Catalog · EDM / neutrino · E008

E008 $\tilde d_q$

Quark chromo-EDM bounds from neutron and mercury EDMs

Status SUBTLETY-ADDED VERIFIED High Code: NO Priority High

Why this constrains the RS scan

Anarchic warped models contain new CP phases and chirality flips in KK-fermion, Higgs, and gauge loops. Even when tree-level $\Delta F=2$ mixing is under control, these loops can generate flavor-diagonal quark EDMs and qCEDMs. The qCEDM lane is therefore a direct probe of RS KK-loop CP violation and wrong-chirality Yukawa structures.

What's changed since the original paper

Relative to the CFW 2008 RS-flavor baseline, the experimental inputs tightened: the direct neutron anchor is now the 2020 PDG limit above, and the 2016 $^{199}\mathrm{Hg}$ result improved the prior mercury limit by a factor of 4 (PDG2026:NeutronEDM; Graner:HgEDM2016; CsakiFalkowskiWeiler:RSFlavor2008). Koenig, Neubert, and Straub 2014 recast electromagnetic and chromomagnetic quark dipoles in partial-compositeness and warped-language Wilson coefficients, finding strong neutron-EDM pressure when wrong-chirality Yukawas are present (KoenigNeubertStraub:DipoleComposite2014). On the theory side, Bhattacharya et al. 2024 target the isovector qCEDM neutron matrix element with lattice QCD and explicit control of power-divergent operator mixing (Bhattacharya:IsoVectorQCEDM2024).

Validity and model dependence

The direct neutron and mercury limits are robust null measurements. The qCEDM bounds are not standalone PDG averages: they assume a low-energy CP-odd basis, neglect cancellations with quark EDMs, semileptonic sources, four-quark operators, $\bar\theta$, and the Weinberg operator, and inherit QCD, nuclear, and atomic matrix-element uncertainties. Mercury is especially powerful for the isovector combination but is also more nuclear-model dependent. 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. Required greps over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no qCEDM, neutron EDM, mercury EDM, or Weinberg-operator constraint. The only nearby dipole implementation is the unrelated $\mu\to e\gamma$ helper in flavorConstraints/muToEGamma.py:3, :21, and :81.

Implementation difficulty

HIGH. A live E008 constraint would need new CP-odd quark EDM/qCEDM operators, loop matching from the RS spectrum, QCD running and threshold mixing, plus hadronic and nuclear matrix-element choices. The existing $\Delta F=2$ SLL/SLR/VLL/VRR/LR basis does not cover this observable.

Reason: Requires new CP-odd quark EDM/qCEDM operators, RS loop matching, QCD running and threshold mixing, and hadronic/nuclear matrix-element choices. 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: PDG2026:NeutronEDM, Graner:HgEDM2016, PospelovRitz:NeutronCEDM2000, OlivePospelovRitzSantoso:HgCEDM2005, CsakiFalkowskiWeiler:RSFlavor2008, KoenigNeubertStraub:DipoleComposite2014, and Bhattacharya:IsoVectorQCEDM2024.

value_summary |d_n| < 1.8 x 10^-26 e cm at 90% CL

RESOLVED

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L17: Canonical direct result:
L18:   <0.18, CL = 90%, ABEL 2020, method MRS UCN.
L19: Converted value:
L20:   |d_n| < 1.8 x 10^-26 e cm at 90% CL.
L21: 
L22: PDG measurement note for ABEL 2020:
L23:   d = (0.0 +/- 1.1 +/- 0.2) x 10^-26 e cm, corresponding to the listed

value_summary d_Hg = (2.20 +/- 2.75_stat +/- 1.48_syst) x 10^-30 e cm; |d_Hg| < 7.4 x 10^-30 e cm at 95% CL

