Vacuum Polarization Research Articles

Electronic current densities and origin-independent property densities induced by optical fields.

The interaction of a molecule with optical fields is customarily interpreted by means of induced time-dependent electric polarizabilities, magnetizabilities and mixed electric-magnetic polarizabilities. In general, these properties can be rationalized by integrals of density functions formulated in terms of induced charge and current densities. In this perspective, we focus on what has been done so far at the theoretical level, and on what can be expected to be unveiled from the topological study of suitable density functions, endowed with the fundamental requirement of origin invariance. Densities characterized by such a property can be integrated all over the configuration space to obtain electric dipole polarizability and optical rotatory power. Corresponding maps visualize domains mainly involved in the molecular response. The diagonal components of origin-independent density tensor functions that, on integration, yield corresponding electric dipole polarizability tensor of benzene, naphthalene, phenanthrene and ovalene, have been computed, confirming the ubiquitous presence of counter-polarization regions in the proximity of the atomic nuclei. They are associated with toroidal electron currents, induced by time derivative of the electric field of impinging radiation. Electron (de)localization in these systems is readily observed and estimated. The optical rotation density of the carbonyl chromophore is studied in detail. Its essential feature is the separation in quadrants of alternating sign of density about the CO bond. The presence of an extrachromophoric perturbation determines asymmetry in the extension of the quadrant distribution, thus causing optical rotation.

Inversion-Based Magnetic Polarizability Tensor Measurement From Time-Domain EMI Data

Inversion-Based Magnetic Polarizability Tensor Measurement From Time-Domain EMI Data

Leading hadronic contribution to the muon g − 2 from lattice QCD

We compute the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. The calculations are performed using four flavors of stout smeared staggered quarks, with quark masses at their physical values. The continuum limit is taken using six different lattice spacings ranging from 0.132 fm down to 0.064 fm. All strong isospin breaking and electromagnetic effects are accounted for to leading order. A controlled infinite volume limit is taken thanks to dedicated simulations performed in box sizes up to 11 fm. Putting all these ingredients together, we find [(gµ − 2)/2]LO−HVP = 707.5[5.5] 10−10, which has a total uncertainty of 0.8%. Compared to determinations based on the e+e− → hadrons cross section, our result significantly reduces the tension between the standard model prediction for the muon g − 2 and its experimental value.

Dispersive determination of the HVP contribution to the muon g − 2

The determination of hadronic vacuum polarization (HVP) from e+e− → hadrons cross-section data, in the energy region relevant for the anomalous magnetic moment of the muon, has recently been challenged by lattice-QCD calculations, especially for the intermediate window in Euclidean time. In these proceedings we review some frequently-asked questions on the comparison between data-driven and lattice-QCD evaluations of the HVP contribution.

Computational approaches to examine the vacuum polarization density

Computational approaches to examine the vacuum polarization density

In English

An influence of the adsorbed molecules layer on the optical characteristics of the spherical metallic nanoparticles has been studied in the work. In order to do this one considers the additional term which takes into account the scattering of electrons at the interface between metal and adsorbate. The analytical expressions for the frequency dependences for the parameter of coherence loss due to the scattering at the interface “metal – adsorbed layer” have been obtained. It has been found that the presence of the adsorbed molecules results in the electron scattering anisotropy, and, hence, in the anisotropy of the optic response of such systems. The result of the indicated anisotropy is the appearance of the additional maximum in the infrared part of the spectrum in the frequency dependences for the optical characteristics. An evolution of the frequency dependences for the components of the polarizability tensor and the absorption cross-section and scattering cross-section for the two-layer spherical nanoparticles of the type “metal – adsorbate” under the variation of their geometrical parameters has been analyzed. It has been shown that the weak maximum of the real, imaginary parts and the module of the transverse component of the polarizability tensor and the absorption and scattering cross-sections in the infrared part of the spectrum appears due to inducing of the local density of the states by adsorbate. The reason of the shift of the maxima of the absorption cross-section and scattering cross-section for the nanoparticles of the constant sizes with the cores of different metals has been found. It has been demonstrated the existence of the small-scale oscillations at the frequency dependences for the components of the polarizability tensor and at the absorption and scattering cross-sections, caused by an oscillating contribution of the surface electron scattering. The dependence of the location and the value of the maximum of the absorption cross-section for the particle “metal – adsorbate” with the constant geometrical parameters and content on the dielectric permittivity of the medium, in which the nanoparticle is situated, has been proved.

