Measurement Of Electric Dipole Moment Research Articles

Calculation of Some Low-Lying Electronic Excitations of Barium Monofluoride Using the Equation of Motion (EOM)-CC3 Method with an Effective Core Potential Approach.

Barium monofluoride (BaF) is a polar molecule of interest in measurements of the electron electric dipole moment. For this purpose, efforts are underway to investigate this molecule embedded within cryogenic matrices, e.g., in solid Ne. For a theoretical understanding of the electronic structure of such an embedded molecule, the need arises for efficient methods which are accurate but also able to handle a number of atoms which surround the molecule. The calculation for gas-phase BaF can be reduced to involve only outer electrons by representing the inner core of Ba with a pseudopotential, while carrying out a non-relativistic calculation with an appropriate basis set. Thus, the method is effectively at a scalar-relativistic level. In this work, we demonstrate to which extent this can be achieved using coupled-cluster methods to deal with electron correlation. As a test case, the SrF(X2Σ+→B2Σ+) transition is investigated, and excellent accuracy is obtained with the EOM-CC3 method. For the BaF(X2Σ+→A'2Δ, X2Σ+→A2Π, X2Σ+→B2Σ+) transitions, various coupled-cluster approaches are compared with very good agreement for EOM-CC3 with experimentally derived spectroscopic parameters, at the level of tens of cm-1. An exception is the excitation to the A'2Δ state, for which the energy is overestimated by 230cm-1. The poor convergence behavior for this particular state is demonstrated by providing results from calculations with basis sets of n = 3, 4, 5)-zeta quality. The calculated excitation energy for the B2Σ+ state agrees better with a deperturbation analysis than with the effective spectroscopic value, with a difference of 120cm-1.

A survey of nuclear quadrupole deformation in order to estimate the nuclear MQM and its relative contribution to the atomic EDM

Measurement of a non-zero permanent electric dipole moment (EDM) in fundamental particles, such as in an electron or a neutron, or in nuclei or atoms, can help us gain a handle on the sources of Charge-Parity (CP) violation, both in the Standard Model (SM) and beyond. The nuclear magnetic quadrupole moment (MQM), the central topic of this work, is also CP, P, and T violating. Nucleons and nuclei have a non-zero MQM from sources within the SM, but the nuclear MQM is dramatically enhanced if the nuclei are structurally quadrupole deformed. Multiple sources contribute to an atomic EDM namely: (i) nuclear EDM through its Schiff moment, which is enhanced by nuclear octupole deformation, (ii) CP violating interactions between the electrons and the nuclei, and (iii) the nuclear MQM that contributes to the atomic EDM in atoms with an unpaired valence electron. Our survey of nuclear quadrupole deformation identified 48 isotopes as ideal systems in which to search for a CP violating EDM via their enhanced nuclear MQM. Of these candidates, 223,225\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{223,225}$$\\end{document}Fr, 223\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{223}$$\\end{document}Ra, 223,225,227\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{223,225,227}$$\\end{document}Ac, 229\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{229}$$\\end{document}Th, and 229\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{229}$$\\end{document}Pa also have maximally enhanced nuclear Schiff moment contribution due to their octupole deformation. Laser cooling of the isotopes of Fr and Ra, among a few others, has already been demonstrated, making 223,225\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{223,225}$$\\end{document}Fr and 223\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{223}$$\\end{document}Ra some of the best systems in which to measure an EDM.

Determination of the Invariant Spin Axis in a COSY model using Bmad

The matter-antimatter asymmetry might be understood by investigating the EDM (Electric Dipole Moment) of elementary particles. A permanent EDM of a subatomic particle violates time reversal and parity symmetry at the same time and would be, with the currently achievable experimental accuracy, an indication for further CP violation than established in the SM (Standard Model of Particle Physics). The JEDI-Collaboration (Jülich Electric Dipole moment Investigations) in Jülich has performed a direct EDM measurement for deuterons with the so-called precursor experiments at the storage ring COSY (COoler SYnchrotron) by measuring the orientation of the ISA (Invariant Spin Axis). In order to interpret the measured data and to disentangle a potential EDM signal from systematic effects, spin tracking simulations in an accurate simulation model of COSY are needed. Therefore a model of COSY was implemented using the software library Bmad. Systematic effects were considered by including element misalignments, effective dipole shortening, longitudinal fields and steerer kicks. These effects rotate the ISA in addition to the EDM and have to be analyzed and understood. The most recent spin tracking results as well as the methods to find the ISA are presented in this paper.