RESOLVED

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L13: Relevant arXiv abstract extract:
L14:   The experiment measures the permanent electric dipole moment of neutral
L15:   199Hg atoms. The reported EDM is
L16:     d_Hg = (2.20 +/- 2.75_stat +/- 1.48_syst) x 10^-30 e cm.
L17:   The result is used to place the limit
L18:     |d_Hg| < 7.4 x 10^-30 e cm at 95% C.L.
L19:   The arXiv abstract states that this improved the previous limit by a factor

formula

d_n = (1 +/- 0.5)[1.1 e(tilde d_d + 0.5 tilde d_u) + 1.4(d_d - 0.25 d_u)] under the Peccei-Quinn convention quoted in the source

RESOLVED

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L16:   including strange-quark tilde d_s, provide significant contributions
L17:   comparable to quark EDM contributions.
L18:   With the theta term removed by Peccei-Quinn symmetry, the abstract gives
L19:     d_n = (1 +/- 0.5) [ 1.1 e (tilde d_d + 0.5 tilde d_u)
L20:                         + 1.4 (d_d - 0.25 d_u) ].
L21: 
L22: Catalog use:

formula d_Hg = 7 x 10^-3 e(tilde d_u - tilde d_d) + 10^-2 d_e + additional four-fermion and semileptonic terms

RESOLVED

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L23:     gbar_piNN^(1)(tilde d_q) ~ 4^{+8}_{-2} (tilde d_u - tilde d_d) GeV^{-1},
L24:   with large uncertainty from cancellations between leading contributions.
L25:   Combining atomic, nuclear, and QCD ingredients, the paper gives
L26:     d_Hg = 7 x 10^-3 e (tilde d_u - tilde d_d) + 10^-2 d_e
L27:            + additional four-fermion and semileptonic terms.
L28:   It states that d_Hg is especially sensitive to the triplet/isovector CEDM
L29:   combination tilde d_u - tilde d_d, with the overall coefficient known only

value_summary RS-flavor baseline quotes generic KK-gluon mass bounds near 21 TeV and pseudo-Goldstone scenario bounds near 33 TeV.

RESOLVED

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L12: Relevant arXiv abstract extract:
L13:   The paper studies flavor in 5D warped models and composite pseudo-Goldstone
L14:   Higgs models. It reports that in standard Randall-Sundrum-type scenarios
L15:   the KK gluon mass should generically be heavier than about 21 TeV.
L16:   In the pseudo-Goldstone scenario, with Yukawa couplings set by a gauge
L17:   coupling, the KK gluon mass should be at least about 33 TeV.
L18:   The abstract states that these strong bounds make a fully anarchic approach

value_summary

Composite/warped dipole analysis using the older neutron limit |d_n| < 2.9 x 10^-26 e cm at 90% CL; one-at-a-time imaginary Wilson-coefficient scale bounds include Q_uug 1.45 TeV and Q_ddg 3.79 TeV.

RESOLVED

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L30:   The paper's then-current neutron limit was
L31:     |d_n| < 2.9 x 10^-26 e cm at 90% C.L.
L32:   Its model-independent table gives one-at-a-time imaginary-coefficient
L33:   scale bounds at 1 TeV, including Q_uug: 1.45 TeV and Q_ddg: 3.79 TeV,
L34:   using that older neutron limit.
L35: 
L36: Catalog use:

value_summary

Lattice-QCD calculation of the isovector qCEDM contribution to the neutron EDM using four 2+1+1 flavor HISQ ensembles and Wilson-clover quarks; controls power-divergent pseudoscalar mixing with the nonsinglet axial Ward identity and converts to MS at leading-log order.

RESOLVED

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L12: 
L13: Relevant arXiv abstract extract:
L14:   The paper presents lattice-QCD results for the contribution of the isovector
L15:   quark cEDM operator to the neutron EDM. The calculation uses four 2+1+1
L16:   flavor highly improved staggered quark ensembles from MILC and Wilson-clover
L17:   quarks for correlation functions. It uses the nonsinglet axial Ward identity,
L18:   with corrections up to O(a), to control power-divergent mixing of the