Scalar-pseudoscalar Interaction Research Articles

Hyperfine and P, T odd properties in BiO: comparison between coupled-cluster method and multi-reference perturbation method based on a Dirac Hamiltonian

Polar diatomic molecules are attractive in the search for the electron electric dipole moment (eEDM) and the scalar-pseudoscalar (S-PS) interaction, both of which violate time-reversal and parity symmetries. In this study, we examined the electronic ground state of BiO and evaluated the effective electric field (E eff) of eEDM and the W s coefficients of the S-PS interaction. BiO forms a complex chemical bond due to the open-shell configurations of Bi (6p) and O (2p). Consequently, we performed four-component relativistic calculations using complete-active-space second-order perturbation theory (CASPT2), as well as coupled-cluster singles and doubles (CCSD) and CCSD perturbative triples (CCSD(T)) methods. Our analysis revealed that BiO exhibited a multiconfigurational character, as the Hartree-Fock configuration accounted for only 68% of the reference wave function for CASPT2. Nevertheless, for the hyperfine coupling constant (A//), CCSD and CCSD(T) reproduced the experimental value better than CASPT2, indicating that CC methods can capture important excited configurations, rendering multireference treatment unnecessary. The deficiency of CASPT2 in reproducing A// could be attributed to the inadequate treatment of orbital relaxation effects. Our proposed values of E eff and W s for BiO (17 GV/cm and −36 kHz, respectively), derived at the CCSD level, were moderately large for the parity, time-odd experiment.

T,P -odd effects in the LuOH+ cation

The LuOH$^+$ cation is a promising system to search for manifestations of time reversal and spatial parity violation effects. Such effects in LuOH$^+$ induced by the electron electric dipole moment $e$EDM and the scalar-pseudoscalar interaction of the nucleus with electrons, characterized by $k_s$ constant, in LuOH$^+$ are studied. The enhancement factors, polarization in the external electric field, hyperfine interaction, rovibrational structure are calculated. The study is required for the experiment preparation and extraction of the eEDM and ks values from experimental data.

Molecular enhancement factors for the P,T -violating electric dipole moment of the electron in BaCH3 and YbCH3 symmetric top molecules

High-precision tests of fundamental symmetries are looking for the parity- ($\mathcal{P}$), time-reversal- ($\mathcal{T}$) violating electric dipole moment of the electron (eEDM) as proof of physics beyond the Standard Model. Particularly, in polyatomic molecules, the complex vibrational and rotational structure gives the possibility to reach high enhancement of the $\mathcal{P},\mathcal{T}$-odd effects in moderate electric fields, and with the possibility of increasing the statistical sensitivity by using laser cooling. In this work, we calculate the $\mathcal{P},\mathcal{T}$-odd molecular enhancement factor of the eEDM (${W}_{\mathrm{d}}$) and of the scalar-pseudoscalar interaction (${W}_{\mathrm{s}}$) necessary for the interpretation of future experiments on the promising candidates ${\mathrm{BaCH}}_{3}$ and ${\mathrm{YbCH}}_{3}$. We employ high-accuracy relativistic coupled cluster methods and systematically evaluate the uncertainties of our computational approach. Compared to other Ba- and Yb-containing molecules, ${\mathrm{BaCH}}_{3}$ and ${\mathrm{YbCH}}_{3}$ exhibit larger ${W}_{\mathrm{d}}$ and ${W}_{\mathrm{s}}$ associated to the increased covalent character of the $M$--C bond. The calculated values are $3.22\ifmmode\pm\else\textpm\fi{}0.12\ifmmode\times\else\texttimes\fi{}{10}^{24}\frac{h\text{Hz}}{e\text{cm}}$ and $13.80\ifmmode\pm\else\textpm\fi{}0.35\ifmmode\times\else\texttimes\fi{}{10}^{24}\frac{h\text{Hz}}{e\text{cm}}$ for ${W}_{\mathrm{d}}$, and $8.42\ifmmode\pm\else\textpm\fi{}0.29\phantom{\rule{4pt}{0ex}}h\mathrm{kHz}$ and $50.16\ifmmode\pm\else\textpm\fi{}1.27\phantom{\rule{4pt}{0ex}}h\mathrm{kHz}$ for ${W}_{\mathrm{s}}$, in ${\mathrm{BaCH}}_{3}$ and ${\mathrm{YbCH}}_{3}$, respectively. The robust, accurate, and cost-effective computational scheme reported in this work makes our results suitable for extracting the relevant fundamental properties from future measurements and also can be used to explore other polyatomic molecules sensitive to various violations of fundamental symmetries.