Systematic errors arising from polarization imperfections in measurements of the electron's electric dipole moment

Systematic errors arising from polarization imperfections in measurements of the electron's electric dipole moment

Calculation of the local environment of a barium monofluoride molecule in a neon matrix

ABSTRACT The local environment of a barium monofluoride (BaF) molecule embedded in a neon matrix is studied theoretically. The energy of the BaF-Ne triatomic system is calculated with a scalar relativistic Hamiltonian, using coupled-cluster theory at the CCSD(T) level for 1625 positions of the Ne atom relative to the BaF molecule. The calculations are repeated with increasing basis sets (from double to quintuple zeta), and are extrapolated to estimate the complete-basis-set limit. Using the potential obtained from these calculations, it is determined that substituting a BaF molecule for ten Ne atoms is favoured compared to substitutions for other numbers of Ne atoms. The equilibrium position and orientation of the BaF molecule and the displacement of its nearby Ne neighbours are determined. The potential barriers that prevent the BaF molecule from migrating and rotating are calculated. These barriers are essential for the EDM 3 collaboration, which is using BaF molecules embedded in a noble-gas solid to perform a precision measurement of the electron electric dipole moment.

Electroweak baryogenesis in the three-loop neutrino mass model with dark matter

Baryon asymmetry of the Universe is evaluated in the model originally proposed in Phys. Rev. Lett. 102 (2009) 051805, where Majorana masses of neutrinos are generated via three-loop diagrams composed of additional scalar bosons including the dark matter candidate which is odd under an unbroken $Z_2$ symmetry. In order for the model to include multiple CP-violating phases, we do not impose the softly broken $Z_2$ symmetry imposed in the original model to avoid the flavor-changing neutral current at tree level. Instead, for simplicity, we assume the flavor alignment structure in the Yukawa interactions. We also simply assume the alignment structure in the Higgs potential so that the Higgs couplings coincide with those in the SM at tree level. Under these phenomenological simplifications, the model still contains multiple CP-violating phases. By using destructive interferences among them, it is compatible with the stringent constraint from the electric dipole moment measurements to generate the observed baryon asymmetry along with the scenario of electroweak baryogenesis. We show a benchmark scenario which can explain neutrino mass, dark matter and baryon asymmetry of the universe simultaneously and can satisfy all the other available experimental data. Some phenomenological predictions of the model are also discussed.

Calculation of the local environment of a barium monofluoride molecule in an argon matrix: a step towards using matrix-isolated BaF for determining the electron electric dipole moment

The local environment of a barium monofluoride (BaF) molecule embedded in an argon matrix is calculated. A substitution of a BaF molecule for four Ar atoms is found to be strongly favoured compared to substitutions for other numbers of Ar atoms. The equilibrium positions of the BaF molecule and its nearby Ar neighbours are found by minimising the total energy. The potential barrier that prevents the migration of the BaF molecule within the solid and the barrier that prevents its rotation are calculated. At the cryogenic temperatures used by the EDM collaboration, these barriers are sufficiently large to fix the position and orientation of the molecule. Knowledge of the local environment of matrix-isolated BaF molecules is essential for the EDM collaboration, which is using them in a precision measurement of the electron electric dipole moment.

The scalar singlet extension of the Standard Model: gravitational waves versus baryogenesis

We study the possible gravitational wave signal and the viability of baryogenesis arising from the electroweak phase transition in an extension of the Standard Model (SM) by a scalar singlet field without a ℤ2 symmetry. We first analyze the velocity of the expanding true-vacuum bubbles during the phase transition, confirming our previous finding in the unbroken ℤ2 symmetry scenario, where the bubble wall velocity can be computed from first principles only for weak transitions with strength parameters α ≲ 0.05, and the Chapman-Jouguet velocity defines the maximum velocity for which the wall is stopped by the friction from the plasma. We further provide an analytical approximation to the wall velocity in the general scalar singlet scenario without ℤ2 symmetry and test it against the results of a detailed calculation, finding good agreement. We show that in the singlet scenario with a spontaneously broken ℤ2 symmetry, the phase transition is always weak and we see no hope for baryogenesis. In contrast, in the case with explicit ℤ2 breaking there is a region of the parameter space producing a promising baryon yield in the presence of CP violating interactions via an effective operator involving the singlet scalar and the SM top quarks. Yet, we find that this region yields unobservable gravitational waves. Finally, we show that the promising region for baryogenesis in this model may be fully tested by direct searches for singlet-like scalars in di-boson final states at the HL-LHC, combined with present and future measurements of the electron electric dipole moment.

