On <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> pair production by colliding electromagnetic pulses

Electron-positron pair production from vacuum in an electromagnetic field created by two counterpropagating focused laser pulses interacting with each other is analyzed. The dependence of the number of produced pairs on the intensity of a laser pulse and the focusing parameter is studied with a realistic three-dimensional model of the electromagnetic field of the focused wave, which is an exact solution of the Maxwell equations. It has been shown that e⁺e^? pair production can be experimentally observed when the intensity of each beam is I～10²⁶ W/cm², which is two orders of magnitude lower than that for a single pulse.     

Electron-positron pair production by electromagnetic pulses

Electron-positron pair production in vacuum by a single focused laser pulse and by two counter-propagating colliding focused pulses is analyzed. A focused laser pulse is described using a realistic three-dimensional model based on an exact solution of Maxwell’s equations. In particular, this model reproduces an important property of focused beams, namely, the existence of two types of waves with a transverse electric or magnetic vector (e-or h-polarized wave, respectively). The dependence of the number of produced pairs on the radiation intensity and focusing parameter is studied. It has been shown that the number of pairs produced in the field of a single e-polarized pulse is many orders of magnitude larger than that for an h-polarized pulse. The pulse-intensity dependence of the number of pairs produced by a single pulse is so sharp that the total energy of pairs produced by the e-polarized pulse with intensity near the intensity I _S = 4.65 × 10²⁹ W/cm² characteristic of QED is comparable with the energy of the pulse itself. This circumstance imposes a natural physical bound on the maximum attainable intensity of a laser pulse. For the case of two colliding circularly polarized pulses, it is shown that pair production becomes experimentally observable when the intensity of each beam is I ～ 10²⁶ W/cm², which is one to two orders of magnitude lower than that for a single pulse.     

Dynamical Schwinger effect and high-intensity lasers. Realising nonperturbative QED

We consider the possibility of experimental verification of vacuum e⁺e^- pair creation at the focus of two counter-propagating optical laser beams with intensities 10²⁰–10²² W/cm²^{22}~{\rm W/cm}^2, achievable with present-day petawatt lasers, and approaching the Schwinger limit: 10²⁹ W/cm²^{29}~{\rm W/cm}^2 to be reached at ELI. Our approach is based on the collisionless kinetic equation for the evolution of the e⁺ and e^- distribution functions governed by a non-Markovian source term for pair production. As possible experimental signals of vacuum pair production we consider e⁺e^- annihilation into γ-pairs and the refraction of a high-frequency probe laser beam by the produced e⁺e^- plasma. We discuss the dependence of the dynamical pair production process on laser wavelength, with special emphasis on applications in the X-ray domain (X-FEL), as well as the prospects for μ⁺μ^- and π⁺π^- pair creation at high-intensity lasers. We investigate perspectives for using high-intensity lasers as “boosters” of ion beams in the few-GeV per nucleon range, which is relevant, e.g., to the exploration of the QCD phase transition in laboratory experiments.     

Estimate of the fraction of primary photons in the cosmic-ray flux at energies ∼1017 eV from the EAS-MSU experiment data

We reanalyze archival EAS-MSU data in order to search for events with an anomalously low content of muons with energies E _μ > 10 GeV in extensive air showers with the number of particles N _e ? 2 × 10⁷. We confirm the first evidence for a nonzero flux of primary cosmic gamma rays at energies E ～ 10¹⁷ eV. The estimated fraction of primary gamma rays in the flux of cosmic particles with energies E ? 5.4 × 10¹⁶ eV is ε_γ = (0.43 _?0.11 ^+0.12 )%, which corresponds to the intensity I _γ = (1.2 _?0.3 ^+0.4 ) × 10^?16 cm^?2 s^?1 sr^?1. The study of arrival directions does not favor any particular mechanism of the origin of the photon-like events.     

Uncertainties in the hadronic contribution to the QED vacuum polarization

We describe an updated evaluation of the hadronic contribution to the QED vacuum polarization. It is obtained from a dispersion integral over the measured cross section ofe ⁺ e ^?→hadrons.     

Nuclear composition of 1-to 20-PeV primary cosmic rays according to lateral features of the electron-photon component of all extensive air showers and of extensive air showers accompanying high-energy gamma rays and hadrons in x-ray emulsion chambers at the Tien Shan level

Data from the Tien Shan array Adron on the dependence of the lateral distributions of the electron-photon component (age parameter S) in extensive air showers of cosmic rays on the number of electrons, N _e , which is a quantity that characterizes the primary-nucleus energy E₀, are subjected to a comparative analysis. The distributions in question are given both for all showers and for showers accompanying high-energy gamma rays and hadrons in x-ray emulsion chambers. According to calculations, events associated with the latter are generated predominantly by primary protons, and this makes it possible to assess their role at various values of E₀. The distributions with respect to S suggest a significant fraction of light nuclei, predominantly protons, in the region after the knee in the spectrum for N _e >10⁶, at least up to N _e =5.6×10⁶ (E₀ ～ 10 PeV).     

