Electron Electric Dipole Moment Research Articles

The role of QED effects in transition energies of heavy-atom alkaline earth monofluoride molecules: A theoretical study of Ba+, BaF, RaF, and E120F.

Heavy-atom alkaline earth monofluoride molecules are considered as prospective systems to study spatial parity or spatial parity and time-reversal symmetry violating effects such as the nuclear anapole moment or the electron electric dipole moment. A comprehensive and highly accurate theoretical study of the electronic structure properties and transition energies in such systems can simplify the preparation and interpretation of the experiments. However, almost no attempts to calculate quantum electrodynamics (QED) effects' contribution into characteristics of these neutral heavy-atom molecules have been performed. Recently, we have formulated and implemented such an approach to calculate QED contributions to transition energies of molecules [L. V. Skripnikov, J. Chem. Phys. 154, 201101 (2021)]. In this paper, we perform a benchmark theoretical study of the transition energies in the Ba+ cation and BaF molecule. The deviation of the calculated values from the experimental ones is of the order 10 cm-1 and is more than an order of magnitude better than the "chemical accuracy," 350 cm-1. The achievement of such an agreement has been provided, in particular, by the inclusion of the QED effects. The latter appeared to be not less important than the high-order correlation effects beyond the coupled cluster with single, double, and perturbative triple cluster amplitude level. We compare the role of QED effects for transition energies with heavier molecules-RaF and E120F, where E120 is the superheavy Z = 120 homologof Ra.

Electron EDM arising from modulus \u03c4 in the supersymmetric modular invariant flavor models

The electric dipole moment (EDM) of electron is studied in the supersymmetric A4 modular invariant theory of flavors with CP invariance. The CP symmetry of the lepton sector is broken by fixing the modulus τ. Lepton mass matrices are completely consistent with observed lepton masses and mixing angles in our model. In this framework, a fixed τ also causes the CP violation in the soft SUSY breaking terms. The electron EDM arises from the CP non-conserved soft SUSY breaking terms. The experimental upper bound of the electron EDM excludes the SUSY mass scale below 4–6 TeV depending on five cases of the lepton mass matrices. In order to see the effect of CP phase of the modulus τ, we examine the correlation between the electron EDM and the decay rate of the μ → eγ decay, which is also predicted by the soft SUSY breaking terms. The correlations are clearly predicted in contrast to models of the conventional flavor symmetry. The branching ratio is approximately proportional to the square of |de/e|. The SUSY mass scale will be constrained by the future sensitivity of the electron EDM, |de/e| ≃ 10−30 cm. Indeed, it could probe the SUSY mass range of 10–20 TeV in our model. Thus, the electron EDM provides a severe test of the CP violation via the modulus τ in the supersymmetric modular invariant theory of flavors.

Supersymmetric alignment models for (g \u2212 2)\u03bc

Hierarchical masses of quarks and leptons are addressed by imposing horizontal symmetries. In supersymmetric Standard Models, the same symmetries play a role in suppressing flavor violating processes induced by supersymmetric particles. Combining the idea of spontaneous CP violation to control contributions to electric dipole moments (EDMs), the mass scale of supersymmetric particles can be lowered. We present supersymmetric models with U(1) horizontal symmetries and discuss CP and flavor constraints. Models with two U(1) symmetries are found to give a viable solution to the muon g − 2 anomaly. Interestingly, the parameter space to explain the anomaly will be probed by future electron EDM experiments.

Quantum sensing of the electron electric dipole moment using ultracold entangled Fr atoms

We propose a method to measure the electron electric dipole moment (eEDM) using ultracold entangled francium (Fr) atoms trapped in an optical lattice, yielding an uncertainty below the standard quantum limit. Among the alkali atoms, Fr offers the largest enhancement factor to the eEDM. With a Fr based experiment, quantum sensing using quantum entangled states could enable a search for the eEDM at a level below 10−30 ecm. We estimate statistical and systematic errors attached to the proposed measurement scheme based on this quantum sensing technique. A successful quantum sensing of the eEDM could enable the exploration of new physics beyond the standard model of particle physics.

Formula omitted]-odd Faraday rotation in intracavity absorption spectroscopy with particle beam as a possible way to improve the sensitivity of the search for the time reflection noninvariant effects in nature

Possible experiments on the observation of the P,T - odd Faraday effect (rotation of polarization plane for the light, propagating through a medium in the presence of an external electric field, P - is the space inversion, T - is the time reflection) caused by the electron electric dipole moment in atoms and molecules, are discussed theoretically. An observation is assumed to be performed on the basis of modern intra-cavity absorption spectroscopy (ICAS) combined with atomic (molecular) beam techniques. The P,T - odd optical rotation is due to the linear Stark splitting of atomic or molecular levels. This leads to the difference between the refractive indexes for the right and left circularly polarized photons.