Probing new physics in the vector-like lepton model by lepton electric dipole moments

We examine the lepton dipole moments in an extension of the Standard Model (SM), which contains vector-like leptons that couple only to the second-generation SM leptons. The model naturally leads to sizable contributions to the muon g − 2 and the muon electric dipole moment (EDM). One feature of this model is that a sizable electron EDM is also induced at the two-loop level due to the existence of new vector-like leptons in the loops. We find parameter regions that can explain the muon g − 2 anomaly and are also consistent with the experimental constraints coming from the electron EDM and the Higgs decay h → μ+μ−. The generated EDMs can be as large as mathcal{O} (10−22)e∙cm for the muon and mathcal{O} (10−30)e∙cm for the electron, respectively, which can be probed in future experiments for the EDM measurements.

Approaches to high-density storage experiments with in-situ production and detection of ultracold neutrons

Low counting statistics is one of the most important challenges in modern experiments with ultracold neutrons (UCN). UCN densities in superthermal sources based on superfluid helium are normally much higher than those after UCN delivery to ex-situ volumes. Therefore, and due to the vanishing neutron absorption of 4He, storage-based experiments performed in-situ promise significant sensitivity gains. Scalable measurements offer a promising path to simultaneously address the inefficient use of cold neutron beams as precursors for UCN production in 4He, by recuperating the unused beam fraction, and confront the practical challenges of large-scale UCN infrastructure. We suggest strategies for the development of modular cryogenic cells, propose a novel approach for in-situ UCN detection, and discuss the ultimate statistical reach of such a multiplexed experiment for measuring the neutron’s permanent electric dipole moment (EDM). While dedicated research and development are needed to evaluate the feasibility for many requirements, a neutron EDM measurement with sensitivity well beyond 10 − 28 e cm seems possible. Such an experiment could be pursued at any compatible cold neutron beamline, e.g., at the Institut Laue–Langevin, or later using the ANNI facility or large beam port (LBP) at the European Spallation Source.

Accurate calculation of the interaction of a barium monofluoride molecule with an argon atom: A step towards using matrix isolation of BaF for determining the electron electric dipole moment

Calculations of the BaF–Ar triatomic system are performed with a relativistic Hamiltonian and coupled cluster theory at the CCSD(T) level for 1386 positions of the Ar atom relative to the BaF molecule. Calculations are repeated with increasing basis sets (double-, triple-, quadruple- and quintuple-zeta), and these are extrapolated to estimate the complete-basis-set limit. The resulting energies provide a potential energy for the interaction of an Ar atom with a BaF molecule. A fit is presented that parametrizes this potential. This work is needed for an understanding of the position, modes of motion and energy shifts of BaF isolated in an Ar matrix. This understanding will guide the EDM3 collaboration in its pursuit of a precision measurement of the electron electric dipole moment using BaF isolated in a cryogenic Ar matrix.

Electric dipole moment of charged particles using storage rings

The Standard Model (SM) of Particle Physics cannot explain the matter-antimatter asymmetry in the Universe. Especially, new sources of CP-violation are necessary, and this is why physics beyond the SM is being explored. The search for permanent Electric Dipole Moments (EDMs) of elementary particles has the potential to provide a powerful tool to discover new sources of CP-violation. Finding an EDM would be a convincing indication for physics beyond the SM. Moreover, a rotating polarized beam used in EDM searches is sensitive to oscillating EDM caused by axions or axion-like particles (ALPs), the candidates for the dark matter. Storage rings are promising devices to measure EDMs of charged particles by observing the effect of the EDM on the spin motion in the ring. The Cooler Synchrotron COSY at the Forschungszentrum Jülich provides polarized protons and deuterons with momenta up to 3.7 GeV/c and it constitutes an suitable testing ground and starting point for an experimental program to search for EDMs of charged particles. This report provides an overview of the current status of the JEDI project for the first direct measurement of the deuteron EDM at COSY. The analysis is currently ongoing. Due to the complexity of storage rings, this study combines high precision measurements and thorough understanding of the systematic uncertainties involved.

