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Polar organic molecules form spontaneous polarization in vacuum-deposited films by permanent dipole orientations in the films, originating from the molecule's potential ability to align itself on the film surface during deposition. This study focuses on developing polar molecules that exhibit spontaneous orientation polarization (SOP) and possess a high surface potential. In the proposed molecular design, a hexafluoropropane (6F) unit facilitates spontaneous molecular orientation to align the permanent dipoles, and a phthalimide unit induces strong molecular polarization. Furthermore, the introduction of phthalimides into the molecular backbone raises the glass transition temperature of the molecules, leading to the suppression of molecular mobility on the film surface during film deposition and an improvement in the dipole orientation. The resulting surface potential slope is approximately 280 mV nm−1 without substrate temperature control. Furthermore, this work proposes a method using position isomers as a design strategy to tune the SOP polarity. The substitution position of the strong polar units influences the direction of the total molecular dipoles and affects the SOP polarity of the 6F-based molecules. The proposed molecular designs in this study provide wide tunability of the SOP intensity and polarity, which contributes to highly efficient organic optoelectronic and energy-harvesting devices. Polar organic molecules form spontaneous polarization in vacuum-deposited films originating from the molecule's potential ability to align itself on the film surface during deposition. Here, the author incorporates fluoroalkyl and phthalimide units to the molecular backbone to improve spontaneous molecular orientation facilitating strong polarization in vacuum deposited films. [ABSTRACT FROM AUTHOR]

One of the fundamental goals of particle physics is to gain a microscopic understanding of the strong interaction. Electromagnetic form factors quantify the structure of hadrons in terms of charge and magnetization distributions. While the nucleon structure has been investigated extensively, data on hyperons are still scarce. It has recently been demonstrated that electron-positron annihilations into hyperon-antihyperon pairs provide a powerful tool to investigate their inner structure. We present a method useful for hyperon-antihyperon pairs of different types which exploits the cross section enhancement due to the effect of vacuum polarization at the J/ψ resonance. Using the 10 billion J/ψ events collected with the BESIII detector, this allows a precise determination of the hyperon structure function. The result is essentially a precise snapshot of the Λ ¯ Σ 0 (Λ Σ ¯ 0 ) transition process, encoded in the transition form factor ratio and phase. Their values are measured to be R = 0.860 ± 0.029(stat.) ± 0.015(syst.), Δ Φ Λ ¯ Σ 0 = (1.011 ± 0.094 (stat.) ± 0.010 (syst.)) r a d and Δ Φ Λ Σ ¯ 0 = (2.128 ± 0.094 (stat.) ± 0.010 (syst.)) r a d . Furthermore, charge-parity (CP) breaking is investigated in this reaction and found to be consistent with CP symmetry. Investigating the inner structure of baryons is important to further our understanding of the strong interaction. Here, the BESIII Collaboration extracts the absolute value of the ratio of the electric to magnetic form factors and its relative phase for e + e − → J/ψ → ΛΣ decays, enhancing the signal thanks to the vacuum polarisation effect at the J/ψ peak. [ABSTRACT FROM AUTHOR]

The vacuum polarization effect of a massive scalar field near the point -like source is considered. The corresponding interaction is introduced within a technique of self-adjoint extension of the Laplace operator. This method has been widely discussed within the framework of quantum mechanics. We propose to use it to investigate vacuum field effects. This approach allows computing the renormalized Hadamard function and the renormalized vacuum energy density for massive real scalar field with minimal curvature coupling. The dependence of the vacuum polarization effect upon the fields's mass is analyzed. [ABSTRACT FROM AUTHOR]

The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald's functions K 0 (b r) and K 1 (b r) . This central potential is of great interest in many QED problems, since it describes the lowest order correction for vacuum polarization in few- and many-electron atoms, ions, muonic and bi-muonic atoms/ions as well as in other similar systems. [ABSTRACT FROM AUTHOR]

We present results for the short-distance window observable of the hadronic vacuum polarization contribution to the muon g – 2, computed via the time-momentum representation (TMR) in lattice QCD. A key novelty of our calculation is the reduction of discretization effects by a suitable subtraction applied to the TMR kernel function, which cancels the leading -behaviour at short distances. To compensate for the subtraction, one must substitute a term that can be reliably computed in perturbative QCD. We apply this strategy to our data for the vector current collected on ensembles generated with 2 + 1 flavours of O(a)-improved Wilson quarks at six values of the lattice spacing and pion masses in the range 130 – 420 MeV. Our estimate at the physical point contains a full error budget and reads = 68.85(14)stat (42)syst·10−10, which corresponds to a relative precision of 0.7%. We discuss the implications of our result for the observed tensions between lattice and data-driven evaluations of the hadronic vacuum polarization. [ABSTRACT FROM AUTHOR]

In this paper, we study the relationship between the Dirac–Fock model and the electron-positron Hartree–Fock model. We justify the Dirac–Fock model as a variational approximation of QED when the vacuum polarization is neglected and when the fine structure constant α is small and the velocity of light c is large. As a byproduct, we also prove, when α is small or c is large, the no-unfilled shells theory in the Dirac–Fock theory for atoms and molecules. The proof is based on some new properties of the Dirac–Fock model. [ABSTRACT FROM AUTHOR]

