Electron Electric Dipole Moment Research Articles

ConstrainingCPT-even and Lorentz-violating nonminimal couplings with the electron magnetic and electric dipole moments

We analyze some dimension-five $CPT$-even and Lorentz-violating nonminimal couplings between fermionic and gauge fields in the context of the Dirac equation. After evaluating the nonrelativistic Hamiltonian, we discuss the behavior of the terms under discrete symmetries and analyze the implied effects. We then use the anomalous magnetic dipole moment and electron electric dipole moment measurements to reach upper bounds of 1 part in ${10}^{20}$ and ${10}^{24}\text{ }\text{ }(\mathrm{eV}{)}^{\ensuremath{-}1}$, improving the level of restriction on such couplings by at least 8 orders of magnitude. These upper bounds are also transferred to the Sun-centered frame by considering the Earth's rotational motion.

TaN molecule as a candidate for the search for aT,P-violating nuclear magnetic quadrupole moment

It is demonstrated that the TaN molecule is the best candidate to search for T,P-violating nuclear magnetic quadrupole moment (MQM), it also looks promising to search for other T,P-odd effects. We report results of coupled-cluster calculations of T,P-odd effects in TaN produced by the Ta nucleus MQM, electron electric dipole moment (EDM), scalar$-$pseudoscalar nucleus$-$electron interactions, also of the molecule-axis hyperfine structure constant and dipole moment. Nuclear calculations of $^{181}$Ta MQM are performed to express the T,P-odd effect in terms of the strength constants of T,P-odd nuclear forces, proton and neutron EDM, QCD parameter $\theta$ and quark chromo-EDM.

Electric dipole moment planning with a resurrected BNL Alternating Gradient Synchrotron electron analog ring

There has been much recent interest in directly measuring the electric dipole moments (EDM) of the proton and the electron. Such a measurement will require storing a polarized beam of "frozen spin" particles in an all-electric storage ring. Only one such relativistic electric accelerator has ever been built---the "Electron Analogue" ring at Brookhaven National Laboratory in 1954. By chance this electron ring, long since dismantled, would have been appropriate both for measuring the electron EDM and to serve as an inexpensive prototype for the arguably more promising, but ten times more expensive, proton EDM measurement. Today it is cheaper yet to "resurrect" the Electron Analogue ring by simulating its performance computationally. This is one purpose for the present paper. To set up these calculations has required a kind of "archeological physics" to reconstitute the detailed Electron Analogue lattice design. The new UAL/ETEAPOT code, described in detail in an accompanying paper, has been developed for modeling storage ring performance, including (exact BMT) spin evolution, in electric rings. Illustrating its use, comparing its predictions with the old observations, and describing new expectations concerning spin evolution and code performance, are other goals of the paper. This paper describes the practical application of the ETEAPOT code and provides sample results, with emphasis on emulating lattice optics in the AGS Analogue ring for comparison with the historical maching studies and to predict the electron spin evolution they would have measured. To exhibit the ETEAPOT code performance and confirm its symplecticity, results are also given for 30 million turn proton spin tracking in an all-electric lattice that would be appropriate for a present day measurement of the proton EDM.

Cancellations Between Two-Loop Contributions to the Electron Electric Dipole Moment with a CP-Violating Higgs Sector.

We present a class of cancellation conditions for suppressing the total contributions of Barr-Zee diagrams to the electron electric dipole moment (eEDM). Such a cancellation is of particular significance after the new eEDM upper limit was released by the ACME Collaboration, which strongly constrains the allowed magnitude of CP violation in Higgs couplings and hence the feasibility of electroweak baryogenesis (EWBG). Explicitly, if both the CP-odd Higgs-photon-photon (Z boson) and the CP-odd Higgs-electron-positron couplings are turned on, a cancellation may occur either between the contributions of a CP-mixing Higgs boson, with the other Higgs bosons being decoupled, or between the contributions of CP-even and CP-odd Higgs bosons. With a cancellation, large CP violation in the Higgs sector is still allowed, yielding successful EWBG. The reopened parameter regions would be probed by future neutron, mercury EDM measurements, and direct measurements of Higgs CP properties at the Large Hadron Collider Run II and future colliders.

Screening of electron electric dipole moment through the Foldy-Wouthuysen representation

The existent of the intrinsic electric dipole moments (EDM) lead to CP violation in a physical system. In the non-relativistic and point like limits, the effects of them in atoms are canceled which is well-known as Schiff screening effects. It is why that the energy shift due to the EDM is proportional to the expectation value of which vanishes in non-relativistic limit. In this paper, using Foldy-Wouthuysen representation we remove the odd terms (those terms mix the positive and negative energy solutions) up to order and then study the Schiff screening effects.