CP violating effects in 210Fr and prospects for new physics beyond the Standard Model

We report theoretical results of the electric dipole moment (EDM) of 210Fr which arises from the interaction of the EDM of an electron with the internal electric field in an atom and the scalar-pseudoscalar electron-nucleus interaction; the two dominant sources of CP violation in this atom. Employing the relativistic coupled-cluster theory, we evaluate the enhancement factors for these two CP violating interactions to an accuracy of about 3% and analyze the contributions of the many-body effects. These two quantities in combination with the projected sensitivity of the 210Fr EDM experiment provide constraints on new physics beyond the Standard Model. Particularly, we demonstrate that their precise values are necessary to account for the effect of the bottom quark in models in which the Higgs sector is augmented by nonstandard Yukawa interactions such as the two-Higgs doublet model.

Fierz-complete NJL model study. III. Emergence from quark-gluon dynamics

Our understanding of the dynamics and the phase structure of dense strong-interaction matter is to a large extent still built on the analysis of low-energy models, such as those of the Nambu-Jona-Lasinio-type. In this work, we analyze the emergence of the latter class of models at intermediate and low energy scales from fundamental quark-gluon interactions. To this end, we study the renormalization group flow of a Fierz-complete set of four-quark interactions and monitor their strength at finite temperature and quark chemical potential. At small quark chemical potential, we find that the scalar-pseudoscalar interaction channel is dynamically rendered most dominant by the gauge degrees of freedom, indicating the formation of a chiral condensate. Moreover, the inclusion of quark-gluon interactions leaves a significant imprint on the dynamics as measured by the curvature of the finite-temperature phase boundary which we find to be in accordance with lattice QCD results. At large quark chemical potential, we then observe that the dominance pattern of the four-quark couplings is changed by the underlying quark-gluon dynamics, without any fine-tuning of the four-quark couplings. In this regime, the scalar-pseudoscalar interaction channel becomes subleading and the dominance pattern suggests the formation of a chirally symmetric diquark condensate. In particular, our study confirms the importance of explicit $U_{\mathrm{A}}(1)$ breaking for the formation of this type of condensate at high densities.

Relativistic coupled-cluster study of diatomic metal-alkali-metal molecules for electron electric dipole moment searches

Recent improvements in experimental techniques for preparing ultracold molecules that contain alkali atoms (e.g. Li, Na, and K) have been reported. Based on these advances in ultracold molecules, new searches for the electric dipole moment of the electron and the scalar-pseudoscalar interaction can be proposed on such systems. We calculate the effective electric fields (Eeff) and the scalar-pseudoscalar coefficients (Ws) of SrA and HgA (A = Li, Na, and K) molecules at the Dirac–Fock (DF) and the relativistic coupled cluster (RCC) levels. We elaborate on the following points: (i) basis set dependence of the molecular properties in HgA, (ii) analysis of Eeff and Ws in SrA and HgA, and comparison with their fluoride and hydride counterparts, (iii) ratio of Ws to Eeff (Ws/Eeff) at the DF and the correlation RCC levels of theory.

Merits of heavy-heavy diatomic molecules for electron electric-dipole-moment searches

The electric dipole moment of the electron (eEDM) and the Scalar-PseudoScalar (S-PS) interaction are probes of new physics beyond the standard model of elementary particles, but experiments to observe them using atoms and molecules are still in progress. Molecules that have a large effective electric field (Eeff), S-PS coefficient (Ws), and permanent electric dipole moment (PDM) are in principle favorable candidates for such experiments, and hence, it is necessary to analyze these properties. In this work, we calculate Eeff, Ws, and PDM for Ra systems; RaF, RaX (X = Cl, Br, I, and At) and RaY (Y = Cu, Ag, and Au) using the Dirac-Fock and the relativistic coupled-cluster methods. We find that RaX and RaY have larger Eeff and Ws,Ra than RaF. We explain this finding by taking into consideration the large s-p mixing for RaX and RaY, similar to what we had done in our previous work using hydrides and fluorides (A. Sunaga et al., Phys. Rev. A 95, 012502 (2017)). We also discuss the suitability of RaX and RaY molecules for eEDM experiments from the viewpoint of their large PDM and small polarizing electric field (Epol).