The QED hadronic vacuum polarization function plays an important role in the determination of precision electroweak observables and of the anomalous magnetic moment of the muon. These contributions have been computed from data, by means of dispersion relations affecting the electron positron hadronic cross sections, or by first principle lattice-QCD computations in the Standard Model. Today there is a discrepancy between the two approaches for determining these contributions, which affects the comparison of the measurement of the anomalous magnetic moment of the muon with the theoretical predictions. In this article, we revisit the idea that this discrepancy may be explained by the presence of a new light gauge boson that couples to the first generation quark and leptons and has a mass below the GeV scale. We discuss the requirements for its consistency with observations and the phenomenological implications of such a gauge extension. [ABSTRACT FROM AUTHOR]

The QED hadronic vacuum polarization function plays an important role in the determination of precision electroweak observables and of the anomalous magnetic moment of the muon. These contributions have been computed from data, by means of dispersion relations affecting the electron positron hadronic cross sections, or by first principle lattice-QCD computations in the Standard Model. Today there is a discrepancy between the two approaches for determining these contributions, which affects the comparison of the measurement of the anomalous magnetic moment of the muon with the theoretical predictions. In this article, we revisit the idea that this discrepancy may be explained by the presence of a new light gauge boson that couples to the first generation quark and leptons and has a mass below the GeV scale. We discuss the requirements for its consistency with observations and the phenomenological implications of such a gauge extension. [ABSTRACT FROM AUTHOR]

The increasing accuracy of current and planned experiments to measure the anomalous magnetic moment of the muon requires more precision and reliability of its theoretical calculation. For this purpose, we calculate the differential cross section for the process of annihilation of an electron-positron pair into two photons, one of which is virtual, accompanied by the emission of soft photons, taking into account radiative corrections of the order α2. The results obtained can be used to improve the accuracy of calculating the contribution of the hadron vacuum polarization to the muon anomalous moment. It is shown that all logarithmically amplified two-loop corrections can be easily found using modern theorems of soft and collinear factorizations and available one-loop results. [ABSTRACT FROM AUTHOR]

We report the development of an efficient method for calculating the number and characteristics of photons emitted by a vacuum polarized by overlapping focused laser pulses. The dependence of the signal on the focusing and polarization of pulses is studied and optimized, and the possibility of its detection on the XCELS multipetawatt facility is substantiated. [ABSTRACT FROM AUTHOR]

Within the framework of one-loop quantum gravity, we consider the vacuum polarization effect of the minimally-coupled massive scalar field near the infinitely-thin straight cosmic string. It is shown that the massive-field relative contribution to the renormalized vacuum mean of the energy density becomes negligible at a distance of several Compton lengths. [ABSTRACT FROM AUTHOR]

Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e+e−→ π+π− channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e+e−→ 3π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ–ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η3π that generalizes the analog treatment of virtual and final-state photons in the 2π case. The global fit to the e+e−→ 3π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives a μ 3 π ≤ 1.8 GeV = 45.91 53 × 10 − 10 for the total 3π contribution to the anomalous magnetic moment of the muon, of which a μ FSR 3 π = 0.51 1 × 10 − 10 and a μ ρ − ω 3 π = − 2.68 70 × 10 − 10 can be ascribed to IB. We argue that the resulting cancellation with ρ–ω mixing in e+e−→ 2π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters Mω = 782.70(3) MeV, Mϕ = 1019.21(2) MeV, Γω = 8.71(3) MeV, and Γϕ = 4.27(1) MeV. [ABSTRACT FROM AUTHOR]

The muon Lamb shift (2 –2 is calculated in electron–muon helium atom on the basis of stochastic variational method. The basis wave functions of muonic helium are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation a computer code is written in the MATLAB system. The corrections to the nucleus structure, vacuum polarization, relativism and radiative corrections are taken into account by the perturbation theory. [ABSTRACT FROM AUTHOR]

In this paper, we study the processes of e+e− annihilation into two body final states, either two pseudoscalar mesons or one meson with a photon. The hadronic vacuum polarization form factors are calculated within the framework of resonance chiral theory in the energy region of E ≲ 2 GeV, with final state interactions taken into account. A joint analysis on the processes of e+e−→ π+π−, K+K−, K L 0 K S 0 , π0γ, and ηγ has been performed, and the latest experimental data are included. Based on the vacuum polarization form factors of these processes, we estimate their contributions to the lowest order of anomalous magnetic moment of the muon, (g – 2)μ. Combined with other contributions from hadronic vacuum polarization and other interactions from the standard model, the discrepancy between theoretical prediction and experimental measurement is ∆aμ = (24.1 ± 5.4) × 10−10, i.e., 4.5σ. [ABSTRACT FROM AUTHOR]

