Parity-violating Effects Research Articles

Anisotropic flow: achievements, difficulties and expectations

Anisotropic flow measurements play a crucial role in understanding the physics and bulk properties of the system created in heavy-ion collisions. In this paper I briefly review the most important results obtained so far, recent developments in the analysis techniques and the interpretation of the results, and what should we expect next, both at RHIC and LHC. I also discuss event anisotropies sensitive to the strong parity violation effects.

Fermions in loop quantum cosmology and the role of parity

Fermions play a special role in homogeneous models of quantum cosmology because the exclusion principle prevents them from forming sizable matter contributions. They can thus describe the matter ingredients only truly microscopically and it is not possible to avoid strong quantum regimes by positing a large matter content. Moreover, possible parity-violating effects are important especially in loop quantum cosmology whose basic object is a difference equation for the wavefunction of the universe defined on a discrete space of triads. The two orientations of a triad are interchanged by a parity transformation, which leaves the difference equation invariant for ordinary matter. Here, we revisit and extend loop quantum cosmology by introducing fermions and the gravitational torsion they imply, which renders the parity issue non-trivial. A treatable locally rotationally symmetric Bianchi model is introduced which clearly shows the role of parity. General wavefunctions cannot be parity-even or odd, and parity-violating effects in matter influence the microscopic big bang transition which replaces the classical singularity in loop quantum cosmology.

SeOClI: A promising candidate for the detection of parity violation in chiral molecules

Parity violation (PV) effects at the Dirac-Hartree-Fock and Dirac-Kohn-Sham level of theory are presented for the chiral molecule SeOClI. The PV energy contribution to the $S$ enantiomer of SeOClI ranges between $\ensuremath{-}7.1$ and $\ensuremath{-}9.2\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$, depending on the level of theory applied. For the Se-O fundamental stretching mode, which lies within the $\mathrm{C}{\mathrm{O}}_{2}$ laser frequency range, we obtain PV energy differences of $110\phantom{\rule{0.3em}{0ex}}\mathrm{mHz}$ between the two enantiomers, which is twice as large compared to the previously investigated C-F stretching mode of CHFBrI.

High-Resolution Spectroscopic Studies and Theory of Parity Violation in Chiral Molecules

We review the high-resolution spectroscopic approach toward the study of intramolecular dynamics, emphasizing molecular parity violation. Theoretical work in the past decade has shown that parity-violating potentials in chiral molecules are much larger (typically one to two orders of magnitude) than anticipated on the basis of older theories. This makes experimental approaches toward small molecular parity-violating effects promising. The concepts and results of intramolecular dynamics derived from spectroscopy are analyzed as a sequence of symmetry breakings. We summarize the concepts of symmetry breakings (de facto and de lege) in view of parity violation in chiral molecules. The experimental schemes and the current status of spectroscopic experiments on molecular parity violation are established. We discuss the promises of detecting and accurately measuring parity-violating energy differences Delta(pv) E on the order of 10(11) J mol(1) (approximately 100 aeV) in enantiomers of chiral molecules with regard to their contribution to fundamental physics in the framework of the standard model of particle physics and more speculative future fundamental symmetry tests such as for the combined charge conjugation, parity, and time-reversal (CPT) symmetry violation.

Parity-violating two-pion exchange nucleon-nucleon interaction

We calculate in chiral perturbation theory the parity-violating two-pion exchange nucleon-nucleon potentials at leading one-loop order. At a distance of $r={m}_{\ensuremath{\pi}}^{\ensuremath{-}1}\ensuremath{\simeq}1.4$ fm they amount to about $\ifmmode\pm\else\textpm\fi{}16%$ of the parity-violating $1\ensuremath{\pi}$ exchange potential. We evaluate also the parity-violating effects arising from $2\ensuremath{\pi}$ exchange with excitation of virtual $\ensuremath{\Delta}(1232)$ isobars. These come out to be relatively small in comparison with those from diagrams with only nucleon intermediate states. The reason for this behavior, which is opposite that of the parity-conserving case, is the blocking of the dominant isoscalar central channel by CP invariance. Furthermore, we calculate the $T$ matrix related to the iteration of the parity-violating $1\ensuremath{\pi}$ exchange with the parity-conserving one. The analytical results presented in this work can be easily implemented into calculations of parity-violating nuclear observables.

