Vacuum Polarization Research Articles

Probing a non-linear electrodynamics black hole with thin accretion disk, shadow, and deflection angle with M87* and Sgr A* from EHT

Non-linear interaction between the electromagnetic fields (EMF) occurs when vacuum polarization in quantum electrodynamics (QED) happens. The field of non-linear electrodynamics, which may result from this interaction, could have important effects on black hole physics. This paper considers the asymptotically flat black hole solution in Einstein-nonlinear electrodynamics (NLE) fields. We study the effect of the NLE parameters on the black hole deflection angle using the Gauss-Bonnet theorem in weak field limits, shadow cast using the null geodesics method, and thin accretion disk using the Novikov-Thorne model. In particular, we studied the time-averaged energy flux, the disk temperature, the differential luminosity, the different emission profiles, and infalling spherical accretion. Then we show how the physical quantities depend on $\beta$ and $C$ parameters of NLE and provide some constraints on the NLE parameters using the observations of M87* and Sgr A* from EHT.

Lower Bounds to the Q Factor of Electrically Small Resonators Through Quasistatic Modal Expansion

The problem of finding the optimal current distribution supported by small radiators yielding the minimum quality (Q) factor is a fundamental problem in electromagnetism. Q factor bounds constrain the maximum operational bandwidth of devices including antennas, metamaterials, and nanoresonators, and have been featured in seminal papers in the past decades. Here, we determine the lower bounds of Q factors of small-size plasmonic and high-permittivity dielectric resonators, which are characterized by quasi-electrostatic and quasi-magnetostatic natural modes, respectively. We expand the induced current density field in the resonator in terms of these modes, leading to closed-form analytical expressions for the electric and magnetic polarizability tensors, whose largest eigenvalue is directly linked to the minimum Q factor. Our results allow also to determine in closed form the corresponding optimal current density field. In particular, when the resonator exhibits two orthogonal reflection symmetries the minimum Q factor can be simply obtained from the Q factors of the single current modes with non-vanishing dipole moments aligned along the major axis of the resonator. Overall, our results open exciting opportunities in the context of nano-optics and metamaterials, facilitating the analysis and design of optimally shaped resonators for enhanced and tailored light-matter interactions.

Quantum corrections to the Schwarzschild metric from vacuum polarization

We explore static and spherically symmetric solutions of the 4-dimensional semiclassical Einstein's equations using the quantum vacuum polarization of a conformal field as a source. These solutions may be of interest for the study of exotic compact objects (ECOs). The full backreaction problem is addressed by solving the semiclassical Tolman-Oppenheimer-Volkoff (TOV) equations making use of effective equations of state inspired by the trace anomaly and an extra simplifying and reasonable assumption. We combine analytical and numerical techniques to solve the resulting differential equations, both perturbatively and nonperturbatively in $\ensuremath{\hbar}$. In all cases the solution is similar to the Schwarzschild metric up to the vicinity of the classical horizon $r=2M$. However, at $r=2M+ϵ$, with $ϵ\ensuremath{\sim}O(\sqrt{\ensuremath{\hbar}})$, we find a coordinate singularity. In the case of matching with a static star, this leads to an upper bound in the compactness, and sets a constraint on the family of stable ECOs. We also study the corrections that the quantum-vacuum polarization induces on the propagation of waves, and discuss the implications. For the pure vacuum case, we can further extend the solution by using appropriate coordinates until we reach another singular point, where this time a null curvature singularity arises and prevents extending beyond. This picture qualitatively agrees with the results obtained in the effective two-dimensional approach, and reinforces the latter as a reasonable method.

Thermal quantum gravity in a general background gauge

We calculate in a general background gauge, to one-loop order, the leading logarithmic contribution from the graviton self-energy at finite temperature $T$, extending a previous analysis done at $T=0$. The result, which has a transverse structure, is applied to evaluate the leading quantum correction of the gravitational vacuum polarization to the Newtonian potential. An analytic expression valid at all temperatures is obtained, which generalizes the result obtained earlier at $T=0$. One finds that the magnitude of this quantum correction decreases as the temperature rises.