In this paper, we study the processes of e+e− annihilation into two body final states, either two pseudoscalar mesons or one meson with a photon. The hadronic vacuum polarization form factors are calculated within the framework of resonance chiral theory in the energy region of E ≲ 2 GeV, with final state interactions taken into account. A joint analysis on the processes of e+e−→ π+π−, K+K−, K L 0 K S 0 , π0γ, and ηγ has been performed, and the latest experimental data are included. Based on the vacuum polarization form factors of these processes, we estimate their contributions to the lowest order of anomalous magnetic moment of the muon, (g – 2)μ. Combined with other contributions from hadronic vacuum polarization and other interactions from the standard model, the discrepancy between theoretical prediction and experimental measurement is ∆aμ = (24.1 ± 5.4) × 10−10, i.e., 4.5σ. [ABSTRACT FROM AUTHOR]

We study the backreaction of quantum fields induced through the vacuum polarization and the conformal anomaly on the collapse of a thin shell of dust. It is shown that the final fate of the collapse process depends on the physical properties of the shell, including its rest and gravitational masses. Investigating the conditions for the formation of black holes, we notice that quantum effects modify the geometry and structure of Schwarzschild space-time in such a way that black holes have two horizons, an inner and an outer horizon. If the gravitational mass of the shell is about that of an ordinary star, then in most cases, the semi-classical collapse will terminate in a singularity, and in general, quantum fluctuations are not strong enough to prevent the creation of the singularity. Although under certain conditions, it is possible to form a non-singular black hole, i.e., a regular black hole. In this way, the collapse stops at a radius much larger than the Planck length below the inner horizon, and the shell bounces and starts an expansion. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In the framework of strong-field QED with x-steps, we study vacuum mean values of the current density and energy–momentum tensor of the quantized spinor field placed in the so-called L-constant electric background. The latter background can be, for example, understood as the electric field confined between capacitor plates, which are separated by a sufficiently large distance L. First, we reveal peculiarities of nonperturbative calculating of mean values in strong-field QED with x-steps in general and, in the L-constant electric field, in particular. We propose a new renormalization and volume regularization procedures that are adequate for these calculations. We find necessary representations for singular spinor functions in the background under consideration. With their help, we calculate the above mentioned vacuum means. In the obtained expressions, we show how to separate global contributions due to the particle creation and local ones due to the vacuum polarization. We demonstrate how these contributions can be related to the renormalized effective Heisenberg–Euler Lagrangian. [ABSTRACT FROM AUTHOR]

We study a quantum scalar field, with general mass and coupling to the scalar curvature, propagating on three-dimensional global anti-de Sitter space-time. We determine the vacuum and thermal expectation values of the square of the field, also known as the vacuum polarisation (VP). We consider values of the scalar field mass and coupling for which there is a choice of boundary conditions giving well-posed classical dynamics. We apply Dirichlet, Neumann and Robin (mixed) boundary conditions to the field at the space-time boundary. We find finite values of the VP when the parameter governing the Robin boundary conditions is below a certain critical value. For all couplings, the vacuum expectation values of the VP with either Neumann or Dirichlet boundary conditions are constant and respect the maximal symmetry of the background space-time. However, this is not the case for Robin boundary conditions, when both the vacuum and thermal expectation values depend on the space-time location. At the space-time boundary, we find that both the vacuum and thermal expectation values of the VP with Robin boundary conditions converge to the result when Neumann boundary conditions are applied, except in the case of Dirichlet boundary conditions. [ABSTRACT FROM AUTHOR]

Based on computational quantum field theory and solutions to the Dirac equation, we show how the vacuum's polarization density induced by strong external field can be calculated based on five independent methods. We compare these methods for a spatially reduced dimensional system and show that some approaches rely on energy renormalizations, energy cutoffs or periodic boundaries. We also illustrate the spatial implications of the breakdown of the linear superposition principle for extremely high intensity fields. A main focus of the article is to discuss future challenges for each approach that might motivate new theoretical and computational studies. [ABSTRACT FROM AUTHOR]

The long-wavelength behavior of vibrational modes plays a central role in carrier transport, phonon-assisted optical properties, superconductivity, and thermomechanical and thermoelectric properties of materials. Here, we present general invariance and equilibrium conditions of the lattice potential; these allow to recover the quadratic dispersions of flexural phonons in low-dimensional materials, in agreement with the phenomenological model for long-wavelength bending modes. We also prove that for any low-dimensional material the bending modes can have a purely out-of-plane polarization in the vacuum direction and a quadratic dispersion in the long-wavelength limit. In addition, we propose an effective approach to treat invariance conditions in crystals with non-vanishing Born effective charges where the long-range dipole-dipole interactions induce a contribution to the lattice potential and stress tensor. Our approach is successfully applied to the phonon dispersions of 158 two-dimensional materials, highlighting its critical relevance in the study of phonon-mediated properties of low-dimensional materials. [ABSTRACT FROM AUTHOR]

For general number of spatial dimensions we investigate the cosmological dynamics driven by a cosmological constant and by a source with barotropic equation of state. It is assumed that for both those sources the energy density can be either positive or negative. Exact solutions of the cosmological equations are provided for flat models. For models with curved space and with zero cosmological constant the general solutions are expressed in terms of the hypergeometric function. The qualitative evolution is described for all values of the equation of state parameter. We specify the values of that parameter and the combinations of the signs for the cosmological constant and matter energy density for which the cosmological dynamics is nonsingular. An example is considered with positive cosmological constant and negative matter energy density induced by the polarization of the hyperbolic vacuum. [ABSTRACT FROM AUTHOR]