RaH as a potential candidate for electron electric-dipole-moment searches

Diatomic polar molecules have been the focus of research in the recent past as candidates for electron electric dipole moment (eEDM), de, measurements. In the present work, we focus on RaH molecule and have calculated three of its properties (in the X2Σ+ state) the effective electric field (Eeff), the scalar-pseudoscalar (S-PS) interaction coefficient (Ws,A), and permanent electric dipole moment (PDM) that play crucial roles in probing fundamental symmetry violations. The calculations were based on the relativistic coupled-cluster singles and doubles (RCCSD) frame work. Our results for Eeff, Ws,A, and PDM are 80.31 GV/cm, 216.82 kHz, and 4.44 D respectively. In addition to possessing high magnitudes of Eeff and Ws,A, RaH also has a large PDM, which is a highly desirable criterion for eEDM experiments. The analysis of our results clearly indicates the spectacular role of electron correlation in enhancing their magnitudes ≈16% for PDM and ≈31% for Eeff and Ws,A. The ratio of Eeff to Ws,A for RaH is 89.56×1018e−1 cm−1. Based on our results and other experimental considerations, we propose RaH as a future candidate for experiments in this field.

Enhancement factors of parity- and time-reversal-violating effects for monofluorides

Heavy polar diatomic molecules are currently one of the leading candidates for probing physics beyond the Standard Model via studies of time-reversal (T) and parity (P) violations. In this work, we analyze the effective electric field (Eeff) that is required for determining the electron electric dipole moment (eEDM), and the scalar-pseudoscalar (S-PS) interaction constant (Ws), in group 12 and group 2 systems. We use a relativistic coupled cluster method for our calculations, and find that group 12 monofluorides have large Eeff and Ws (for example, the values of Eeff and Ws of CnF, the heaviest group 12 fluoride, are 662 GV/cm and 3360 kHz, respectively). The reason for this is the contraction of the valence s and p orbitals due to the weak screening effect of the outermost core's d electron. The calculations of Eeff and Ws show that their ratio, (Ws/Eeff), increases with Z. Based on these results, as well as experimental suitability, we propose SrF and CdF as new candidate molecules for experiment.

P,T -odd and magnetic hyperfine-interaction constants and excited-state lifetime for HfF+

Parity- and time-reversal-symmetry violating interaction constants required for the interpretation of a recent measurement (arXiv:1704.07928 [physics.atom-ph]) of corresponding symmetry violations in the $\Omega=1$ (${^3\Delta}_1$) science state of the HfF$^+$ molecular ion are reported. Using a relativistic four-component all-electron multi-reference configuration interaction model the nucleon-electron scalar-pseudoscalar interaction constant is determined as $W_S = 20.0$ [kHz]. An updated result for the electron electric-dipole-moment effective electric field of $|E_{\text{eff}}| = 22.7 \left[\frac{\rm GV}{\rm cm}\right]$ is obtained. Further results of relevance in the context of the search for leptonic charge-parity violation such as magnetic hyperfine interaction constants and electronic $G$-tensor for HfF$^+$ are presented.

Electron–nucleus scalar–pseudoscalar interaction in PbF: Z-vector study in the relativistic coupled-cluster framework

ABSTRACTThe scalar–pseudoscalar interaction constant of PbF in its ground state electronic configuration is calculated using the Z-vector method in the relativistic coupled-cluster framework. The precise calculated value is very important to set upper bound limit on -odd scalar–pseudoscalar interaction constant, ks, from the experimentally observed -odd frequency shift. Further, the ratio of the effective electric field to the scalar–pseudoscalar interaction constant is also calculated which is required to get an independent upper bound limit of electric dipole moment of electron, de, and ks and how these (de and ks) are interrelated is also presented here.