MUonE, muon g−2 and electroweak precision constraints within 2HDMs

Two Higgs doublet models are attractive scenarios for physics beyond the Standard Model. In particular, lepton-specific manifestations remain contenders to explain the observed discrepancy between the anomalous magnetic moment of the muon $a_\mu$ predicted within the Standard Model and recent observations at Fermilab and BNL. Dominant uncertainties that affect $a_\mu$ have motivated the MUonE experiment to access the hadronic vacuum polarisation contribution that impacts $a_\mu$ via elastic muon-electron scattering. In this work, we contrast the high precision that is achievable within the MUonE context with constraints from flavour physics, precision electroweak constraints and LHC searches as well as their extrapolations for a range of two Higgs doublet models with a softly broken $\mathbb{Z}_2$ symmetry. We find that the sensitivity of MUonE does not extend beyond the parameter regions that are already excluded by other constraints. MUonE will therefore provide a detailed measurement of the hadronic vacuum polarisation contribution which then transparently informs $a_\mu$ interpretations in 2HDMs without modifications of correlations from beyond the Standard Model interactions. In passing we extend earlier results of LHC and flavour projections to lepton-specific 2HDM (Types X and Y) scenarios, and comment on the possibility of modifying the value of the W-boson mass; we briefly discuss the implications for a strong first-order electroweak phase transition for these models.

Effects of the long-range neutrino-mediated force in atomic phenomena

As known, electron vacuum polarisation by nuclear Coulomb field produces the Uehling potential with the range . Similarly, neutrino vacuum polarisation by the Z boson field produces a long-range potential with a very large range . Measurements of macroscopic effects produced by the potential give limits on the effective interaction constant which exceed Fermi constant by many orders of magnitude, while limits from the spectroscopy of simple atomic systems are approaching the Standard Model predictions. In this paper, we consider limits on from hydrogen, muonium, positronium, deuteron and molecular hydrogen. Constraints are also obtained on fifth force parameterised by Yukawa-type potential mediated by a scalar particle.

On the intensity of light scattered by molecular liquids-Comparison of experiment and quantum chemical calculations.

The intensity of light scattered by liquids has been studied for over a century since the valuable microscopic information about the molecules can be obtained, such as the anisotropy of the molecular polarizability tensor or preferred orientations of neighboring molecules. However, in modern dynamic light scattering experiments, the scattering intensity is usually disregarded, unlike in dielectric spectroscopy, which can be considered as a complementary experimental method, where the dielectric strength is routinely evaluated. The reason lies partly on the fact that the exact form of the equations relating the macroscopically measured light scattering intensity to the microscopic properties of the molecules is debated in the literature. Therefore, as a first step, we compare anisotropy parameters from the literature, calculated from light scattering intensities using different equations, with quantum chemical calculations for over 150 medium-sized molecules. This allows us to identify a consistent form of equations. In a second part, we turn to the depolarized light scattering spectra of 13 van der Waals liquids and some mixtures thereof, recorded with a combination of Tandem-Fabry-Perót and Raman spectroscopies, giving direct access to the reorientational dynamics of the molecules. We discuss how the strength of the structural α-relaxation is connected to the anisotropy parameter, what implication this has for the shape of the α-relaxation, how the components of a mixture-also for the case of ionic liquids-can be identified in this way, and how orientational correlation parameters can be extracted. Additionally, we point out for the example of n-alkanes that for highly flexible molecules, the reorientational motion might not be the decisive source of the depolarized scattered light. We also show that light scattering might serve as a sensitive tool to check the accuracy of a conformer ensemble obtained by quantum chemical calculations.

Addendum: Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment (2022 J. Phys. G: Nucl. Part. Phys. 49 055001)

This addendum provides results complementary to those obtained in [J. Phys. G 49, 055001 (2022)]. Specifically, an equivalent form of the relation, which binds together the ‘spacelike’ kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment , is obtained. It is shown that the infrared limiting value of the ‘spacelike’ and ‘timelike’ kernel functions, which enter the representations for involving the Adler function and the R-ratio, is identical to the corresponding QED contribution to the muon anomalous magnetic moment of the preceding order in the electromagnetic coupling. The next-to-leading order contributions (which includes the leptonic and hadronic insertions) and (which includes the double hadronic insertion), are studied. The three kernel functions appearing in the representations for , which involve the hadronic vacuum polarization function, Adler function, and the R-ratio, are presented for the cases of the electron and τ-lepton loop insertions.