Spontaneous CP violation and horizontal symmetry in the MSSM: toward lepton flavor naturalness

We study the contributions of supersymmetric models with a U(1) horizontal symmetry and only spontaneous CP breaking to various lepton flavor observables, such as μ → eγ and the electron electric dipole moment. We show that both a horizontal symmetry and a lack of explicit CP violation can alleviate the existing bounds from such observables. The undetermined mathcal{O} (1) coefficients in such mass matrix models muddle the interpretation of the bounds from various flavor observables. To overcome this, we define a new fine-tuning measure for different observables in such setups. This allows us to study how naturally the observed IR flavor observables can emerge from a given mass matrix model. We use our flavor-naturalness measure in study of our supersymmetric models and quantify the degree of fine tuning required by the bounds from various lepton flavor observables at each mass scale of sleptons, neutralinos, and charginos.

Radiative lepton mass and muon g \u2212 2 with suppressed lepton flavor and CP violations

The recent experimental status, including the confirmation of the muon g − 2 anomaly at Fermilab, indicates a Beyond Standard Model (BSM) satisfying the following properties: 1) it enhances the g − 2 2) suppresses flavor violations, such as μ → eγ, 3) suppresses CP violations, such as the electron electric dipole moment (EDM). In this letter, I show that the eigenbasis of the mass matrix and higher dimensional photon operators can be automatically aligned if the masses of heavy leptons are generated radiatively together with the g − 2. As a result, the muon g − 2 is enhanced but the EDM of the electron and μ → eγ rate are naturally suppressed. Phenomenology and applications of the mechanism to the B-physics anomalies are argued.

Interaction potentials, electric moments, polarizabilities, and chemical reactions of YbCu, YbAg, and YbAu molecules

Ultracold YbAg molecules have been recently proposed as promising candidates for electron electric dipole moment searches Verma et al (2020 Phys. Rev. Lett. 125 153201). Here, we calculate potential energy curves, permanent electric dipole and quadrupole moments, and static electric dipole polarizabilities for the YbCu, YbAg, and YbAu molecules in their ground electronic states. We use the coupled cluster method restricted to single, double, and noniterative triple excitations with large Gaussian basis sets, while the scalar relativistic effects are included within the small-core energy-consistent pseudopotentials. We find that the studied molecules are relatively strongly bound with the well depths of 5708 cm−1, 5253 cm−1, and 13349 cm−1 and equilibrium distances of 5.50 bohr, 5.79 bohr, and 5.55 bohr for YbCu, YbAg, and YbAu, respectively. They have large permanent electric dipole moments of 3.2D, 3.3D, and 5.3D at equilibrium distances, respectively. We also calculate equilibrium geometries and energies of corresponding trimers. The studied molecules are chemically reactive unless they are segregated in an optical lattice or shielded with external fields. The investigated molecules may find application in ultracold controlled chemistry, dipolar many-body physics, or precision measurement experiments.

Calculations of time-reversal-symmetry-violation sensitivity parameters based on analytic relativistic coupled-cluster gradient theory

We develop an analytic-gradient based method for relativistic coupled-cluster calculations of effective electric field, $\mathcal{E}_{\text{eff}}$, with improved efficiency and robustness over the previous state of the art. The enhanced capability to calculate this time-reversal symmetry violation sensitivity parameter enables efficient screening of candidate molecules for the electron electric dipole moment (eEDM) search. As examples, the |$\mathcal{E}_{\text{eff}}$| values of metal methoxides including BaOCH$_3$, YbOCH$_3$, and RaOCH$_3$ are shown to be as large as those of the corresponding fluorides and hydroxides, which supports the recent proposal of using these symmetric-top molecules to improve the sensitivity of eEDM measurements. The computational results also show that molecules containing late actinide elements, NoF, NoOH, LrO, and LrOH$^+$, exhibit particularly large |$\mathcal{E}_{\text{eff}}$| values of around 200 GV/cm.