Ac Stark effect in ThOH3Δ1for the electron electric-dipole-moment search

A method and code for calculations of diatomic molecules in the external variable electromagnetic field have been developed. Code applied for calculation of systematics in the electron's electric dipole moment search experiment on ThO $H^3\Delta_1$ state related to geometric phases, including dependence on $\Omega$-doublet, rotational level, and external static electric field. It is found that systematics decrease cubically with respect to the frequency of the rotating transverse component of the electric field. Calculation confirms that experiment on ThO $H^3\Delta_1$ state is very robust against systematic errors related to geometric phases.

On the electric dipole moment of the electron and the P,T-odd electron–nucleus interaction in highly-charged heavy ions

It is demonstrated that the effect of the electric dipole moment of electron and of the P,T-odd electron–nucleus interaction can be well distinguished in the experiments with H-like (or Li-like) highly charged ions in storage rings. These two effects cannot be separated in the experiments with a certain atom or molecule. Possible experiments for the search of P,T-odd effects with H-like ions in storage rings are discussed and the parameters of these experiments (observation time, field control) are estimated.

Enhancement ofBr(Bd→μ+μ−)/Br(Bs→μ+μ−)in supersymmetric unified models

We explain the 2.3 sigma deviation in the recent measurements of the neutral B mesons decay into muon pairs from the standard model prediction in the framework of supersymmetric grand unified models using anti-symmetric coupling as a new source of flavor violation. We show a correlation between the B_d -> mu^+mu^- decay and the CP phase in the B_d -> J/psi K decay and that their deviations from the standard model predictions can be explained after satisfying constraints arising from various hadronic and leptonic rare decay processes, B-bar{B}, K-bar{K} oscillations data and electric dipole moments of electron and neutron. The allowed parameter space is typically represented by pseudoscalar Higgs mass m_A < 1 TeV and tan beta_H (= {v_u}/{v_d}) < 20 for squark and gluino masses around 2 TeV.

Experimental constraints on the coupling of the Higgs boson to electrons

In the standard model (SM), the coupling of the Higgs boson to electrons is real and very small, proportional to the electron mass. New physics could significantly modify both real and imaginary parts of this coupling. We discuss experiments which are sensitive to the Higgs-electron coupling and derive the current bounds on new physics contributing to this coupling. The strongest constraint follows from the ACME bound on the electron electric dipole moment (EDM). We calculate the full analytic two-loop result for the electron EDM and show that it bounds the imaginary part of the Higgs-electron coupling to be less than 1.7 x 10^-2 times the SM electron Yukawa coupling. Deviations of the real part are much less constrained. We discuss bounds from Higgs decays, resonant Higgs production at electron colliders, Higgs mediated B -> e^+ e^- decays, and the anomalous magnetic moment of the electron. Currently, the strongest constraint comes from h -> e^+ e^- at the LHC, bounding the coupling to be less than ~600 times the SM Yukawa coupling. Important improvements can be expected from future EDM measurements as well as from resonant Higgs production at a next-generation high-luminosity e^+ e^- collider.

Theoretical study ofThF+in the search forT,P-violation effects: Effective state of a Th atom inThF+and ThO compounds

We report the results of a theoretical investigation of the electronic structure of the ${\mathrm{ThF}}^{+}$ cation, which is one of the most interesting systems to search for the electron electric dipole moment $(e\mathrm{EDM})$ [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science 342, 1220 (2013)] and other effects of violation of time reversal (T) and spatial parity (P) symmetries in fundamental interactions. For the working ${}^{3}{\ensuremath{\Delta}}_{1}$ state we find a quite high value of the effective electric field acting on unpaired electrons (37.3 GV/cm). The field will be required to interpret the experiment planned on ${\mathrm{ThF}}^{+}$ in terms of the $e\mathrm{EDM}$. Within the concept of atoms in compounds [A. V. Titov, Y. V. Lomachuk, and L. V. Skripnikov, Phys. Rev. A 90, 052522 (2014)], we compare the ${\mathrm{ThF}}^{+}$ electronic structure with that of ThO. Also, we calculate other parameters of T,P-odd interactions: ${W}_{T,P}$, which is needed for interpretation of the experiment in terms of the dimensionless constant ${k}_{T,P}$ characterizing the strength of the $T,P$-odd pseudoscalar-scalar electron-nucleus neutral current interaction (50 kHz); and ${W}_{M}$, which is required to search for the $^{229}\mathrm{Th}$ nuclear magnetic quadrupole moment in ${}^{229}{\mathrm{ThF}}^{+}$ (0.88 $\frac{{10}^{33}\phantom{\rule{0.28em}{0ex}}\mathrm{Hz}}{e\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}})$. A number of properties which can be measured are also calculated: the hyperfine structure constant, molecule-frame dipole moment, and $g$ factor.