In analogy with GRB 190114C, we here analyze the ultrarelativistic prompt emission (UPE) of GRB 180720B observed in the rest-frame time interval t rf = 4.84 –10.89 s by Fermi-GBM. We reveal the UPE hierarchical structure from the time-resolved spectral analysis performed in time sub-intervals: the spectrum in each shorter time interval is always fitted by a composite blackbody plus cutoff power-law model. We explain this structure with the inner engine of binary-driven hypernova (BdHN) model operating in a quantum electrodynamics (QED) regime. In this regime, the electric field induced by the gravitomagnetic interaction of the newborn Kerr BH with the surrounding magnetic field is overcritical, i.e., | E | ≥ E c , where E c = m e 2 c 3 / (e ħ) . The overcritical field polarizes the vacuum leading to an e + e - pair plasma that loads baryons from the surroundings during its expansion. We calculate the dynamics of the self-acceleration of the pair-electromagnetic-baryon (PEMB) pulses to their point of transparency. We characterize the quantum vacuum polarization process in the sequences of decreasing time bins of the UPE by determining the radiation timescale, Lorentz factors, and transparency radius of the PEMB pulses. We also estimate the strength of the surrounding magnetic field ∼ 10 14 G, and obtain a lower limit to the BH mass, M = 2.4 M ⊙ , and correspondingly an upper limit to the spin, α = 0.6 , from the conditions that the UPE is powered by the Kerr BH extractable energy and its mass is bound from below by the NS critical mass. [ABSTRACT FROM AUTHOR]

The scattering of Dirac fermions on the sine-Gordon kink is studied both analytically and numerically. To achieve invariance with respect to a discrete symmetry, the sine-Gordon model is treated as a nonlinear σ -model with a circular target space that interacts with fermionic isodublets through the Yukawa interaction. It is shown that the diagonal and antidiagonal parts of the fermionic wave function interact independently with the external field of the sine-Gordon kink. The wave functions of the fermionic scattering states are expressed in terms of the Heun functions. General expressions for the transmission and reflection coefficients are derived, and their dependences on the fermion momentum and mass are studied numerically. The existence condition is found for two fermionic zero modes, and their analytical expressions are obtained. It is shown that the zero modes do not lead to fragmentation of the fermionic charge, but can lead to polarization of the fermionic vacuum. The scattering of the diagonal and antidiagonal fermionic states is found to be significantly different; this difference is shown to be due to the different dependences of the energy levels of these bound states on the fermion mass, and is in accordance with Levinson's theorem. [ABSTRACT FROM AUTHOR]

We study the influence of light quark loops on the Wigner phase by solving coupled Dyson–Schwinger equations for quark propagator and gluon propagator. We take the gluon propagator in the Nambu phase from N f = 2 unquenched lattice QCD and choose various phenomenological models for the quark-gluon vertex. The gluon propagator in Wigner phase is assumed to be different from that in the Nambu phase only due to the vacuum polarization of the quark loop. We obtain the Wigner solution of the coupled equations, compared with that from solving only the equation of the quark propagator. We discussed the corrections by the light quark loops and the dependence on various models of the quark-gluon vertex. [ABSTRACT FROM AUTHOR]

The MUonE proposal at the CERN SPS consists in extracting the value of the hadronic vacuum polarization self-energy function (HVP) from its contribution to the differential cross-section of elastic muon-electron scattering. The HVP contribution to the muon anomalous magnetic moment can then be obtained from a weighted integral of the measured HVP self-energy function. This, however, requires a knowledge of the HVP function in its full integration domain. This paper discusses a procedure to reconstruct the HVP function in the regions not directly accessible to measurement. The method is based on the so-called transfer theorems, due to Flajolet and Odlyzko, which we explain and adapt to HVP. [ABSTRACT FROM AUTHOR]

The electromagnetic form factors of charged and neutral kaons are strongly constrained by their low-energy singularities, in the isovector part from two-pion intermediate states and in the isoscalar contribution in terms of ω and ϕ residues. The former can be predicted using the respective π π → K ¯ K partial-wave amplitude and the pion electromagnetic form factor, while the latter parameters need to be determined from electromagnetic reactions involving kaons. We present a global analysis of time- and spacelike data that implements all of these constraints. The results enable manifold applications: kaon charge radii, elastic contributions to the kaon electromagnetic self energies and corrections to Dashen's theorem, kaon boxes in hadronic light-by-light (HLbL) scattering, and the ϕ region in hadronic vacuum polarization (HVP). Our main results are: ⟨ r 2 ⟩ c = 0.359 (3) fm 2 , ⟨ r 2 ⟩ n = - 0.060 (4) fm 2 for the charged and neutral radii, ϵ = 0.63 (40) for the elastic contribution to the violation of Dashen's theorem, a μ K -box = - 0.48 (1) × 10 - 11 for the charged kaon box in HLbL scattering, and a μ HVP [ K + K - , ≤ 1.05 GeV ] = 184.5 (2.0) × 10 - 11 , a μ HVP [ K S K L , ≤ 1.05 GeV ] = 118.3 (1.5) × 10 - 11 for the HVP integrals around the ϕ resonance. The global fit to K ¯ K gives M ¯ ϕ = 1019.479 (5) MeV , Γ ¯ ϕ = 4.207 (8) MeV for the ϕ resonance parameters including vacuum-polarization effects. [ABSTRACT FROM AUTHOR]