An ultracold molecular beam for testing fundamental physics

We use two-dimensional transverse laser cooling to produce an ultracold beam of YbF molecules. Through experiments and numerical simulations, we study how the cooling is influenced by the polarization configuration, laser intensity, laser detuning and applied magnetic field. The ultracold part of the beam contains more than 2 × 105 molecules per shot and has a temperature below 200 μK, and the cooling yields a 300-fold increase in the brightness of the beam. The method can improve the precision of experiments that use molecules to test fundamental physics. In particular, the beam is suitable for measuring the electron electric dipole moment with a statistical precision better than 10−30 e cm.

Electric-field-dependent g factor for the ground state of lead monofluoride, PbF

The electric-field-dependent $g$ factor and the electron electric dipole moment (eEDM)-induced Stark splittings for the lowest rotational levels of $^{207,208}$PbF are calculated. Observed and calculated Zeeman shifts for $^{207}$PbF are found to be in very good agreement. It is shown that the $^{207}$PbF hyperfine sublevels provide a promising system for the eEDM search and related experiments.

CP violation from charged Higgs bosons in the three Higgs doublet model

We demonstrate a new type of cancellation of contributions to the electron and neutron electric dipole moments (EDMs) that occurs in three Higgs doublet models (3HDMs) when CP violation appears in the charged Higgs sector. The cancellation becomes exact when the two physical charged Higgs bosons in the model are degenerate in mass. Depending on the model parameters, degeneracies at the 10% level are however sufficient to evade current bounds on the electron and neutron EDMs. We demonstrate that viable parameter space remains with both charged Higgs bosons lighter than 500 GeV and large CP-violating phases while also satisfying theoretical constraints from perturbativity and experimental ones from overline{B} → Xsγ and direct searches.

Domain walls and CP violation with left right supersymmetry: implications for leptogenesis and electron EDM

Low scale leptogenesis scenarios are difficult to verify due to our inability to relate the parameters involved in the early universe processes with the low energy or collider observables. Here we show that one can in principle relate the parameters giving rise to the transient CP violating phase involved in leptogenesis with those that can be deduced from the observation of electric dipole moment (EDM) of the electron. We work out the details of this in the context of the left right symmetric supersymmetric model (LRSUSY) which provides a strong connection between such parameters. In particular, we show that baryon asymmetry requirements imply the scale MB−L of U(1)B−L symmetry breaking to be larger than 104.5 GeV. Moreover the scale MR of SU(2)R symmetry breaking is tightly constrained to lie in a narrow band significantly below {M}_{B-L}^2/{M}_{EW} . These are the most stringent constraints on the parameter space of LRSUSY model being considered.

Probing dark sector CP violation with electric dipole moments and colliders

We study the experimental constraints on dark sector CP violation that enters the visible sector through a Higgs portal coupling $H^{\dagger} H Z^{\prime}_{\mu\nu} \widetilde Z^{\prime \mu\nu}$, where the $Z^{\prime}$ is from a new U(1) gauge symmetry which is assumed to couple to lepton number. We compute explicitly the leading two-loop contribution of this effective operator to the electron electric dipole moment (EDM) and show that the resulting constraints are comparable to those from direct $Z^{\prime}$ searches at electron-positron colliders when the effective operator is generated at tree level. We also examine an explicit UV completion for this effective operator that was first introduced to achieve electroweak baryogenesis and show that collider constraints from $B$-factories already exclude viable baryogenesis for $Z^{\prime}$ masses below 10 GeV, and that future electron-positron Higgs factories will exclude viable baryogenesis for $Z^{\prime}$ masses up to the $e^+e^-$ center-of-mass energy if anticipated luminosities are achieved. For higher $Z^{\prime}$ masses, the full viable baryogenesis parameter space lies within six orders of magnitude of the current upper bound on the electron EDM.

Axion-mediated electron-electron interaction in ytterbium monohydroxide molecule.

The YbOH triatomic molecule can be efficiently used to measure the electron electric dipole moment, which violates time-reversal (T) and spatial parity (P) symmetries of fundamental interactions [Kozyryev and Hutzler, Phys. Rev. Lett. 119, 133002 (2017)]. We study another mechanism of the T, P-violation in the YbOH molecule-the electron-electron interaction mediated by the low-mass axionlike particle. For this, we calculate the molecular constant that characterizes this interaction and use it to estimate the expected magnitude of the effect to be measured. It is shown that this molecular constant has the same order of magnitude as the corresponding molecular constant corresponding to the axion-mediated electron-nucleus interaction. According to our estimation, an experiment on YbOH will allow one to set updated laboratory constraints on the CP-violating electron-axion coupling constants.