Signatures of the Unruh effect via high-power, short-pulse lasers

The ultra-high fields of high-power short-pulse lasers are expected to contribute to understanding fundamental properties of the quantum vacuum and quantum theory in very strong fields. For example, the neutral QED vacuum breaks down at the Schwinger field strength of 1.3×10¹⁸ V/m, where a virtual e⁺e^- pair gains its rest mass energy over a Compton wavelength and materializes as a real pair. At such an ultra-high field strength, an electron experiences an acceleration of a_S=2×10²⁸g and hence fundamental phenomena such as the long predicted Unruh effect start to play a role. The Unruh effect implies that the accelerated electron experiences the vacuum as a thermal bath with the Unruh temperature. In its accelerated frame the electron scatters photons off the thermal bath, corresponding to the emission of an entangled pair of photons in the laboratory frame. While it remains an experimental challenge to reach the critical Schwinger field strength within the immediate future even in view of the enormous thrust in high-power laser developments in recent years, the near-future laser technology may allow to probe the signatures of the Unruh effect mentioned above. Using a laser-accelerated electron beam (γ～300) and a counter-propagating laser beam acting as optical undulator should allow to create entangled Unruh photon pairs (i.e., signatures of the Unruh effect) with energies of the order of several hundred keV. An even substantially improved experimental scenario can be realized by using a brilliant 20 keV photon beam as X-ray undulator together with a low-energy (γ≈2) electron beam. In this case the separation of the Unruh photon pairs from background originating from linearly accelerated electrons (classical Larmor radiation) is significantly improved. Detection of the Unruh photons may be envisaged by Compton polarimetry in a 2D-segmented position-sensitive germanium detector.     

On EAS spectrum with extremely low content of hadrons in the primary-energy range ∼10<Superscript>14</Superscript>−10<Superscript>15</Superscript> eV

The distribution of energy fluxes of the hadron component of extensive air showers through an ion-ization calorimeter in the primary-energy range ～3 × 10¹³?10¹⁶ eV is considered. Extensive air showers with zero and minimum energy fluxes of the hadron component are selected. It is concluded that the primary-energy range E ₀ ≈ 1 × 10¹⁴?2 × 10¹⁵ eV contains isotropic γ radiation with a spectrum close to bell-shaped, having a maximum near E ₀ ≈ 2.2 × 10¹⁴ eV and an additional peak near E ₀ ≈ 1.6 × 10¹⁵ eV.     

Klein paradox in a kerr geometry

The crossing of the classical positive and negative energy states E⁺ and E^? introduced by Christodoulou-Ruffini and interpreted within the framework of a relativistic quantum field theory by Deruelle and Ruffini, leads to a Klein paradox. It has been shown by Euler and Heisenberg that when the transmission coefficient T² through the barrier between the E⁺ and E^? states is small it is proportional to the probability of pair creation. Numerical computations show that, in the case of a small Kerr black hole (GM/c² ??/muc), the probability of pair creation of particles of mass μ is maximum when $\text{E ～ ?Ω}$, where E is the energy of the created particles and Ω and M the angular velocity and the mass of the back hole.     

The Schwinger effect and possibilities for its observation using optical and X-ray lasers

The probability W of e ⁺ e ^? pair production from a vacuum in an intense variable electric field generated with powerful optical or X-ray lasers is calculated. Two characteristic ranges are considered: γ ? 1 and γ ? 1, where γ is the adiabaticity parameter. The probability W is shown to increase sharply with γ (at a fixed field strength F). The dependence of W and the momentum spectrum of electrons and positrons on the laser pulse shape is discussed in detail. Numerical calculations were performed for a laser pulse with a Gaussian envelope and for some pulsed fields.     

Pair creation by a photon in an electric field

The process of pair creation by a photon in a constant and homogeneous electric field is investigated basing on the polarization operator in the field. The total probability of the process is found in a relatively simple form. At high energy the quasiclassical approximation is valid. The corrections to the standard quasiclassical approximation (SQA) are calculated. In the region of relatively low photon energies, where SQA is unapplicable, the new approximation is used. It is shown that in this energy interval the probability of pair creation by a photon in electric field exceeds essentially the corresponding probability in a magnetic field. This approach is valid at the photon energy much larger than the “vacuum” energy in electric field: ω?eE/m. For smaller photon energies the low energy approximation is developed. At ω?eE/m the found probability describes the absorption of soft photon by the particles created by an electric field.     

Neutrino Self-Energy and Index of Refraction in Strong Magnetic Field: A New Approach

The Ritus E_p eigenfunction method is extended to the case of spin-1 charged particles in a constant electromagnetic field and used to calculate the one-loop neutrino self-energy in the presence of a strong magnetic field. From the obtained self-energy, the neutrino dispersion relation and index of refraction in the magnetized vacuum are determined within the field range m²_e?eB?M²_W. The propagation of neutrinos in the magnetized vacuum is anisotropic due to the dependence of the index of refraction on the angle between the directions of the neutrino momentum and the external field. Possible cosmological implications of the results are discussed.     