U-boson production ine+e−annihilations,ψandΥdecays, and light dark matter

We recall how a new light gauge boson emerged in supersymmetric extensions of the standard model with an extra singlet chiral superfield, and how it could often behave very much as a light pseudoscalar, with the corresponding symmetry broken at a scale higher than electroweak. (I) The possible existence of such a new gauge boson $U$, light and very weakly coupled, allows for light dark matter particles, which could be at the origin of the 511 keV line from the galactic bulge. Could such a light gauge boson be found directly in ${e}^{+}{e}^{\ensuremath{-}}$ annihilations? Not so easily, in fact, due to various constraints limiting the size of its couplings, especially the axial ones, leading to an axionlike behavior or extra parity-violation effects. In particular, searches for the decay $\ensuremath{\Upsilon}\ensuremath{\rightarrow}\ensuremath{\gamma}+\mathrm{\text{invisible}}\text{ }\text{ }U$ may be used to constrain severely the axial coupling of the $U$ to the electron, ${f}_{eA}={f}_{bA}$, to be less than about ${10}^{\ensuremath{-}6}{m}_{U}(\mathrm{MeV})$, 50 times smaller than the $\ensuremath{\simeq}5\text{ }{10}^{\ensuremath{-}5}{m}_{U}(\mathrm{MeV})$ that could otherwise have been allowed from ${g}_{e}\ensuremath{-}2$. (II) The vector coupling of the $U$ to the electron may in principle be larger, but is also limited in size. Even under favorable circumstances (no axial couplings to quarks and charged leptons, and very small couplings to neutrinos), taking also into account possible $Z\mathrm{\text{\ensuremath{-}}}U$ mixing effects, we find from ${g}_{\ensuremath{\mu}}\ensuremath{-}2$, under reasonable assumptions (no cancellation effect, lepton universality), that the vector coupling of the $U$ to the electron can be at most as large as $\ensuremath{\simeq}1.3\text{ }{10}^{\ensuremath{-}3}$, for ${m}_{U}l{m}_{\ensuremath{\mu}}$. Such a coupling to the muon of the order of ${10}^{\ensuremath{-}3}$ could also be responsible for the somewhat large value of the measured ${g}_{\ensuremath{\mu}}\ensuremath{-}2$, as compared to standard model expectations, should this effect turn out to be real. (III) The $U$ couplings to electrons are otherwise likely to be smaller, e.g. $\ensuremath{\lesssim}3\text{ }{10}^{\ensuremath{-}6}{m}_{U}(\mathrm{MeV})$, if the couplings to neutrinos and electrons are similar. This restricts significantly the possibility of detecting a light $U$ boson in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\gamma}U$, making this search quite challenging. Despite the smallness of these couplings, $U$ exchanges can provide annihilation cross sections of light dark matter (LDM) particles of the appropriate size, even if this may require that light dark matter be relatively strongly self-interacting.

Vibrational spectra obtained from high quality potential energy surfaces spanned by low level normal coordinates: application to CHFClI and CDFClI

The impact of approximate normal coordinates for spanning high level potential energy surfaces on vibrational frequencies is studied within the framework of vibrational SCF and configuration interaction calculations (VCI). The use of low level normal coordinates avoids expensive geometry optimizations and harmonic frequency calculations and thus allows for a significant reduction in CPU time. Benchmark calculations are provided for a set of molecules ranging from 5 to 7 atoms. An application to CHFClI and CDFClI shows that this approximation still allows for very accurate results. These molecules are of particular interest for studying parity violation effects.