Reduced nuclear helicity amplitudes for deuteron electrodisintegration and other processes

We extend the original idea of reduced nuclear amplitudes to capture individual helicity amplitudes and discuss various applications to exclusive processes involving the deuteron. Specifically, we consider deuteron form factors, structure functions, tensor polarization observables, photodisintegration, and electrodisintegration. The basic premise is that nuclear processes at high momentum transfer can be approximated by tree graphs for point-like nucleons supplemented by empirical form factors for each nucleon. The latter represent the internal structure of the nucleon, and incorporate nonperturbative physics, which can allow for early onset of scaling behavior. The nucleon form factors are evaluated at the net momentum transfer experienced by the given nucleon, with use of ${G}_{E}$ for a no-flip contribution and ${G}_{M}$ for a helicity-flip contribution. Results are compared with data where available. The deuteron photodisintegration asymmetry $\mathrm{\ensuremath{\Sigma}}$ is obtained with a value of $\mathrm{\ensuremath{\Sigma}}({90}^{\ensuremath{\circ}})\ensuremath{\simeq}\ensuremath{-}0.06$, which is much closer to experiment than the value of $\ensuremath{-}1$ originally expected. The method also provides an estimate of the momentum transfer values required for scaling onset. We find that the deuteron structure function $B$ is a good place to look, above momentum transfers of 10 ${\mathrm{GeV}}^{2}$.

Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, ${a}_{\ensuremath{\mu}}^{\mathrm{HVP}}$, in the so-called short and intermediate time-distance windows, ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}$ and ${a}_{\ensuremath{\mu}}^{\mathrm{W}}$, defined by the RBC/UKQCD Collaboration [Phys. Rev. Lett. 121, 022003 (2018)]. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with ${N}_{f}=2+1+1$ flavors of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavors tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to $\ensuremath{\simeq}0.057$, 0.068 and 0.080 fm with spatial lattice sizes up to $L\ensuremath{\simeq}7.6\text{ }\text{ }\mathrm{fm}$. For the short-distance window we obtain ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}(\mathrm{ETMC})=69.27(34)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which is consistent with the recent dispersive value of ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}({e}^{+}{e}^{\ensuremath{-}})=68.4(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Phys. Lett. B 833, 137313 (2022)]. In the case of the intermediate window we get the value ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{ETMC})=236.3(1.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which is consistent with the result ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{BMW})=236.7(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Nature (London) 593, 51 (2021)] by the BMW Collaboration as well as with the recent determination by the CLS/Mainz group of ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{CLS})=237.30(1.46)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Phys. Rev. D 106, 114502 (2022)]. However, it is larger than the dispersive result of ${a}_{\ensuremath{\mu}}^{\mathrm{W}}({e}^{+}{e}^{\ensuremath{-}})=229.4(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ by approximately 3.6 standard deviations. The tension increases to approximately 4.5 standard deviations if we average our ETMC result with those by BMW and CLS/Mainz. Our accurate lattice results in the short and intermediate windows point to a possible deviation of the ${e}^{+}{e}^{\ensuremath{-}}$ cross section data with respect to Standard Model predictions in the low- and intermediate-energy regions but not in the high-energy region.

Observation of an Inner-Shell Orbital Clock Transition in Neutral Ytterbium Atoms.

We observe a weakly allowed optical transition of atomic ytterbium from the ground state to the metastable state 4f^{13}5d6s^{2} (J=2) for all five bosonic and two fermionic isotopes with resolved Zeeman and hyperfine structures. This inner-shell orbital transition has been proposed as a new frequency standard as well as a quantum sensor for new physics. We find magic wavelengths through the measurement of the scalar and tensor polarizabilities and reveal that the measured trap lifetime in a three-dimensional optical lattice is 1.9(1)s, which is crucial for precision measurements. We also determine the g factor by an interleaved measurement, consistent with our relativistic atomic calculation. This work opens the possibility of an optical lattice clock with improved stability and accuracy as well as novel approaches for physics beyond the standard model.

On the axial chirality of leucoindigo.