QED corrections to the forward backward asymmetry with extraZ bosons fore + e −→f + f −

The complete standard model corrections together with the QED contributions from an additionalZ boson to the forward backward asymmetry of the reactione ⁺ e ^?→(ψ,Z, Z′, ...)→f ⁺ f ⁺ are calculated. They include soft photon exponentiation and a cut on the photon energy. Some numerical applications are considered forE ₆ generated extraZ bosons. Though being small at TRISTAN and LEP1 energies, the QED corrections due toZ′ exchange are very important near and above theZ′ peak.     

An investigation of the processes e+e−→μ+μ−γ and e+e−→e+e−γ

The reactions e⁺e^?→μ⁺μ^?γ and e⁺e^?→e⁺e^?γ have been studied with the CELLO detector at the PETRA storage ring. Data have been collected from $\text{s}\text{=14}\text{GeV up to}\text{46.8}\text{GeV}$. In a Dalitz plot analysis of the data, good agreement is found with QED, except for the region Mx_μγe>0.8 where the probability that QED describes the high energy data is at the percent level.     

Production of high-energy muons in gamma showers

We have calculated the number of high-energy muons in gamma showers generated by photoproduction and by muon pair creation. The prompt muons have flatter energy spectrum than the muons, which come from photoproduction and contribute significant fraction of the total muon rates for E_μ ? 1 TeV. The total rate of high-energy muons in gamma showers is, however, very low.     

Heavy ion e+e− pairs to all orders in Zα

The heavy ion cross section for continuum e⁺e^? pair production has been calculated to all orders in Zα. Comparison is made with available CERN SPS and RHIC STAR data. Computed cross sections are found to be reduced from perturbation theory with increasing charge of the colliding heavy ions and for all energy and momentum regions investigated. Au or Pb total cross sections are reduced by 28% (SPS), 17% (RHIC) and 11% (LHC). For very high energy (E _e ⁺, E _e ^?>3 GeV) forward pairs at LHC the reduction from perturbation theory is a bit larger (17%). Use of zero degree calorimeter triggering (and thus small impact parameter weighting) makes impact parameter representation of exact pair production useful. Preliminary exact calculations in the zero impact parameter limit show a much larger reduction from perturbation theory (about 40%) at both RHIC and LHC.     

Fully quantum treatment of the Landau-Pomeranchik-Migdal effect in QED and QCD

A rigorous quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD is given for the first time. The rate of photon (gluon) radiation by an electron (quark) in a medium is expressed in terms of the Green’s function of a two-dimensional Schrödinger equation with an imaginary potential. In QED this potential is proportional to the dipole cross section for scattering of an e ⁺ e ^? pair off an atom, while in QCD it is proportional to the cross section of interaction of the color singlet quark-antiquark-gluon system with a color center.     

X-ray spectroscopic diagnostics of ultrashort laser-cluster interaction at the stage of the nonadiabatic scattering of clusters

X-ray spectroscopic diagnostics of laser-cluster interaction at the stage of nonadiabatic scattering of clusters and formation of a spatially uniform plasma channel has been performed. The experimental investigations have been carried out on a Ti:Sa laser setup with a pulse duration of about 65 fs and an energy up to 600 mJ. It has been shown that, within 10 ps from the beginning of a laser femtosecond pulse, the laser-cluster interaction forms a uniform plasma channel with a length of 0.4 to 1 mm with the parameters N _e ～ 10¹⁹?10²⁰ cm^?3 and T _e ～ 100 eV.     

Spatial distribution of EAS radio emission at 32 MHz

The results of the reprocessing of the experimental data on radio emission from extensive air showers (EAS) earlier obtained at the EAS facility (Moscow State University) are reported. The maximum depth distribution of showers is found from analysis of the width of the spatial distribution of radio emission. The average maximum depth is X _max = 655 ± 8 g/cm² for the primary particle energy E ₀ ～ (3–4) × 10¹⁷ eV. The normalized field strength at E ₀ = 10¹⁷ eV is 3.2 ± 0.6 and 2.8 ± 0.4 μV/(m MHz) at distances of 50 and 100 m from the axis, respectively. The accuracy of E ₀ determination from the radio emission field strength at 50 m from the axis is about 20%.     

QED polarization asymmetries fore + e − scattering due to helicity flips

The polarization asymmetries for thee ⁺ e ^? scattering with polarized incoming and outgoing beams, which are proportional to the amplitudes? ₅ describing one helicity flip and? ₅ describing two helicity flips, have been calculated including their pure QED radiative corrections. These asymmetries are partly large and can be observed well at low energies.