The effect of parity violation on kinetic models of enantioselective autocatalysis

A detailed analysis of enantioselective autocatalytic reaction models is carried out using both deterministic and stochastic approaches. The models include the small differences between the total energies of enantiomers (DeltaE(PV) approximately 10(-13) J mol(-1)) that arise due to parity violation. Different possible orders of autocatalysis are considered, and the reasons why the predictions of the stochastic and deterministic approaches are different under certain conditions are explored. The continuous time discrete state (CDS) stochastic approach is clearly superior to the deterministic approach. It is concluded that the small difference between enantiomers caused by DeltaE(PV) cannot be amplified under conditions reasonable for the generation of biological chirality. It also seems highly unlikely that biological chirality was determined by any intrinsic difference between enantiomers.

Parity-violating effects in electron spin resonance g-tensors

We investigate the effects of parity-violating electroweak interaction in the g-tensor of electron spin resonance spectroscopy. We present a leading-order perturbational theory for these contributions and evaluate them using density-functional theory in a series of chiral radicals, CH 3XHO (X = N, P, As, Sb). The present formulation is independent of the parameters related to the nuclear structure and hence allows for an estimation of the scale of the parity-violating effects in magnetic resonance parameters.

Relativistic electronic structure theory. Part 2. Applications, edited by P. Schwedtfeger (Elsevier: Amsterdam 2004)

The last three decades have seen considerable advances in the theory and implementation of quantum mechanical methods, both relativistic and nonrelativistic. Coupled with the remarkable advances in computing technology, high-level calculations can now be performed that accurately interpret experimental results, and in some cases even rival experiments. Although the relativistic methods have tended to lag the nonrelativistic methods, they are in routine use in many places. The two volumes of “Relativistic Electronic Structure Theory” embody the culmination of efforts, in relativistic method development and offer a wide overview of the state of the art in relativistic computations on atoms, molecules, and solids. The second volume is devoted to applications (backed with the necessary theory), and ranges from QED and parity-violation effects to the properties of solids. The volume opens with an overview of the chemistry of the heaviest elements—the actinides and transactinides—covering both experiment and theory, and showing how relativistic atomic and molecular calculations have helped to elucidate and inform the experiments on superheavy elements whose half-lives are less than a second and for which the challenge of obtaining experimental data is formidable. The theme of property prediction for superheavy elements continues in the following chapter with a review of highly accurate calculations on atoms, where the surprising trends due to relativity in the seventh period are illustrated: the change of ground state for the noblemetals from d10s1 for Au to d9s2 for Rg, the large increase

Vibrational analyses for CHFClBr and CDFClBr based on high level ab initio calculations

Anharmonicity corrections to the harmonic vibrational spectra of CHFClBr and its deuterated isotopomer were computed by means of variational and perturbational approaches. A comparison of both methods is provided. Based on CCSD(T)/aug-cc-pVTZ electronic structure calculations excellent agreement with experimental data was obtained. Absolute mean deviations are in the range of about 4 cm(-1) for the fundamental modes, while slightly larger values of about 7 cm(-1) were found for the first vibrational overtones. In addition, vibrationally averaged structural parameters are provided for both molecules. The calculations will serve as a future starting point for parity-violation effects in vibrational transitions in these chiral molecules.

Dynamic Stark effect and forbidden-transition spectral line shapes

We report on an experimental and theoretical study of the dynamic (ac) Stark effect on a forbidden transition. A general framework for parameterizing and describing off-resonant ac-Stark shifts is presented. A model is developed to calculate spectral line shapes resulting from resonant excitation of atoms in an intense standing light-wave in the presence of off-resonant ac-Stark shifts. The model is used in the analysis and interpretation of a measurement of the ac-Stark shifts of the static-electric-field-induced \mbox{${\rm 6s^2}~ ^1{\rm S}_0~\to ~{\rm 5d6s}~ ^3{\rm D}_1\:$} transition at 408 nm in atomic Yb. The results are in agreement with estimates of the ac-Stark shift of the transition under the assumption that the shift is dominated by that of the ${\rm 6s^2 \:} ^1{\rm S}_0\:$ ground state. A detailed description of the experiment and analysis is presented. A bi-product of this work is an independent determination (from the saturation behavior of the 408-nm transition) of the Stark transition polarizability, which is found to be in agreement with our earlier measurement. This work is part of the ongoing effort aimed at a precision measurement of atomic parity-violation effects in Yb.