Scalar-pseudoscalar interaction in the francium atom

Fr atom can be successively used to search for the atomic permanent electric dipole moment (EDM) [Hyperfine Interactions 236, 53 (2015); Journal of Physics: Conference Series 691, 012017 (2016)]. It can be induced by the permanent electron EDM predicted by modern extensions of the standard model to be nonzero at the level accessible by the new generation of EDM experiments. We consider another mechanism of the atomic EDM generation in Fr. This is caused by the scalar-pseudoscalar nucleus-electron neutral current interaction with the dimensionless strength constant, $k_{T,P}$. Similar to the electron EDM this interaction violates both spatial parity and time-reversal symmetries and can also induce permanent atomic EDM. It was shown in [Phys. Rev. D 89, 056006 (2014)] that the scalar-pseudoscalar contribution to the atomic EDM can dominate over the direct contribution from the electron EDM within the standard model. We report high-accuracy combined all-electron and two-step relativistic coupled cluster treatment of the effect from the scalar-pseudoscalar interaction in the Fr atom. Up to the quadruple cluster amplitudes within the CCSDT(Q) method were included in correlation treatment. This calculation is required for the interpretation of the experimental data in terms of $k_{T,P}$. The resulted EDM of the Fr atom expressed in terms of $k_{T,P}$ is $d_{\rm Fr}= k_{T,P} \cdot 4.50\cdot10^{-18} e\cdot {\rm cm}$, where $e$ is the charge of the electron. The value of the ionization potential of the $^2S_{1/2}$ ground state of Fr calculated within the same methods is in a very good agreement with the experiment.

In search of discrete symmetry violations beyond the standard model: Thorium monoxide reloaded.

We present an updated electron electric dipole moment (EDM) effective electric field of Eeff= 75.2 GV/cm and 229Th magnetic hyperfine interaction constant A|| = -1266 MHz, the nucleon-electron scalar-pseudoscalar interaction constant WS = 106.0 kHz, and the molecule-frame static electric dipole moment D = -4.41 D for the Δ13 science state of ThO. The criticisms of the results from Fleig and Nayak [J. Mol. Spectrosc. 300, 16 (2014)] made in Skripnikov and Titov [J. Chem. Phys. 142, 024301 (2015)] are addressed and largely found to be unsubstantiated within the framework of the present approach. The present findings confirm the slightly relaxed constraints on relevant beyond-standard-model parameters, in particular the electron EDM, de, and the nucleon-electron scalar-pseudoscalar coupling constant, CS.

Relativistic coupled-cluster calculation of the electron-nucleus scalar-pseudoscalar interaction constant Ws in YbF

The scalar-pseudoscalar (S-PS) interaction, which has been predicted between the electrons and nuclei of atoms and molecules, violates parity- ($P$-) and time- ($T$-) reversal symmetries. The electric dipole moment of the electron (eEDM) and the S-PS interaction together give rise to an energy shift in paramagnetic polar molecules, which in principle can be measured. The determination of the S-PS interaction constant, ${k}_{s,A}$, for an atom $A$ could be a sensitive probe of physics beyond the standard model. The upper limit for it can be obtained by combining the results of the measured energy shift mentioned above and the accurate quantum chemical calculation of the S-PS coefficient, ${W}_{s,A}$. In this work, we use a method based on the four-component relativistic coupled-cluster singles and doubles (RCCSD) method to calculate this coefficient for YbF, one of the most promising candidates for the search of the eEDM and the S-PS interaction. We obtain ${W}_{s,\mathrm{Yb}}=\ensuremath{-}40.5\phantom{\rule{0.28em}{0ex}}(\mathrm{kHz})$ with an estimated error of less than 10% for YbF. We also calculate the effective electric field (${E}_{\mathrm{eff}}$), the molecular dipole moment, and the parallel component of the hyperfine coupling constant (${A}_{\ensuremath{\parallel}}$) by the RCCSD method. The discrepancies in the results of these calculations with those of accurate measurements are used to estimate the accuracy of our calculation of ${W}_{s,\mathrm{Yb}}$.

Ab initiostudy of radium monofluoride (RaF) as a candidate to search for parity- and time-and-parity–violation effects

Relativistic ab initio calculations have been performed to assess the suitability of RaF for experimental search of P- and T,P-violating interactions. The parameters of P- and T,P-odd terms of the spin-rotational Hamiltonian have been calculated for the ${^2}\Sigma$ electronic ground state of RaF molecule. They include the parameter $W_a$, which is critical in experimental search for nuclear anapole moment and the parameters $W_d$ and $W_{\rm SP}$ required to obtain restrictions on the electric dipole moment of the electron and T,P-odd scalar-pseudoscalar interactions, respectively. The parameter $X$ corresponding to the "volume effect" in the T,P$-$odd interaction of the $^{223}$Ra nuclear Schiff moment with electronic shells of RaF has also been computed. Spectroscopic and hyperfine structure constants for $^{223}$RaF and $^{223}$Ra$^+$ have been computed as well, demonstrating the accuracy of the methods employed.