We have performed atomic structure calculations of Be-like C, N, O and Ne ions using systematically enlarged multiconfiguration Dirac–Fock wavefunctions. Present calculations are fully relativistic in nature with Breit interaction and quantum electrodynamic (QED) corrections such as vacuum polarization and self-energy correction to obtain low lying energy levels, transition probability, oscillator strength and line strength. Selective radiative data for electric dipole, magnetic quadrupole and fine structure data in terms of hyperfine coupling constants and isotopic shift parameters are also reported. Comparisons are made with the existing available results and a good agreement has been found. Additionally, an attempt is made to study the impact of relativistic and QED corrections on forbidden and allowed transitions. We have also used the above-computed transition probabilities here to provide the line intensity ratio and plasma parameters of optically thin and moderately dense plasma. We believe that the detailed atomic data computed here will be further helpful in line identification and plasma modeling studies for laboratory plasma devices like ITER and astrophysical plasma work related to elemental abundance calculations from solar corona to active galactic nuclei. [ABSTRACT FROM AUTHOR]

The generic hidden local symmetry (HLS) model has recently given rise to its BHLS 2 variant, defined by introducing symmetry breaking mostly in the vector meson sector; the central mechanism is a modification of the covariant derivative at the root of the HLS approach. However, the description of the τ dipion spectra, especially the Belle one, is not fully satisfactory, whereas the simultaneous dealing with its annihilation sector ( e + e - → π + π - / π + π - π 0 / π 0 γ / η γ / K + K - / K L K S ) is optimum. We show that this issue is solved by means of an additional breaking term which also allows us to consistently include the mixing properties of the [ π 0 , η , η ′ ] system within this extended BHLS 2 ( EBHLS 2 ) scope. This mechanism, an extension of the usual 't Hooft determinant term, only affects the kinetic energy part of the BHLS 2 Lagrangian. One thus obtains a fair account for the τ dipion spectra which complements the fair account of the annihilation channels already reached. The Belle dipion spectrum is found to provide evidence in favor of a violation of the conserved vector current (CVC) in the τ lepton decay; this evidence is enforced by imposing the conditions < 0 | J μ q | [ q ′ q ′ ¯ ] (p) > = i p μ f q δ q q ′ , { [ q q ¯ ] , q = u , d , s } on EBHLS 2 axial current matrix elements. EBHLS 2 is found to recover the usual (completed) formulae for the [ π 0 , η , η ′ ] mixing parameters, and the global fits return mixing parameter values in agreement with expectations and better uncertainties. Updating the muon hadronic vacuum polarization (HVP), one also argues that the strong tension between the KLOE and BaBar pion form factors imposes to provide two solutions, namely a μ H V P - L O (KLOE) = 687.48 ± 2.93 and a μ H V P - L O (BaBar) = 692.53 ± 2.95 , in units of 10 - 10 , rather than some combination of these. Taking into account common systematics, their differences from the experimental BNL-FNAL average value exhibit significance > 5.4 σ (KLOE) and > 4.1 σ (BaBar), with fit probabilities favoring the former. [ABSTRACT FROM AUTHOR]

Non-perturbatively computing the hadronic vacuum polarization at large photon virtualities and making contact with perturbation theory enables a precision determination of the electromagnetic coupling at the Z pole, which enters global electroweak fits. In order to achieve this goal ab initio using lattice QCD, one faces the challenge that, at the short distances which dominate the observable, discretization errors are hard to control. Here we address challenges of this type with the help of static screening correlators in the high-temperature phase of QCD, yet without incurring any bias. The idea is motivated by the observations that (a) the cost of high-temperature simulations is typically much lower than their vacuum counterpart, and (b) at distances x3 far below the inverse temperature 1/T, the operator-product expansion guarantees the thermal correlator of two local currents to deviate from the vacuum correlator by a relative amount that is power-suppressed in (x3T). The method is first investigated in lattice perturbation theory, where we point out the appearance of an O(a2 log(1/a)) lattice artifact in the vacuum polarization with a prefactor that we calculate. It is then applied to non-perturbative lattice QCD data with two dynamical flavors of quarks. Our lattice spacings range down to 0.049 fm for the vacuum simulations and down to 0.033 fm for the simulations performed at a temperature of 250 MeV. [ABSTRACT FROM AUTHOR]