Spectral polarization features of the macroscopic manifestation of parity violation in gaseous media

A formalism based on macroscopic Maxwell equations is developed for the case of media with violations of the space symmetry and time reversal. It is demonstrated that the parity violation in a medium is equivalent to the manifestation of spatial dispersion and natural optical activity. The proposed formalism makes it possible to uniquely calculate the macroscopic parameters of equations in terms of the microscopic theory. The parameters of gyrotropy and dichroism of a gaseous medium are determined within a model describing an interaction of resonance radiation with transitions to states that have different parities and are mixed by a weak interaction of an electron with the nucleus of the atom. It is established that, in the range of the resonance with a magnetic dipole transition, the effect of parity violation is enhanced as a result of the considerable difference between the natural broadenings of the electric and magnetic dipole transitions. This enhancement is suppressed when the dominant Doppler broadening of the atomic transitions is taken into account. It is shown that, owing to the unitarity of the weak interaction, the effects of parity violation are alternating functions of the radiation frequency and are integrally absent in the entire spectrum.

The polarized electron target as a new solar-neutrino detector

In this paper, we analyze the scattering of solar neutrinos on the polarized electron target, and predict how the effect of parity violation in weak interactions may help to distinguish neutrino signal from detector background. We indicate that the knowledge of the Sun motion across the sky is sufficient to predict the day/night asymmetry in the (νee−) scattering on the polarized electron target. To make this detection feasible, the polarized electron target for solar neutrinos needs to be build from magnetic materials, e.g., from ferromagnetic iron foils, paramagnetic scintillator crystals or scintillating ferrofluids.

Perturbational calculations of parity-violating effects in nuclear-magnetic-resonance parameters

We investigate the effects of the parity-violating electroweak interaction in the spectral parameters of nuclear magnetic resonance. Perturbational theory of parity-violating effects in the nuclear magnetic shielding is presented to the order of G(F)alpha, and in the indirect spin-spin coupling, to the order of G(F)alpha3. These leading-order parity-violating corrections are evaluated using analytical linear-response theory methods based on Hartree-Fock and density-functional theory reference states. Parity-violating contributions to spin-spin couplings are evaluated for the first time at the first-principles level. Calculations are carried out for two chiral halomethanes, bromochlorofluoromethane and bromofluoroiodomethane.

Mesoscopic quantum effect of symmetry breaking for magnetic-dipolar oscillating modes

In quasi-two-dimensional systems the dipolar interaction can play an essential role in determine the magnetic properties. In a case of magnetic-dipolar modes in a normally magnetized thin-film ferrite disk, the oscillations can be considered as the motion process of certain quasiparticles—the light magnons—having quantization of energy and characterizing by effective masses depending on the energy levels. One of the features of magnetic-dipolar oscillations in a normally magnetized ferrite disk resonator is the presence of helicoidal surface magnetic currents. These currents lead to the parity violation effects in magnetic-dipolar oscillations and appearance of anapole moments. Recent experiments show that magnetic-dipolar oscillations in a normally magnetized ferrite disk are strongly affected by a normal component of the external RF electric field. The anapole-moment model gives very convincing arguments for explaining these experimental data.