Approaching meV level for transition energies in the radium monofluoride molecule RaF and radium cation Ra+ by including quantum-electrodynamics effects.

Highly accurate theoretical predictions of transition energies in the radium monofluoride molecule, 226RaF, and radium cation, 226Ra+, are reported. The considered transition X2Σ1/2 → A2Π1/2 in RaF is one of the main features of this molecule and can be used to laser-cool RaF for a subsequent measurement of the electron electric dipole moment. For molecular and atomic predictions, we go beyond the Dirac-Coulomb Hamiltonian and treat high-order electron correlation effects within the coupled cluster theory with the inclusion of quadruple and ever higher amplitudes. The effects of quantum electrodynamics (QED) are included non-perturbatively using the model QED operator that is now implemented for molecules. It is shown that the inclusion of the QED effects in molecular and atomic calculations is a key ingredient in resolving the discrepancy between the theoretical values obtained within the Dirac-Coulomb-Breit Hamiltonian and the experiment. The remaining deviation from the experimental values is within a few meV. This is more than an order of magnitude better than the "chemical accuracy," 1 kcal/mol = 43 meV, that is usually considered as a guiding thread in theoretical molecular physics.

Flavor and CP-violating Higgs sector in two Higgs doublet models with $$U(1)'$$

We investigate the role of a local $U(1)'$ symmetry for the problem of CP violation in the effective theory for two Higgs doublet models and its microscopic counterparts. First, in two Higgs doublet models with $U(1)'$, we show that the higher-dimensional operators in the scalar potential violate the CP symmetry with an interplay with the mixing mass parameter, giving rise to small mixings between CP-even and CP-odd scalars. Motivated by the $B$-meson anomalies in recent years, we take the flavored $U(1)'$ to be a benchmark model for specifying the flavor structure. Then, we calculate the electric dipole moment of electron (eEDM) at two loops due to the CP-violating higher-dimensional operators and identify the correlation between the masses of heavy Higgs bosons and the cutoff scale from the bound on eEDM. We also comment on the possibility of making an independent test of the CP violation in the collider searches for heavy Higgs bosons. Finally, we show how the obtained eEDM results in the effective theory can be used to constrain microscopic models with an explicit CP violation in the partially decoupled or dark sectors.

Electric dipole moments in the extended scotogenic models

Electric dipole moments (EDMs) of charged leptons arise from a new source of CP violation in the lepton sector. In this paper, we calculate the EDMs of the charged leptons in the minimal scotogenic model with two singlet fermions, and the models extended with one or two triplet fermions instead of the singlet fermions, taking into account the constraints of the neutrino oscillation data, the charged lepton flavor violation and perturbative unitarity bound for the Yukawa couplings. We show that the hybrid model with one singlet and one triplet fermions predicts an electron EDM larger than the other models in both normal and inverted neutrino mass hierarchy. We find some parameter space has already been ruled out by the current upper bound of the electron EDM and further parameter space can be explored by future experiments.

P,T−odd Faraday rotation in intracavity absorption spectroscopy with a molecular beam as a possible way to improve the sensitivity of the search for time-reflection-noninvariant effects in nature

The present constraint on the space parity ($\mathcal{P}$) and time reflection invariance ($\mathcal{T}$) violating electron electric dipole moment ($e$EDM) is based on the observation of the electron spin precession in an external electric field using the ThO molecule. We propose an alternative approach: observation of the $\mathcal{P}$,~$\mathcal{T}$-odd Faraday effect in an external electric field using the cavity-enhanced polarimetric scheme in combination with a molecular beam crossing the cavity. Our theoretical simulation of the proposed experiment with the PbF and ThO molecular beams shows that the present constraint on the $e$EDM in principle can be improved by a few orders of magnitude.

P, T -odd effects for the RaOH molecule in the excited vibrational state

Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. This makes it a promising candidate for experimental study of the $\mathcal{P}$,$\mathcal{T}$-violation. Previous studies concentrated on the calculations for different geometries without the averaging over the rovibrational wave function and stressed the possibility that the dependence of the $\mathcal{P}$, $\mathcal{T}$ parameters on the bond angle may significantly alter the observed value. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian. The potential surface is constructed based on the two-component relativistic CCSD(T) computation employing the generalized relativistic effective core potential (GRECP) for the Radium atom. The averaged values of the parameters $E_{\rm eff}$ and $E_s$ describing the sensitivity of the system to the electron electric dipole moment and the scalar-pseudoscalar nucleon-electron interaction are calculated and the value of $l$-doubling is obtained.