The diagonal components and the trace of two tensors which account for chiroptical response of the leucoindigo molecule that is, static anapole magnetizability, and dynamic electric dipole-magnetic dipole polarisability depending on the frequency of impinging light, are a function of the dihedral angle of torsion about the central CC bond, assumed to lie in the direction of the coordinate system. They vanish for symmetry reasons at and , corresponding respectively to and point group symmetries, that is, cis and trans conformers characterized by the presence of molecular symmetry planes. Nonetheless, diagonal components and average value of static anapole polarizability and optical rotation tensors vanish at , where leucondigo is unquestionably chiral from the geometrical viewpoint. Vanishing values of the average chiroptical properties have been observed also in the proximity of other angles. Attempts have been made to explain the occurrence of accidental zeros of chiroptical properties in terms of transition frequencies and scalar products appearing in the numerator of their quantum mechanical definitions. Within the electric dipole approximation, the presence of anomalous vanishing values of tensor components of anapole magnetizability and electric-magnetic dipole polarizability is ascribed to physical achirality, arising from the lack of either toroidal or spiral electron flow along the , and directions.

Analysis of transmitarray antenna elements using polarizability tensors

This paper presents an analytical approach to analyze transmitarray (TA) antenna elements using generalized boundary conditions (GBCs) and polarizability tensors. The proposed method analyzes multi-layer TA elements, which are composed of scatterers and dielectric substrates. The method combines an equivalent circuit model and network theory to evaluate total transmission matrix of multi-layer elements. Initially, each layer of scatterers is modeled by its collective polarizability tensor, which is calculated from individual polarizabilities of scatterers and their interactions. Next, analytical sheet admittance of layers is derived from their collective polarizabilities. Finally, total transmission matrix of multi-layer elements is calculated, taking into account the effect of resonant layers and dielectric spacers.This method determines the contribution of different items in the scattering properties of the elements separately, including the angle and polarization of the incident wave, the geometry and material of scatterers, and the array period. To validate the proposed model, several examples of multi-layer elements are analyzed, and the analytical results are compared with full-wave simulation results. A good agreement between them is achieved.The proposed approach is an efficient tool for the precise and fast design of transmitarray antennas, particularly where the effect of the incident angle needs to be considered.

Ion-Neutral Collision Cross Section as a Function of the Static Dipole Polarizability and the Ionization Energy of the Ion.

Ion mobility spectrometry is becoming more and more popular as a fast, efficient, and sensitive tool for the separation and identification of ionized molecules in the gas phase. An ion traveling through a drift tube at atmospheric pressure under the influence of an electric field collides with the buffer gas molecules. The mobility of the ion depends inversely on the ion-neutral collision cross section. In the simplest hard-sphere approximation, the collision cross section is the area of the conventional geometric cross section. However, deviations are expected because of the physical interactions between the colliding species. More than a century ago, Langevin described a model for the interaction between a point-charge ion and a polarizable atom (molecule). Since then, the model has been modified many times to include better approximations of the interaction potential, usually preserving the point-charge nature of the ion. Although more advanced approaches allow for considering polarizable ions with dissimilar sizes and shapes, still explicit analytical dependencies on the properties of the ion remain elusive. In this work, an extended version of the Langevin model is proposed and solved using algebraic perturbation theory. A simple analytical expression of the collision cross section depending explicitly on both the static dipole polarizability and the ionization energy of the ion is found. The equation is validated using ion mobility data. Surprisingly, even low-level calculations of the polarizability tensors produce results that are consistent with the experimental observations. This fact makes the equation very attractive for helping applications in different areas, such as the deconvolution of mobilograms of protomers, ion-molecule chemical kinetics, and others.