Zeroth-order regular approximation approach to molecular parity violation

We present an ab initio (quasirelativistic) two-component approach to the computation of molecular parity-violating effects which is based on the zeroth-order regular approximation (ZORA). As a first application, we compute the parity-violating energy differences between various $P$ and $M$ conformations of ${C}_{2}$-symmetric molecules belonging to the series ${\mathrm{H}}_{2}{\mathrm{X}}_{2}$ with $\mathrm{X}=\mathrm{O}$, S, Se, Te, Po. The results are compared to previously reported (relativistic) four-component Dirac-Hartree-Fock-Coulomb (DHFC) data. Relative deviations between ZORA and DHFC values are well below 2% for diselane and the heavier homologs whereas somewhat larger relative deviations are observed for the lighter homologs. The larger deviations for lighter systems are attributed to the (nonlocal) exchange terms coupling large and small components, which have been neglected in the present ZORA implementation. For heavier systems these play a minor role, which explains the good performance of the ZORA approach. An excellent performance, even for lighter systems, is expected for a related density-functional-theory-based ZORA because then the exchange terms coupling large and small components are absent.

Density functional calculations of molecular parity-violating effects within the zeroth-order regular approximation

A (quasirelativistic) two-component density functional theory (DFT) approach to the computation of parity-violating energy differences between enantiomers is presented which is based on the zeroth-order regular approximation (ZORA). This approach is employed herein to compute parity-violating energy differences between several P and M conformations of dihydrogen dichalcogenides (H2X2 with X=O, S, Se, Te, Po), of which some compounds have recently been suggested as potential molecular candidates for the first experimental measurement of parity-violating effects in chiral molecules. The DFT ZORA results obtained in this work with "pure" density functionals are anticipated to deviate by well less than 1% from data that would be computed within related (relativistic) four-component Dirac-Kohn-Sham-Coulomb schemes. In our implementation of the ZORA slightly larger relative deviations are expected for hybrid functionals, depending on the amount of "exact" exchange. For B3LYP (20% exact exchange) differences are estimated to amount to at most 3% in hydrogen peroxide, 2% in disulfane, and 1% or less for the heavier homologs. Thus, the present two-component approach is expected to perform excellently when compared to four-component density functional schemes while being at the same time computationally more efficient. The ZORA approach will therefore be of particular interest for the prediction of parity-violating vibrational frequency shifts, for instance, in isotopomers of H(2)Se(2) and H(2)Te(2).

Relativistic second-order many-body and density-functional theory for the parity-violation contribution to theC‐Fstretching mode in CHFClBr

Relativistic four-component electronic structure theory using both wave-function (Dirac-Coulomb-Hartree-Fock and second-order many-body perturbation-theory) and density-functional based methods (local density, hybrid, and generalized gradient approximations) is applied to discuss the current status on the accuracy of parity-violation calculations for molecules. As a test case we choose the C-F stretching mode of CHFClBr, which is currently being investigated by molecular-beam spectroscopy. We show that electron correlation effects are important and cannot be neglected anymore for the parity nonconservation contribution to the total electronic energy. However, electron correlation contributions to parity violation in vibrational transitions of the C-F stretching mode are less important. The density functionals tested give somewhat different results, but the Becke three-parameter Lee-Yang-Parr functional agrees quite well with the second-order many-body perturbation-theory values. The calculations suggest that electron correlation effects have to be considered for future investigations in parity-violation effects in electronic transitions. The performance of density-functional based methods for this property needs further statistics.

Recent experimental and theoretical developments towards the observation of parity violation (PV) effects in molecules by spectroscopy

Parity violation (PV) at the molecular level is known to be responsible for a tiny energy difference between the two enantiomers of a chiral molecule. This parity violation energy difference (PVED) has not yet been detected by experiment. In the last few years, the search for PV effects in molecules has made important steps ahead for several reasons. On one hand, very accurate infra-red spectroscopy measurements were performed by metrologists on bromochlorofluoromethane (CHFClBr) with a 10 Hz accuracy, which so far is the most precise. On the other hand, relativistic calculations were used for the evaluation of DeltaE(PV) allowing for a screening of favorable molecules for future measurements. The synthesis of such chiral molecules with high parity violation effects is currently being investigated. In memory of Professor Jean-Bernard Robert.