Theoretical study on ThF+, a prospective system in search of time-reversal violation

The low-lying electronic states of ThF+, a possible candidate in the search for - and -violation, have been studied using high-level correlated relativistic ab initio multi-reference coupled-cluster and configuration interaction approaches. For the state component with Ω = 1 (electron electric dipole moment ‘science state’) we obtain an effective electric field of , a - and -odd electron–nucleon interaction constant of kHz, a magnetic hyperfine interaction constant of MHz for 229Th (), and a very large molecular dipole moment of 4.03 D. The Ω = 1 state is found to be more than 300 cm−1 lower in energy than (), challenging the state assignment from an earlier theoretical study on this species (Barker et al 2012 J. Chem. Phys. 136 104305).

Electric dipole moments: A global analysis

We perform a global analysis of searches for the permanent electric dipole moments (EDMs) of the neutron, neutral atoms, and molecules in terms of six leptonic, semileptonic, and nonleptonic interactions involving photons, electrons, pions, and nucleons. Translating the results into fundamental CP-violating effective interactions through dimension six involving Standard Model particles, we obtain rough lower bounds on the scale of beyond the Standard Model CP-violating interactions ranging from 1.5 TeV for the electron EDM to 1300 TeV for the nuclear spin-independent electron-quark interaction. We show that future measurements involving systems or combinations of systems with complementary sensitivities to the low-energy parameters may extend the mass reach by an order of magnitude or more.

Effective interaction of electroweak-interacting dark matter with Higgs boson and its phenomenology

We study phenomenology of electroweak-interacting fermionic dark matter (DM) with a mass of O(100) GeV. Constructing the effective Lagrangian that describes the interactions between the Higgs boson and the SU(2)L isospin multiplet fermion, we evaluate the electric dipole moment (EDM) of electron, the signal strength of Higgs boson decay to two photons and the spin-independent elastic-scattering cross section with proton. As representative cases, we consider the SU(2)L triplet fermions with zero/nonzero hypercharges and SU(2)L doublet fermion. It is found that the electron EDM gives stringent constraints on those model parameter spaces. In the cases of the triplet fermion with zero hypercharge and the doublet fermion, the Higgs signal strength does not deviate from the standard model prediction by more than a few % once the current DM direct detection constraint is taken into account, even if the CP violation is suppressed. On the contrary, O(10–20)% deviation may occur in the case of the triplet fermion with nonzero hypercharge. Our representative scenarios may be tested by the future experiments.

Theoretical study of thorium monoxide for the electron electric dipole moment search: Electronic properties of H3Δ1 in ThO

Recently, improved limits on the electron electric dipole moment, and dimensionless constant, kT,P, characterizing the strength of the T,P-odd pseudoscalar–scalar electron–nucleus neutral current interaction in the H3Δ1 state of ThO molecule were obtained by the ACME collaboration [J. Baron et al., Science 343, 269 (2014)]. The interpretation of the experiment in terms of these fundamental quantities is based on the results of theoretical study of appropriate ThO characteristics, the effective electric field acting on electron, Eeff, and a parameter of the T,P-odd pseudoscalar–scalar interaction, WT,P, given in Skripnikov et al. [J. Chem. Phys. 139, 221103 (2013)] by St. Petersburg group. To reduce the uncertainties of the given limits, we report improved calculations of the molecular state–specific quantities Eeff, 81.5 GV/cm, and WT,P, 112 kHz, with the uncertainty within 7% of the magnitudes. Thus, the values recommended to use for the upper limits of the quantities are 75.8 GV/cm and 104 kHz, correspondingly. The hyperfine structure constant, molecule-frame dipole moment of the H3Δ1 state, and the H3Δ1 → X1Σ+ transition energy which, in general, can serve as a measure of reliability of the obtained Eeff and WT,P values are also calculated. In addition, we report the first calculation of g-factor for the H3Δ1 state of ThO. The results are compared to the earlier experimental and theoretical studies, and a detailed analysis of uncertainties of the calculations is given.

Electron and neutron electric dipole moment in the 3-3-1 model with heavy leptons

We calculate the electric dipole moment for the electron and neutron in the framework of the 3-3-1 model with heavy charged leptons. We assume that the only source of $CP$ violation arises from a complex trilinear coupling constant and the three complex vacuum expectation values. However, two of the vacua phases are absorbed and the other two are equal up to a minus sign. Hence only one physical phase survives. In order to be compatible with the experimental data this phase has to be smaller than $10^{-6}$.