Data-based determination of the isospin-limit light-quark-connected contribution to the anomalous magnetic moment of the muon

We describe how recent determinations of exclusive-mode contributions to $a_\mu^{\rm LO,HVP}$, the leading-order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, can be used to provide, up to small electromagnetic (EM) corrections accessible from the lattice, a data-based dispersive determination of $a_\mu^{\rm lqc;\, IL}$, the isospin-limit, light-quark-connected contribution to $a_\mu^{\rm LO,HVP}$. Such a determination is of interest in view of the existence of a number of lattice results for this quantity, emerging evidence for a tension between lattice and dispersive determinations of $a_\mu^{\rm LO,HVP}$, and the desire to clarify the source of this tension. Taking as input for the small EM correction that must be applied to the purely data-driven dispersive determination the result $-0.93(58)\times 10^{-10}$ obtained in a recent BMW lattice study, we find $a_\mu^{\rm lqc;\, IL}$ to be $635.0(2.7)\times 10^{-10}$ if the results of Keshavarzi, Nomura and Teubner are used for the exclusive-mode contributions and $638.4(4.1)\times 10^{-10}$ if instead those of Davier, H\"ocker, Malaescu and Zhang are used.

Characteristic Substituent Effect Model for the Infrared Intensities of the X2CY (X = H, F, Cl, Br; Y = O, S) Molecules.

Many years ago, the gas-phase infrared fundamental intensities of Cl2CS were determined within experimental error from the experimental intensities and frequencies of F2CO, Cl2CO, and F2CS. An additive characteristic substituent shift relationship between atomic polar tensors of these molecules formed the basis for these calculations. Here, QCISD/cc-pVTZ-level Quantum Theory of Atoms In Molecules (QTAIM) individual charge, charge transfer, and polarization contributions to these atomic polar tensor elements are shown to obey the same basic relationship for the extended X2CY (Y = O, S; X = H, F, Cl, Br) family of molecules. QTAIM charge and polarization contributions, as well as the total equilibrium dipole moments of the X2CY molecules, also follow this characteristic substituent shift model. The root-mean-sqaure error for the 231 estimates of these parameters is 0.14 e or only about 1% of the total 10 e range of the Atomic Polar Tensor (APT) contributions determined from the wave functions. The substituent effect APT contribution estimates were used to calculate the infrared intensities of the X2CY molecules. Although one serious discrepancy was observed for one of the CH stretching vibrations of H2CS, accurate values were within 45 km·mol-1 or about 7% of the 656 km·mol-1 intensity range predicted by the QCISD/cc-pVTZ wave functions. Hirshfeld charge, charge transfer, and polarization contributions are also found to follow this model, although their charge parameters do not follow electronegativity expectations.

A Polarization Tensor for Neutron Optics

A rank 2 dimension 3 tensor formulation for polarized neutron transport in a magnetic field is derived. Using this formulation, the rotating magnetic field problem is revisited to produce a single 3 × 3 vector-transformation matrix that describes the polarization transport. That result is then used to fashion a new strategy for a numerical approximation of polarization transport in an arbitrary magnetic field using time-dependent perturbation theory.

On the time momentum representation of hadronic vacuum polarization and gμ − 2

We propose a new set of model independent approximants adapted to the time momentum representation (TMR) of hadronic vacuum polarization (HVP) and its contribution to gμ– 2. They provide a way to extrapolate lattice QCD (LQCD) results obtained in an optimal time-region, to the full range required for an evaluation of the HVP contribution to gμ– 2. They offer as well a new way to confront LQCD results in restricted TMR regions, with the full contribution obtained from data driven determinations.

Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale Λ ~ 400 MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale Λ, and a UV-finite long-distance part to be treated with coordinate-space methods, thereby avoiding power-law finite-size effects altogether. In order to predict the long-distance part, we express the UV-regulated e.m. correction to the HVP via the forward hadronic light-by-light (HLbL) scattering amplitude and relate the latter via a dispersive sum rule to γ∗γ∗ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level γ∗γ∗→ e+e− cross-section, we predict the expected lattice-QCD integrand resulting from the γ∗γ∗→ π0 process.

Generating tensor polarization from shear stress

We derive an expression for the tensor polarization of a system of massive spin-1 particles in a hydrodynamic framework. Starting from quantum kinetic theory based on the Wigner-function formalism, we employ a modified method of moments which also takes into account all spin degrees of freedom. It is shown that the tensor polarization of an uncharged fluid is determined by the shear-stress tensor. In order to quantify this novel polarization effect, we provide a formula which can be used for numerical calculations of vector-meson spin alignment in relativistic heavy-ion collisions.