We provide a novel explanation to the muon g − 2 excess with new physics contributions at the two-loop level. In this scenario, light millicharged particles are introduced to modify the photon vacuum polarization that contributes to muon g − 2 at one additional loop. The muon g − 2 excess can be explained with the millicharged particle mass mχ around 10 MeV and the product of the multiplicity factor and millicharge squared of Nχε2 ∼ 10−3. The minimal model faces severe constraints from direct searches at fixed-target experiments and astrophysical observables. However, if the millicharged particles are also charged under a hidden confining gauge group SU(Nχ) with a confinement scale of MeV, hidden-sector hadrons are unstable and can decay into neutrinos, which makes this scenario consistent with existing constraints. This explanation can be well tested at low-energy lepton colliders such as BESIII and Belle II as well as other proposed fixed-target experiments. [ABSTRACT FROM AUTHOR]

We consider quantum gravitational corrections to Maxwell's equations on flat space background. Although the vacuum polarization is highly gauge dependent, we explicitly show that this gauge dependence is canceled by contributions from the source which disturbs the effective field and the observer who measures it. Our final result is a gauge independent, real and causal effective field equation that can be used in the same way as the classical Maxwell equation. [ABSTRACT FROM AUTHOR]

We show that the leading derivative corrections to the Heisenberg-Euler effective action can be determined efficiently from the vacuum polarization tensor evaluated in a homogeneous constant background field. After deriving the explicit parameter-integral representation for the leading derivative corrections in generic electromagnetic fields at one loop, we specialize to the cases of magnetic- and electric-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field. In these cases, closed-form results and the associated all-orders weak- and strong-field expansions can be worked out. One immediate application is the leading derivative correction to the renowned Schwinger-formula describing the decay of the quantum vacuum via electron-positron pair production in slowly-varying electric fields. [ABSTRACT FROM AUTHOR]

We consider black hole solutions with electric and magnetic sources in the four-dimensional Einstein-Born-Infeld-AdS theory with spherical, planar and hyperbolic horizon geometries. Exact analytical solutions for the metric function, electric and magnetic fields were obtained and they recover the RN-AdS black hole in the limit β → + ∞ for spherical horizon in the absence of the magnetic charge. Expressions for temperature, electric and magnetic potential were obtained and they satisfy the first law of the extended black hole thermodynamics, where a negative cosmological constant is associated with thermodynamic pressure. Also, the Born-Infeld vacuum polarization term B d β was included into the first law in order to satisfy the Smarr relation. Critical behavior of the black hole was examined and condition on electric and magnetic charges were obtained when phase transition appears. Also, the critical ratio and capacity at constant pressure were calculated. Electric and magnetic charges enter into the metric function and thermodynamic quantities symmetrically and thus the presence of the magnetic charge does not bring very significant new features. Finally, we examine the Joule-Thomson expansion if the black hole mass is fixed. The inversion and isenthalpic curves were plotted and the cooling and heating regions were demonstrated. These results recover the Joule-Thomson expansion recently considered for the RN-AdS black hole in the corresponding limit. [ABSTRACT FROM AUTHOR]

We consider nonperturbative vacuum polarization effects in the supercritical region for a planar Dirac–Coulomb system with a supercritical extended axially symmetric Coulomb source with a charge and radius in the magnetic field with an axial-vector potential. We study the behavior of the vacuum charge and vacuum current densities, and . We focus on the divergence in the theory corresponding to the renormalization and convergence of partial series for and . We stress that in contrast to the vacuum charge density, the partial channels with large values of the third projection of the total angular momentum must be taken into account in calculating the vacuum current density in the presence of an external magnetic field localized in the range . We show that in the presence of a supercritical Coulomb source, the induced magnetic field can enhance the original magnetic field for certain values of parameters of the external vector potential. [ABSTRACT FROM AUTHOR]

While conducting analysis related to a DARPA-funded project to evaluate possible structure of the energy density present in a Casimir cavity as predicted by the dynamic vacuum model, a micro/nano-scale structure has been discovered that predicts negative energy density distribution that closely matches requirements for the Alcubierre metric. The simplest notional geometry being analyzed as part of the DARPA-funded work consists of a standard parallel plate Casimir cavity equipped with pillars arrayed along the cavity mid-plane with the purpose of detecting a transient electric field arising from vacuum polarization conjectured to occur along the midplane of the cavity. An analytic technique called worldline numerics was adapted to numerically assess vacuum response to the custom Casimir cavity, and these numerical analysis results were observed to be qualitatively quite similar to a two-dimensional representation of energy density requirements for the Alcubierre warp metric. Subsequently, a toy model consisting of a 1 μ m diameter sphere centrally located in a 4 μ m diameter cylinder was analyzed to show a three-dimensional Casimir energy density that correlates well with the Alcubierre warp metric requirements. This qualitative correlation would suggest that chip-scale experiments might be explored to attempt to measure tiny signatures illustrative of the presence of the conjectured phenomenon: a real, albeit humble, warp bubble. [ABSTRACT FROM AUTHOR]

We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g − 2. [ABSTRACT FROM AUTHOR]

