proton EDM response S=cndn+cpdpS=c_nd_n+c_pd_p — with quantified, controlled uncertainties, namely an explicit error budget dominated by the systematic truncation error in which each coefficient is quoted with its own uncertainty, resolving the documented disagreement across existing nuclear-structure calculations (in which a0a_0 spans roughly three orders of magnitude and a1a_1 spans −0.027-0.027 to +0.090 e fm3+0.090\ e\,{\rm fm}^3, including a sign flip), with the absolute target that each coefficient is determined to a fractional uncertainty of at most 10% — small enough that the a1a_1 result excludes zero at the 95% confidence level and the sign of the gˉ1\bar g_1 contribution is settled — and that the residual a0a_0 spread across methods is shown to arise from identified, quantified truncation and systematic effects; (2) consolidate the atomic conversion factor α\alpha (currently −2.4×10−17 e⋅-2.4\times10^{-17}\ e\cdotcm per e fm3e\,{\rm fm}^3 at the 10-25% level) to a quantified uncertainty at or below 10%, so that the atomic error is subdominant to the nuclear uncertainty of component (1); and (3) show, by design and simulation, that the dominant experimental systematic — HV-correlated motion of the vapor cells or vessel in residual magnetic-field gradients, which contributed 1.26×10−30 e⋅1.26\times10^{-30}\ e\cdotcm of the 1.48×10−30 e⋅1.48\times10^{-30}\ e\cdotcm systematic budget of the standing measurement — can be suppressed or projected out at the level required for a next-generation measurement below the 10−30 e⋅10^{-30}\ e\cdotcm scale (a design-and-simulation projection satisfies this component; a completed apparatus demonstration is not required). All three components are required, and a partial program that omits any of them does not resolve the task. These components serve one objective: converting the strongest diamagnetic-atom EDM bound — and any future improvement of it — into limits on gˉ0,1,2\bar g_{0,1,2}, dn,pd_{n,p}, θˉQCD\bar\theta_{\rm QCD}, and the light-quark chromo-EDMs, each limit carrying the single-source assumption as at present; unambiguous simultaneous extraction of several CPCP-violating parameters additionally requires non-null results or comparably sensitive limits in several different systems, a stated limitation of any single-system answer.

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