Electronic Configuration Assignments for UO from Electric Dipole Moment Measurements.

Diatomic UO has more than 48 bound states within 10000 cm-1 of the ground state. This electronic state congestion has been attributed to interleaved states from the electronic configurations U2+(5f37s)O2- and U2+(5f27s2)O2-, respectively. Ligand field theory predicts that each electronic configuration will exhibit states with distinguishable, characteristic vibrational and rotational constants. However, vibronic state mixing modifies the observed vibration-rotation constants, leading to uncertainty in the configurational assignments. The permanent electric dipole moment (μe) of an electronic state should also manifest a value that is characteristic of the parent electronic configuration. μe and other electrostatic and magnetostatic properties should be less influenced by the vibronic state mixing, providing more robust indicators for configurational assignments. In the present study, we have measured the μe values for four electronic states of UO. The results clearly demonstrate that the ground state (X(1)4) and the first electronically excited state ((2)4) are derived from the U2+(5f37s)O2- and U2+(5f27s2)O2- configurations, respectively.

Difference of measured proton and He3 EDMs: a reduced systematics test of T-reversal invariance

The upper limit on (time reversal symmetry T-violating) permanent hadron electric dipole moments (EDMs) is the PSI neutron EDM value; dn = (0.0 ± 1.1stat ± 0.2sys × 10-26) e cm. This paper describes an experiment to be performed at a BNL-proposed CLIP project which is to be capable of producing intense polarized beams of protons, p, helions (He3 nuclei), h, and other isotopes. The EDM prototype ring PTR (proposed at COSY Lab, Juelich) is expected to measure individual particle EDMs (for example EDM_p for the proton) using simultaneous counter-rotating polarized proton beams, with statistical error ±10-30e.cm after one year running time, four orders of magnitude less than the PSI neutron EDM upper limit, and with comparable systematic error. A composite particle, the helion faces T-symmetry constraints more challenging than the proton. Any measurably large value of Δ= EDM h - EDM p , the difference of helion and proton EDMs, would represent BSM physics. The plan is to replicate PTR at BNL. The dominant systematic error would be canceled two ways, both made possible by phase-locking “doubly-magic” 38.6 MeV proton and 39.2 MeV helion spin tunes. This stabilizes their MDM-induced in-plane precessions, without affecting their EDM-induced out-of-plane precessions. The dominant systematic error would therefore cancel in the meaurement of Δ in a fixed field configuration. Another systematic error cancellation will come from averaging runs for which both magnetic field and beam circulation directions are reversed. Precise magnetic field reversal is made possible by the reproducible absolute frequency phase-locking over long runs to eliminate the need for (impractically precise) magnetic field measurement. Risk of EDM measurement failure is discussed in a final appendix.

Precision measurement and suppression of low-frequency noise in a current source with double-resonance alignment magnetometers

Low-noise high-stability current sources have essential applications such as neutron electric dipole moment measurement and high-stability magnetometers. Previous studies mainly focused on frequency noise above 0.1 Hz while less on the low-frequency noise/drift. We use double resonance alignment magnetometers (DRAMs) to measure and suppress the low-frequency noise of a homemade current source (CS) board. The CS board noise level is suppressed by about 10 times in the range of 0.001–0.1 Hz and is reduced to at 0.001 Hz. The relative stability of CS board can reach 2.2 × 10–8. In addition, the DRAM shows a better resolution and accuracy than a commercial 7.5-digit multimeter when measuring our homemade CS board. Further, by combining the DRAM with a double resonance orientation magnetometer, we may realize a low-noise CS in the 0.001–1000 Hz range.