Lightness of Higgs boson and spontaneousCPviolation in the Lee model

We proposed a mechanism in which the lightness of Higgs boson and the smallness of charge parity ($CP$) violation are correlated based on the Lee model, namely, the spontaneous $CP$-violation two-Higgs-doublet model. In this model, the mass of the lightest Higgs boson ${m}_{h}$ as well as the quantities $K$ and $J$ are $\ensuremath{\propto}{t}_{\ensuremath{\beta}}{s}_{\ensuremath{\xi}}$ in the limit ${t}_{\ensuremath{\beta}}{s}_{\ensuremath{\xi}}\ensuremath{\rightarrow}0$ (see text for definitions of ${t}_{\ensuremath{\beta}}$ and $\ensuremath{\xi}$), namely, the $CP$ conservation limit. Here, $K$ and $J$ are the measures for $CP$-violation effects in scalar and Yukawa sectors, respectively. It is a new way to understand why the Higgs boson discovered at the LHC is light. We investigated the important constraints from both high energy LHC data and numerous low energy experiments, especially the measurements of electric dipole moments of electron and neutron as well as the quantities of B meson and kaon. Confronting all data, we found that this model is still viable. It should be emphasized that there is no standard-model limit for this scenario; thus it is always testable for future experiments. In order to pin down the Lee model, it is important to discover the extra neutral and charged Higgs bosons and measure their $CP$ properties and the flavor-changing decays. At the LHC with $\sqrt{s}=14\text{ }\text{ }\mathrm{TeV}$, this scenario is favored if there is significant suppression in the $b\overline{b}$ decay channel or any vector boson fusion, $\mathrm{V}+\mathrm{H}$ production channels. On the contrary, it will be disfavored if the signal strengths are standard-model--like more and more. It can be easily excluded at $(3--5)\ensuremath{\sigma}$ level with several ${\mathrm{fb}}^{\ensuremath{-}1}$ at future ${e}^{+}{e}^{\ensuremath{-}}$ colliders, via accurately measuring the Higgs boson production cross sections.

Method for the production of highly charged ions with polarized nuclei and zero total electron angular momentum

The capture of polarized electrons by H-like ions provides a method for polarizing the nuclei of He-like heavy ions with zero total electron angular momentum in storage rings for high-energy ions. A detailed analysis for $_{63}^{151}\mathrm{Eu}$ ions with nuclear spin $I=5/2$ predicts a nuclear polarization degree of about $47%$ already after one passage through a target containing $100%$ polarized electrons. Almost $50%$ of the polarized He-like ions are predicted to be in states with zero total electron angular momentum. Such ions were recently considered as the most promising candidates in experiments at storage rings for the search for violations of the fundamental symmetries and for a nuclear and an electron electric dipole moment.

Experimental search for the electron electric dipole moment with laser cooled francium atoms

A laser cooled heavy atom is one of the candidates to search for the permanent electric dipole moment (EDM) of the electron due to the enhancement mechanism and its long coherence time. The laser cooled francium (Fr) factory has been constructed to perform the electron EDM search at the Cyclotron and Radioisotope Center, Tohoku University. The present status of Fr production and the EDM measurement system is presented.

Electroweak baryogenesis, electric dipole moments, and Higgs diphoton decays

We study the viability of electroweak baryogenesis in a two Higgs doublet model scenario augmented by vector-like, electroweakly interacting fermions. Considering a limited, but illustrative region of the model parameter space, we obtain the observed cosmic baryon asymmetry while satisfying present constraints from the non-observation of the permanent electric dipole moment (EDM) of the electron and the combined ATLAS and CMS result for the Higgs boson diphoton decay rate. The observation of a non-zero electron EDM in a next generation experiment and/or the observation of an excess (over the Standard Model) of Higgs to diphoton events with the 14 TeV LHC run or a future $e^+e^-$ collider would be consistent with generation of the observed baryon asymmetry in this scenario.

Time-reversal symmetry violation in molecules induced by nuclear magnetic quadrupole moments.

Recent measurements in paramagnetic molecules improved the limit on the electron electric dipole moment (EDM) by an order of magnitude. Time-reversal (T) and parity (P) symmetry violation in molecules may also come from their nuclei. We point out that nuclear T, P-odd effects are amplified in paramagnetic molecules containing deformed nuclei, where the primary effects arise from the T, P-odd nuclear magnetic quadrupole moment (MQM). We perform calculations of T, P-odd effects in the molecules TaN, ThO, ThF+, HfF+, YbF, HgF, and BaF induced by MQMs. We compare our results with those for the diamagnetic TlF molecule, where the T, P-odd effects are produced by the nuclear Schiff moment. We argue that measurements in molecules with MQMs may provide improved limits on the strength of T, P-odd nuclear forces, on the proton, neutron, and quark EDMs, on quark chromo-EDMs, and on the QCD θ term and CP-violating quark interactions.