Catalog · EDM / neutrino · E006

E006 $d_{Hg}$

Mercury-199 electric dipole moment

Status SUBTLETY-ADDED VERIFIED High Code: NO Priority Medium

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
Mercury-199 atomic electric dipole moment	7.4e-30 e cm	2016	Graner et al., Phys. Rev. Lett. 116, 161601 (2016); arXiv:1601.04339	source ↑
Improvement of the 199Hg EDM bound relative to the previous limit	4 dimensionless improvement factor	2016	Graner et al., Phys. Rev. Lett. 116, 161601 (2016); arXiv:1601.04339	source ↑
Theory-derived neutron EDM rows using 199Hg atom EDM	?	2026	PDG Live 2026 S017EDM neutron electric dipole moment datablock	source ↑
Selected interpretation-level limits derived from 199Hg	?	2017	Sahoo, Phys. Rev. D 95, 013002 (2017); arXiv:1612.09371	source ↑

Why this constrains the RS scan

Warped or composite anarchic flavor models generically contain new CP phases. Loop matching can generate quark EDMs, quark chromo-EDMs, the Weinberg three-gluon operator, and semileptonic CP-odd operators. In a diamagnetic closed-shell atom such as $^{199}\mathrm{Hg}$, the dominant hadronic sensitivity is usually phrased through the nuclear Schiff moment and CP-odd pion-nucleon interactions, rather than through a simple elementary fermion EDM. The observable is therefore complementary to the neutron EDM: it probes a different linear combination of CP-odd low-energy operators and nuclear matrix elements.

What's changed since the original paper

Relative to the 2008 CFW warped-flavor baseline (CsakiFalkowskiWeiler:RSFlavor2008), the main experimental update is the 2016 Washington $^{199}\mathrm{Hg}$ measurement (Graner:HgEDM2016), which improved the previous Hg bound by a factor of $4$ and remains the standard diamagnetic-atom benchmark. The post-2008 theory update represented here by Sahoo 2017 (Sahoo:HgEDMTheory2017) combines the Hg atom limit with relativistic atomic calculations and quotes derived limits including $d_n<2.2\times10^{-26}\ |e|\,\mathrm{cm}$, $d_p<2.1\times10^{-25}\ |e|\,\mathrm{cm}$, $|\bar\theta|<1.1\times10^{-10}$, and $|\tilde d_u-\tilde d_d|<5.5\times10^{-27}\ |e|\,\mathrm{cm}$ (Sahoo:HgEDMTheory2017).

Validity and model dependence

The experimental atom-EDM bound is robust as a null search for a $P$- and $T$-violating energy shift. Translating it into RS parameters is model-dependent: the result depends on the chosen CP-odd operator basis, QCD running and thresholds, atomic many-body coefficients, nuclear Schiff moments, hadronic matrix elements, and possible cancellations among sources. It should be treated as an EDM-adjacent loop/nuclear-translation constraint, not as a direct $\Delta F=2$ bound in the current quark scan. For anarchic CP phases, EDM constraints should be reviewed jointly with the flavor branching rows that share the same Wilson coefficients (relevant cross-refs: K001, K003, B011, B033, B034), not as an isolated appendix.

Code coverage in this repo

NO. The required catalog greps and a focused search for Hg, mercury, 199Hg, d\_Hg, Schiff, diamagnetic, chromo-EDM, Weinberg, and generic EDM/dipole terms over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no $^{199}\mathrm{Hg}$ EDM implementation. The only nearby dipole code is the off-diagonal $\mu\to e\gamma$ helper in flavorConstraints/muToEGamma.py:3, :21, and :81.

Implementation difficulty

HIGH. A live constraint would require new CP-odd quark/gluon and semileptonic operator matching, RG running to hadronic scales, and an atomic/nuclear translation layer for $^{199}\mathrm{Hg}$. The existing SLL/SLR/VLL/VRR/LR $\Delta F=2$ basis and the $\mu\to e\gamma$ NDA helper do not cover this observable.

Reason: Requires new CP-odd quark/gluon and semileptonic operator matching, QCD running and thresholds, and atomic/nuclear translation for the 199Hg Schiff-moment dominated response. Existing $\Delta F = 2$ and $\mu \to e \gamma$ code paths do not provide this observable.

Key references

Process-local source keys before bibliography consolidation: Graner:HgEDM2016, PDG2026:NeutronEDMHgCrossref, Sahoo:HgEDMTheory2017, and CsakiFalkowskiWeiler:RSFlavor2008.

value_summary |d_Hg| < 7.4 x 10^-30 e cm at 95% CL

RESOLVED

Match snapshot line 23

L20:   d_Hg = (2.20 +/- 2.75_stat +/- 1.48_syst) x 10^-30 e cm.
L21: 
L22: Canonical limit:
L23:   |d_Hg| < 7.4 x 10^-30 e cm at 95% C.L.
L24: 
L25: Notes:
L26:   The abstract states that this improves the previous limit by a factor of 4

value_units_fallback 4 dimensionless improvement factor

RESOLVED

Match snapshot line 26

L23:   |d_Hg| < 7.4 x 10^-30 e cm at 95% C.L.
L24: 
L25: Notes:
L26:   The abstract states that this improves the previous limit by a factor of 4
L27:   and discusses implications for CP-violating observables beyond the Standard
L28:   Model.
L29:   PDG Live S017EDM cites the published PRL and its PRL 119, 119901 (2017)

value_summary

Graner 2016 row <0.16 and Sahoo 2017 row <0.22 in units of 10^-25 e cm, both at 95% CL; these are not direct Hg atom EDM values.

RESOLVED

Match snapshot line 18

L15: 
L16: Relevant PDG rows:
L17:   S017EDM neutron EDM table units: 10^-25 e cm.
L18:   Sahoo 2017 row: <0.22 at 95% CL, comment "199Hg atom EDM + theory".
L19:   Graner 2016 row: <0.16 at 95% CL, comment "MRS 199Hg atom EDM + theory".
L20: 
L21: Relevant PDG note:

value_summary

d_n < 2.2 x 10^-26 |e| cm, d_p < 2.1 x 10^-25 |e| cm, |theta_bar| < 1.1 x 10^-10, |tilde d_u - tilde d_d| < 5.5 x 10^-27 |e| cm.

RESOLVED

Match snapshot line 20

L17:   coupling and nuclear Schiff-moment interactions.
L18: 
L19: Selected numerical limits from the arXiv abstract:
L20:   d_n < 2.2 x 10^-26 |e| cm.
L21:   d_p < 2.1 x 10^-25 |e| cm.
L22:   |theta_bar| < 1.1 x 10^-10.
L23:   |tilde{d}_u - tilde{d}_d| < 5.5 x 10^-27 |e| cm.