Mapping of the magnetic field to correct systematic effects in a neutron electric dipole moment experiment

Experiments dedicated to the measurement of the electric dipole moment of the neutron require outstanding control of the magnetic field uniformity. The neutron electric dipole moment (nEDM) experiment at the Paul Scherrer Institute uses a 199Hg co-magnetometer to precisely monitor magnetic field variations. This co-magnetometer, in the presence of field non-uniformity, is responsible for the largest systematic effect of this measurement. To evaluate and correct that effect, offline measurements of the field non-uniformity were performed during mapping campaigns in 2013, 2014 and 2017. We present the results of these campaigns, and the improvement the correction of this effect brings to the neutron electric dipole moment measurement.

Gravitational wave and electroweak baryogenesis with two Higgs doublet models

We study stochastic gravitational wave production and baryon number generation at electroweak phase transition with the two Higgs doublet models. The produced stochastic gravitational wave during the strongly first-order phase transition can be probed by future space-based interferometers. The nonlocal electroweak baryogenesis cannot address the observed Baryon asymmetry of the Universe successfully in the strongly first-order phase transition parameter spaces due to the CP violation phase is severely bounded by the electron electric dipole moment measurement ACMEII.

Improved Indirect Limits on Muon Electric Dipole Moment.

Given current discrepancy in muon g-2 and future dedicated efforts to measure muon electric dipole moment (EDM) d_{μ}, we assess the indirect constraints imposed on d_{μ} by the EDM measurements performed with heavy atoms and molecules. We notice that the dominant muon EDM effect arises via the muon-loop induced "light-by-light" CP-odd amplitude ∝BE^{3}, and in the vicinity of a large nucleus the corresponding parameter of expansion can be significant, eE_{nucl}/m_{μ}^{2}∼0.04. We compute the d_{μ}-induced Schiff moment of the ^{199}Hg nucleus, and the linear combination of d_{e} and semileptonic C_{S} operator (dominant in this case) that determine the CP-odd effects in the ThO molecule. The results, d_{μ}(^{199}Hg)<6×10^{-20} e cm and d_{μ}(ThO)<2×10^{-20} e cm, constitute approximately threefold and ninefold improvements over the limits on d_{μ} extracted from the Brookhaven National Laboratory muon beam experiment.

Spectroscopy on the electron-electric-dipole-moment–sensitive states of ThF+

An excellent candidate molecule for the measurement of the electron's electric dipole moment (eEDM) is thorium monofluoride (ThF$^+$) because the eEDM-sensitive state, $^3\Delta_1$, is the electronic ground state, and thus is immune to decoherence from spontaneous decay. We perform spectroscopy on $X\,^3\Delta_1$ to extract three spectroscopic constants crucial to the eEDM experiment: the hyperfine coupling constant, the molecular frame electric dipole moment, and the magnetic $g$-factor. To understand the impact of thermal blackbody radiation on the vibrational ground state, we study the lifetime of the first excited vibrational manifold of $X\,^3\Delta_1$. We perform ab initio calculations, compare them to our results, and discuss prospects for using ThF$^+$ in a new eEDM experiment at JILA.

Normal Mode Analysis, Electronic Descriptors, NLO Properties 8 Molecular Docking of "Butein, 2',3,4,4'- Tetrahydroxychalcone: A DFT approach"

Study of modern medicine is a flourishing field with activity revolving around the identification, characterization and assessment of therapeutic potential of phytochemicals in various disease conditions. Chalconoids, being prominently present in various medicinal herbs are being widely studied to unravel the molecular mechanisms associated with their effects. This paper describes the molecular structure of well known compound “(Butein, 2',3,4,4'- Tetrahydroxychalcone [C15H12O5]”, which has been optimized and its structural parameters have been calculated by DFT/B3LYP method using 6-311++G(d,p) basis set. The fundamental vibrational wavenumbers and their intensities were calculated and a good agreement between the observed FTIR spectrum and scaled calculated wavenumbers has been achieved. The electronic properties of the compound are explained using HOMO-LUMO and MEPS descriptors. The Non-Linear Optical parameters (NLO) are discussed using electrical parameters like electric dipole moment, molecular polarizability and hyperpolarizability measurements. We have done the molecular docking analysis also, in order to get a better perception into its observed physiological effects which are a prerequisite for determining its therapeutic potential. We hereby report a strong interaction of butein with the protein 1OG6, an enzyme of cytochrome P450 series designated CYP2C9 which is intricately involved in oxidative metabolic pathways. This provides a plausible mechanism for anti-oxidant properties of butein.