In recent years, the anomalous magnetic moment of the muon has triggered a lot of activity in the lattice QCD community because a persistent tension of about 3.5 σ is observed between the phenomenological estimate and the Brookhaven measurement. The current best phenomenological estimate has an uncertainty comparable to the experimental one and the error is completely dominated by hadronic effects: the leading order hadronic vacuum polarization (HVP) contribution and the hadronic light-by-light (HLbL) scattering contribution. Both are accessible via lattice simulations and a reduction of the error by a factor 4 is required in view of the forthcoming experiments at Fermilab and J-PARC whose results, expected in the next few years, should reduce the experimental precision down to the level of 0.14 ppm. In this article, I review the status of lattice calculations of those quantities, starting with the HVP. This contribution has now reached sub-percent precision and requires a careful understanding of all sources of systematic errors. The HLbL contribution, that is much smaller, still contributes significantly to the error. This contribution is more challenging to compute, but rapid progress has been made on the lattice in the last few years. [ABSTRACT FROM AUTHOR]

We have calculated the effect of compressing the radioactive atoms in the crystal lattice environments on their electron capture nuclear decay rates. The electronic structure calculations of solids using the density functional techniques have been used to calculate the change of electron density at the nuclei and the corresponding change of electron capture nuclear decay rate of the radioactive atoms confined to the interstitial spaces of different crystal lattices. The effects of finite nuclear size and vacuum polarization were considered in the calculations. It has been found that the calculations significantly underpredict the experimentally measured increase of electron capture nuclear decay rate under compression. The increase of decay rate due to compression-induced quantum anti-Zeno effect is generally believed to be very small because of very short duration of initial nonexponential decay time for the nuclear decays. However, this effect could be observable for the electron capture nuclear decay of 163 Ho, because of its very low decay energy. Moreover, certain models of quantum measurement indicate much longer initial nonexponential decay time and the corresponding implication on the increase of decay rate under compression is still not known. It is important to understand the large discrepancy between the measured and calculated increase of electron capture nuclear decay rate under compression and the associated role of quantum anti-Zeno effect because of their possible implications in various astrophysical and geophysical calculations. [ABSTRACT FROM AUTHOR]

A coherent study of e+e− annihilation into two (π+π−, K+K−) and three (π+π−π0, π+π−η) pseudoscalar meson production is carried out within the framework of resonance chiral theory in energy region E ≲ 2 GeV. The work of [L.Y. Dai, J. Portolés, and O. Shekhovtsova, Phys. Rev. D88 (2013) 056001] is revisited with the latest experimental data and a joint analysis of two pseudoscalar meson production. Hence, we evaluate the lowest order hadronic vacuum polarization contributions of those two and three pseudoscalar processes to the anomalous magnetic moment of the muon. We also estimate some higher-order additions led by the same hadronic vacuum polarization. Combined with the other contributions from the standard model, the theoretical prediction differs still by (21.6 ± 7.4) × 10−10 (2.9σ) from the experimental value. [ABSTRACT FROM AUTHOR]

The Scharnhorst effect—a photon flying across a gap between large conducting plates parallel to each other has a speed slightly higher than the speed of light in vacuum because of the polarization of the system—is qualitatively considered. [ABSTRACT FROM AUTHOR]

Properties and different representations of the Uehling potential are investigated. Based on these properties and by using our formulas for the Fourier transform of the Uehling potential we have developed the new analytical, logically closed and physically transparent procedure which can be used to evaluate the lowest-order vacuum polarization correction to the cross sections of a number of QED processes, including the Mott electron scattering, bremsstrahlung, creation and/or annihilation of the (e - , e +) - pair in the field of a heavy Coulomb center, e.g., atomic nucleus. [ABSTRACT FROM AUTHOR]

Due to precision tests of quantum electrodynamics (QED), determination of accurate values of fundamental constants, and constraints on new physics, it is important in a consistent way to evaluate a number of QED observables such as the Lamb shift in hydrogen-like atomic systems. Even in a pure leptonic case, those QED variables are in fact not pure QED ones since hadronic effects are involved through intermediate states while accounting for higher-order effects. One of them is hadronic vacuum polarization (hVP). Complex evaluations often involve a number of QED quantities, for which treatment of hVP is not consistent. The highest accuracy for a calculation of the hVP term is required for the anomalous magnetic moment of a muon. However, a standard data-driven treatment of hVP, based on a dispersion integration of experimental data on electron-positron annihilation to hadrons and some other phenomena, leads to a contradiction with the experimental value of a μ . This experimental value can be considered as an indirect determination of the hVP contribution to a μ and the scatter of theory and experiment allows one to obtain a conservative estimation of the related hVP contribution. In this paper, we derive exact and approximate relations between the leading-order (LO) hVP contributions to various observables. Using those relations, we obtain for them a consistent set of the results, based on the scatter of a μ values. While calculating the LO hVP term, we have to remember that next-to-LO (NLO) hVP corrections are often comparable with the uncertainty of the LO term. Special attention is payed to hVP contribution to simple atoms. In particular, we discuss the NLO contribution to the Lamb shift in ordinary and muonic hydrogen and other two-body atoms for Z ≤ 10 . We also consider the NLO contribution of the muonic vacuum polarization to the Lamb shift in hydrogen-like atoms. With the a μ puzzle unresolved, one may still require present-days values of the hVP contributions to various observable for comparison to experiment etc. the presence of contradicting values and a lack of consistency means an additional uncertainty for a μ and for key contributions to it, including the LO hVP one. We present here an estimation of such a propagated uncertainty in hVP contributions to different QED observables and recommend a consistent set of the related LO hVP contributions. [ABSTRACT FROM AUTHOR]