Minimal Object Characterizations Using Harmonic Generalized Polarizability Tensors and Symmetry Groups

Minimal Object Characterizations Using Harmonic Generalized Polarizability Tensors and Symmetry Groups

Polarizations of gravitational waves in the bumblebee gravity model

Lorentz violation modifies the dispersion relation of gravitational waves (GWs), and induces birefringence and anisotropy in propagation. Our study shows that Lorentz violation can also activate multiple polarizations of GWs. We use the gauge invariants to investigate the polarizations of GWs in the bumblebee gravity model, and obtain the following results. (i) For a vector background ${b}^{\ensuremath{\mu}}$ with only a nonzero temporal component ${b}^{t}$, there are five independent propagating degrees of freedom (d.o.f.), which is similar to the Einstein-\ae{}ther theory. (ii) The presence of a spatial component in the background defines a preferred spatial direction which breaks rotational symmetry. We denote $\stackrel{^}{\mathbit{b}}$ as the direction of the spatial part of the background and ${b}_{s}$ as its length. If GWs propagate along $\stackrel{^}{\mathbit{b}}$, the polarization content is similar to the purely timelike case. (iii) If the propagation direction of GWs is separated by an angle $\ensuremath{\beta}$ to $\stackrel{^}{\mathbit{b}}$, and $\ensuremath{\beta}=\mathrm{arccos}({b}^{t}/{b}_{s})$, there are only two tensor polarizations. (iv) If $\ensuremath{\beta}\ensuremath{\ne}\mathrm{arccos}({b}^{t}/{b}_{s})$, there are only two independent d.o.f., and the vector and scalar modes degenerate with the tensor modes. The tensor perturbations can activate a mixture of all six polarizations simultaneously. Finally, we point out the difference in GWs between the bumblebee gravity model and the minimal Standard-Model Extension framework in the linearized regime. Current observations have placed stringent constraints on the anisotropy induced by the background, while our theoretical study still reveals some novel phenomena and provides more understanding about the interaction between the Lorentz-violating vector field and gravity.

Window observable for the hadronic vacuum polarization contribution to the muon g−2 from lattice QCD

Euclidean time windows in the integral representation of the hadronic vacuum polarization contribution to the muon $g-2$ serve to test the consistency of lattice calculations and may help in tracing the origins of a potential tension between lattice and data-driven evaluations. In this paper, we present results for the intermediate time window observable computed using O($a$) improved Wilson fermions at six values of the lattice spacings below 0.1\,fm and pion masses down to the physical value. Using two different sets of improvement coefficients in the definitions of the local and conserved vector currents, we perform a detailed scaling study which results in a fully controlled extrapolation to the continuum limit without any additional treatment of the data, except for the inclusion of finite-volume corrections. To determine the latter, we use a combination of the method of Hansen and Patella and the Meyer-Lellouch-L\"uscher procedure employing the Gounaris-Sakurai parameterization for the pion form factor. We correct our results for isospin-breaking effects via the perturbative expansion of QCD+QED around the isosymmetric theory. Our result at the physical point is $a_\mu^{\mathrm{win}}=(237.30\pm0.79_{\rm stat}\pm1.22_{\rm syst})\times10^{-10}$, where the systematic error includes an estimate of the uncertainty due to the quenched charm quark in our calculation. Our result displays a tension of 3.9$\sigma$ with a recent evaluation of $a_\mu^{\mathrm{win}}$ based on the data-driven method.

Collective modes of gluons in an anisotropic thermomagnetic medium

We study the collective modes of gluons in an anisotropic thermal medium in the presence of a constant background magnetic field using the hard-thermal-loop perturbation theory. The momentum space anisotropy of the medium has been incorporated through the generalized Romatschke-Strickland form of the distribution function, whereas the magnetic modification arising from the quark loop contribution has been taken into account in the lowest Landau level approximation. We consider two special cases: (i) a spheroidal anisotropy with the anisotropy vector orthogonal to the external magnetic field and (ii) an ellipsoidal anisotropy with two mutually orthogonal vectors describing anisotropies along and orthogonal to the field direction. The general structure of the polarization tensor in both cases is equivalent and consists of six independent basis tensors. We find that the introduction of momentum anisotropy ingrains azimuthal angular dependence in the thermomagnetic collective modes. Our study suggests that the presence of a strong background magnetic field can significantly reduce the growth rate of the unstable modes, which may have important implications in the equilibration of magnetized quark-gluon plasma.

Simultaneously characterized Stokes parameters of a lightwave utilizing the tensor polarization holography theory.

Polarization is a natural property of a lightwave and makes a significant contribution to various scientific and technological applications, due to the different states of polarization (SoP) of a lightwave that may manifest distinct behaviors. Hence, it is important to determine the SoP of the lightwave. Generally, the SoP of a lightwave can be recognized by the Stokes parameters. In this paper, we proposed a novel method to simultaneously characterize the Stokes parameters of a lightwave, by employing the tensor polarization holography theory. This is done through merely a piece of polarization-sensitive material. Compared with the traditional method, this method requires only one measurement to obtain all the Stokes parameters, without using additional polarizing elements. The experimental result shows excellent agreement with the theoretical one, which confirmed the reliability and accuracy of the proposed method. We believe that this work may broaden the application field of polarization holography.