SENSING HYPERFINE-STRUCTURE, ELECTROWEAK INTERACTION AND PARITY NON-CONSERVATION EFFECT IN HEAVY ATOMS AND NUCLEI: NEW NUCLEAR QED APPROACH

It is presented the new theoretical approach for sensing hyperfine structure parameters, scalar-pseudoscalar interaction constant and parity non-conservation effect in heavy atomic and nuclear systems, based on the combined QED perturbation theory formalism and relativistic nuclear mean-field theory. Results of estimating these constants in different heavy atoms and nuclei are presented.

Three-flavor Nambu–Jona-Lasinio model at finite isospin chemical potential

QCD at finite isospin chemical potential $\mu_{\text I}$ possesses a positively definite fermion determinant and the lattice simulation can be successfully performed. While the two-flavor effective models may be sufficient to describe the phenomenon of pion condensation, it is interesting to study the roles of the strangeness degree of freedom and the U$_{\rm A}(1)$ anomaly. In this paper, we present a systematic study of the three-flavor Nambu--Jona-Lasinio model with a Kobayashi-Maskawa-'t Hooft (KMT) term that mimics the U$_{\rm A}(1)$ anomaly at finite isospin chemical potential. In the mean-field approximation, the model predicts a phase transition from the vacuum to the pion superfluid phase, which takes place at $\mu_{\rm I}$ equal to the pion mass $m_\pi$. Due to the U$_{\rm A}(1)$ anomaly, the strangeness degree of freedom couples to the light quark degrees of freedom and the strange quark effective mass depends on the pion condensate. However, the strange quark condensate and the strange quark effective mass change slightly in the pion superfluid phase, which verifies the validity of the two-flavor models. The effective four-fermion interaction of the Kobayashi-Maskawa-'t Hooft term in the presence of the pion condensation is constructed. Due to the U$_{\rm A}(1)$ anomaly, the pion condensation generally induces scalar-pseudoscalar interaction. The Bethe-Salpeter equation for the mesonic excitations is established and the meson mass spectra are obtained at finite isospin chemical potential and temperature. Finally, the general expression for the topological susceptibility $\chi$ at finite isospin chemical potential $\mu_{\rm I}$ is derived. In contrast to the finite temperature effect which suppresses $\chi$, the isospin density effect leads to an enhancement of $\chi$.

Model independent analysis of B → $ K_2^{ * } $ (1430)μ + μ −decay

A detailed study of the impact of New Physics (NP) operators with different Lorentz structures, which are absent in the Standard Model Hamiltonian, on the B → $ K_2^{ * } $ (1430)μ + μ − decay is performed. In this context, the various observables such as branching ratio, forward-backward asymmetry of leptons, lepton polarization asymmetries and the helicity fractions of the final state K2(1430) meson have been studied. We have examined the effects of new vector-axial vector, scalar-pseudoscalar and tensor type interactions for this decay B → $ K_2^{ * } $ (1430)μ + μ − by using the constraints on different NP couplings which come from the Bs → μ+μ−, B → Xsμ+μ− and $ \overline B $ → $ \overline K $ ∗μ+μ− decays. It is found that the effects of V A, SP and T operators are significant on the zero position of AF B (q2) as well as on its magnitude. In addition to this these NP operators also give significant effects on the differential decay rate, lepton polarization asymmetries and helicities fractions of final state $ K_2^{ * } $ (1430) meson.

Search for a permanent electric-dipole moment using atomic indium

We propose indium (In) as a possible candidate for observing the permanent electric dipole moment (EDM) arising from the violations of parity (P) and time-reversal (T) symmetries. This atom has been laser cooled and therefore the measurement of its EDM has the potential of improving on the current best EDM limit for a paramagnetic atom which comes from thallium. We report the results of our calculations of the EDM enhancement factor due to the electron EDM and the ratio of the atomic EDM to the electron-nucleus scalar-pseudoscalar (S-PS) interaction coupling constant in In in the framework of the relativistic coupled cluster theory. It might be possible to get new limits for the electron EDM and the S-PS CP violating coupling constant by combining the results of our calculations with the measured value of the EDM of In when it is available. These limits could have important implications for the standard model (SM) of particle physics.

Multiconfiguration Dirac-Hartree-Fock calculations for the hyperfine-structure parameters and the scalar-pseudoscalar interaction constant of 133Cs

In this work we investigate the applicability of the multiconfiguration Dirac-Hartree-Fock (MCDHF) method for calculating parity and time reversal symmetry violations in many-electron atoms. As an example we show results from calculations of the scalar-pseudoscalar interaction constant for 133Cs. Calculated limits of this interaction constant are in a good agreement with other theories.