Coordinate-space calculation of the window observable for the hadronic vacuum polarization contribution to (g−2)μ

The `intermediate window quantity' of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon allows for a high-precision comparison between the data-driven approach and lattice QCD. The existing lattice results, which presently show good consistency among each other, are in strong tension with the data-driven determination. In order to check for a potentially common source of systematic error of the lattice calculations, which are all based on the time-momentum representation (TMR), we perform a calculation using a Lorentz-covariant coordinate-space (CCS) representation. We present results for the isovector and the connected strange-quark contributions to the intermediate window quantity at a reference point in the $(m_\pi,m_K)$ plane, in the continuum and infinite-volume limit, based on four different lattice spacings. Our results are in good agreement with those of the recent TMR-based Mainz-CLS publication.

New Structure in the Deuteron.

We demonstrate that a paradigm shift from considering the deuteron as a system of a bound proton and neutron to that of a pseudovector system in which we observe a proton and neutron results in the possibility of probing a new "incomplete" P-statelike structure on the light front (LF). This occurs at extremely large internal momenta, which can be achieved in a high energy transfer electrodisintegration of the deuteron. Investigating the deuteron on the light front, where the vacuum fluctuations are suppressed, we found that this new structure, together with the conventional S and D states, is leading order in transferred energy of the reaction and thus not suppressed on the light front. The incompleteness of the observed P state results in a violation of the angular condition that can happen only if the deuteron contains non-nucleonic structures, such as Δ Δ, N^{*}N or hidden color components. We demonstrate that experimentally verifiable signatures of incomplete P states are angular anisotropy of the light front momentum distribution of the nucleon in the deuteron, as well as an enhancement of the tensor polarization strength beyond the S- and D-wave predictions at large internal momenta in the deuteron.

On the non-minimal coupling of magnetic fields with gravity in Schwarzschild spacetime

In this work we study the effects of non-minimal coupling between electromagnetism and gravity, which are motivated by quantum effects such as vacuum polarization. We investigate the modification of both asymptotically dipole and uniform magnetic fields around a Schwarzschild black hole that come as the result of non-minimal coupling. While in both cases the magnetic field gets enhanced or suppressed with respect to the case of minimal coupling, depending on the sign of non-minimal coupling parameter, in the case of a background uniform magnetic field the direction of the magnetic field also alters in the vicinity of the black hole horizon. We have discussed the possible astrophysical and cosmological sources for which the vacuum polarization may be at play, while also discussing the observational effects, in particular the possibility of synchrotron radiation from the vicinity of a black hole. We conclude that such observations could be used to constrain the value of the non-minimal coupling parameter.

Collision-induced three-body polarizability of helium.

We present the first-principles determination of the three-body polarizability and the third dielectric virial coefficient of helium. Coupled-cluster and full configuration interaction methods were used to perform electronic structure calculations. The mean absolute relative uncertainty of the trace of the polarizability tensor, resulting from the incompleteness of the orbital basis set, was found to be 4.7%. Additional uncertainty due to the approximate treatment of triple and the neglect of higher excitations was estimated at 5.7%. An analytic function was developed to describe the short-range behavior of the polarizability and its asymptotics in all fragmentation channels. We calculated the third dielectric virial coefficient and its uncertainty using the classical and semiclassical Feynman-Hibbs approaches. The results of our calculations were compared with experimental data and with recent Path-Integral Monte Carlo (PIMC) calculations [Garberoglio et al., J. Chem. Phys. 155, 234103 (2021)] employing the so-called superposition approximation of the three-body polarizability. For temperatures above 200K, we observed a significant discrepancy between the classical results obtained using superposition approximation and the ab initio computed polarizability. For temperatures from 10K up to 200K, the differences between PIMC and semiclassical calculations are several times smaller than the uncertainties of our results. Except at low temperatures, our results agree very well with the available experimental data but have much smaller uncertainties. The data reported in this work eliminate the main accuracy bottleneck in the optical pressure standard [Gaiser et al., Ann. Phys. 534, 2200336 (2022)] and facilitate further progress in the field of quantum metrology.