Effects of external field wavelength and solvation on the photophysical property and optical nonlinearity of 1,3-thiazolium-5-thiolates mesoionic compound

The photophysical property and optical nonlinearity of an electronic push–pull mesoionic compound, 2-(4-trifluoromethophenyl)-3-methyl-4-(4-methoxyphenyl)-1,3-thiazole-5-thiolate, were theoretically investigated with a reliable computing strategy. The essence of the optical properties were then explored through a variety of wavefunction analysis methods, including the natural transition orbital analysis, hole-electron analysis, (hyper)polarizability density analysis, decomposition of the (hyper)polarizability contribution, and (hyper)polarizability tensor analysis, at the level of electronic structure. The influences of the electric field and solvation on the absorption spectrum and (hyper)polarizability of the molecule are highlighted and clarified. The results are expected to provide guidance for people to understand the effects of external field wavelength and solvation on the optical properties of mesoscopic molecules.

Constraining the extra polarization modes of gravitational waves with double white dwarfs

The detection of gravitational wave (GW) has opened a new window to test the theory of gravity in the strong field regime. In general relativity (GR), GW can only possess two tensor polarization modes, which are known as the $+$ and $\times$ modes. However, vector and scalar modes can exist in some modified theories of gravity, and we can test the gravitational theories by probing these extra polarization modes. As a space-borne GW detector, TianQin will be launched in the 2030s, and it is expected to observe plenty of GW signals, including those from nearly ten-thousands double white dwarfs (DWDs) in our galaxy. This offers an excellent chance for testing the existence of extra polarization modes. In this article, we analyze the capability of detecting the extra polarization modes with DWDs. For the extra modes, we consider both the leading order dipole radiation and the subleading quadrupole radiation. We find that the capability of TianQin has very strong dependency on the source orientation. We also analyze all the verification binaries with determined position and frequency, and find that ZTF J1539 can give the best constraint on the extra polarization modes. We have also considered the case of TianQin twin constellation, and the joint observation with LISA.

Holographic Floquet states in low dimensions (II)

We continue the study in [1] of a strongly coupled (2+1)-dimensional gauge theory subject to an external rotating electric field. The system is modelled holographically as a D3/D5 probe intersection. We add temperature to the D3 background and analyze the phase diagram. Also here, the conductive phase extends down to vanishing external electric field at discrete values of the frequencies where vector meson Floquet condensates form. For all temperatures, at given intercalated frequencies, we find new dual states that we name Floquet suppression points where the vacuum polarization vanishes even in the presence of an electric field. From the data we infer that these states exist both in the conductive and insulating phases. In the massless limit we find a linear and instantaneous conductivity law, recovering known general results in 2+1 dimensions. We also examine the photovoltaic AC and DC current as the response to an oscillating probe electric field and see that rising the temperature suppresses the photovoltaic Hall current. All the results obtained carry over qualitatively unaltered to the case of D3/D7.

Finite-Basis-Set Approach to the Two-Center Heteronuclear Dirac Problem

The rigorous two-center approach based on the dual-kinetically balanced finite-basis-set expansion is applied to one-electron, heteronuclear diatomic Bi-Au, U-Pb, and Cf-U quasimolecules. The obtained 1σ ground-state energies are compared with previous calculations, when possible. Upon analysis of three different placements of the coordinate system’s origin in the monopole approximation of the two-center potential: (1) in the middle, between the nuclei, (2) in the center of the heavy nucleus, and (3) in the center of the light nucleus, a substantial difference between the results is found. The leading contributions of one-electron quantum electrodynamics (self-energy and vacuum polarization) are evaluated within the monopole approximation as well.

Derivation and implementation of the optical rotation tensor for chiral crystals.

This paper reports the derivation and implementation of the electric dipole-magnetic dipole and electric dipole-electric quadrupole polarizability tensors at the density functional theory level with periodic boundary conditions (DFT-PBC). These tensors are combined to evaluate the Buckingham/Dunn tensor that describes the optical rotation (OR) in oriented chiral systems. We describe several aspects of the derivation of the equations and present test calculations that verify the correctness of the tensor formulation and their implementation. The results show that the full OR tensor is completely origin invariant as for molecules and that PBC calculations match molecular cluster calculations on 1D chains. A preliminary investigation on the choice of density functional, basis set, and gauge indicates a similar dependence as for molecules: the functional is the primary factor that determines the OR magnitude, followed by the basis set and to a much smaller extent the choice of gauge. However, diffuse functions may be problematic for PBC calculations even if they are necessary for the molecular case. A comparison with experimental data of OR for the tartaric acid crystal shows reasonable agreement given the level of theory employed. The development presented in this paper offers the opportunity to simulate the OR of chiral crystalline materials with general-purpose DFT-PBC methods, which, in turn, may help to understand the role of intermolecular interactions on this sensitive electronic property.