Log-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe5 and HfTe5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned to a much smaller value due to the reduction of the vacuum polarization effect. The decreasing of the scale factor demonstrates the many-body effect on the DSI, which has rarely been discussed hitherto. Furthermore, the cut-offs of oscillations are quantitatively explained by considering the Thomas-Fermi screening effect. Our work clarifies the many-body effect on DSI and paves a way to tune the DSI in quantum materials. [ABSTRACT FROM AUTHOR]

In nonlinear electromagnetism in vacuum, a classical electromagnetic wave itself can generate another wave. A classical field can become a source for a nonlinear correction via the polarization and magnetization of vacuum. We elucidate that a resonant generation is intrinsic to the theoretical structure of nonlinear electromagnetism. The resonance can take place when the phases, or the cycles of the source and the nonlinear correction match. We demonstrate two specific systems as examples. For a plane wave and constant fields, nonlinear corrective electromagnetic fields are resonantly enhanced with distance. It is shown in a stationary special solution. For more realistic system, we have considered the case of a standing wave in a cavity with an appropriate initial and boundary conditions. As a result, the corrections are resonantly enhanced with time. The resonance effect in the cavity is shown to be observed more effectively by combining a static magnetic flux density. We have evaluated the resonant effect using concrete parameters of current experiments. The demonstrated resonance can be combined with existing proposals to enable experimental detection of nonlinear optical effects of vacuum easier. [ABSTRACT FROM AUTHOR]

The hadronic vacuum polarization function Π h for two light flavors is computed on the entire domain of spacelike and timelike momenta using a framework of Dyson–Schwinger equations. The analytical continuation of the function Π h is based on the utilization of the Gauge Technique with the entry of QCD Green's functions determined from generalized quark spectral functions. For the first time, the light quark spectral functions are extracted from the solution of the gap equation for the quark propagator. The scale is set up by the phenomena of dynamical chiral symmetry breaking, which is a striking feature of low energy QCD. [ABSTRACT FROM AUTHOR]

We show that in the presence of the torsion tensor S ij k , the quantum commutation relation for the four-momentum, traced over spinor indices, is given by [ p i , p j ] = 2 i ħ S ij k p k . In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin of fermions, this relation in a coordinate frame reduces to a commutation relation of noncommutative momentum space, [ p i , p j ] = i ϵ ijk U p 3 p k , where U is a constant on the order of the squared inverse of the Planck mass. We propose that this relation replaces the integration in the momentum space in Feynman diagrams with the summation over the discrete momentum eigenvalues. We derive a prescription for this summation that agrees with convergent integrals: ∫ d 4 p (p 2 + Δ) s → 4 π U s - 2 ∑ l = 1 ∞ ∫ 0 π / 2 d ϕ sin 4 ϕ n s - 3 [ sin ϕ + U Δ n ] s , where n = l (l + 1) and Δ does not depend on p. We show that this prescription regularizes ultraviolet-divergent integrals in loop diagrams. We extend this prescription to tensor integrals. We derive a finite, gauge-invariant vacuum polarization tensor and a finite running coupling. Including loops from all charged fermions, we find a finite value for the bare electric charge of an electron: ≈ - 1.22 e . This torsional regularization may therefore provide a realistic, physical mechanism for eliminating infinities in quantum field theory and making renormalization finite. [ABSTRACT FROM AUTHOR]

The MUonE experiment aims at a precision measurement of the hadronic vacuum polarization contribution to the muon g − 2, via elastic muon-electron scattering. Since the current muon g − 2 anomaly hints at the potential existence of new physics (NP) related to the muon, the question then arises as to whether the measurement of hadronic vacuum polarization in MUonE could be affected by the same NP as well. In this work, we address this question by investigating a variety of NP explanations of the muon g − 2 anomaly via either vector or scalar mediators with either flavor-universal, non-universal or even flavor-violating couplings to electrons and muons. We derive the corresponding MUonE sensitivity in each case and find that the measurement of hadronic vacuum polarization at the MUonE is not vulnerable to any of these NP scenarios. [ABSTRACT FROM AUTHOR]

There are two types of fluctuations in the quantum vacuum: type 1 vacuum fluctuations are on shell and can interact with matter in specific, limited ways that have observable consequences; type 2 vacuum fluctuations are off shell and cannot interact with matter. A photon will polarize a type 1, bound, charged lepton–antilepton vacuum fluctuation in much the same manner that it would polarize a dielectric, suggesting the method used here for calculating the permittivity ϵ 0 of the vacuum. In a model that retains only leading terms, ϵ 0 ≅ (6 μ 0 / π) (8 e 2 / ħ) 2 = 9.10 × 10 - 12 C/(Vm). The calculated value for ϵ 0 is 2.7% more than the accepted value. The permittivity of the vacuum, in turn, determines the speed c of light in the vacuum. Since the vacuum is at rest with respect to every inertial frame of reference, c is the same in every inertial reference frame. [ABSTRACT FROM AUTHOR]