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We propose a new model of nonlinear electrodynamics with three parameters. Born-Infeld electrodynamics and exponential electrodynamics are particular cases of this model. The phenomenon of vacuum birefringence is studied. We show that there is not singularity of the electric field at the origin of point-like charged particles. The corrections to Coulomb's law at $r\rightarrow\infty$ are obtained. We calculate the total electrostatic energy of charges for different parameters of the model which is finite., Comment: 13 pages, 1 figure, 1 table, extended journal version, to appear in MPLA

An exponential model of nonlinear electrodynamics coupled with the gravitational field is analyzed. It was shown that weak, dominant, and strong energy conditions are satisfied. We obtain corrections to Coulomb's law at $r\rightarrow\infty$. It was demonstrated that electric-magnetic duality between ${\cal F}$ and ${\cal P}$ frames is violated. The asymptotic black hole solution at $r\rightarrow \infty$ is found that contains corrections to the Reissner-Nordstr\"om solution. The electromagnetic mass of the black hole is calculated, expressed through the parameter $\beta$ of the model., Comment: 12 pages, 2 figures, to appear in Europhys. Letters

A model of nonlinear electrodynamics coupled with the gravitational field is studied. We obtain the asymptotic black hole solutions at $r\rightarrow 0$ and $r\rightarrow \infty$. The asymptotic at $r\rightarrow 0$ is shown, and we find corrections to the Reissner-Nordstr\"om solution and Coulomb's law at $r\rightarrow\infty$. The mass of the black hole is evaluated having the electromagnetic origin. We investigate the thermodynamics of charged black holes and their thermal stability. The critical point corresponding to the second-order phase transition (where heat capacity diverges) is found. If the mass of the black hole is greater than the critical mass, the black hole becomes unstable., Comment: 16 pages, 6 figures

A model of nonlinear electrodynamics with the Lagrangian density ${\cal L} = -(1/\beta)\arcsin(\beta F_{\mu\nu}F^{\mu\nu}/4)$ is proposed. The scale invariance and the dual invariance of electromagnetic fields are broken in the model. In the limit $\beta\rightarrow 0$ one comes to Maxwell's electrodynamics and the scale and dual invariances are recovered. We investigate the effect of coupling electromagnetic fields with the gravitational field. The asymptotic black hole solution is found which is similar to the Reissner-Nordstr\"om solution. We obtain corrections to Coulomb's law and to the Reissner-Nordstr\"om solution in the model proposed. The existence of the regular asymptotic at $r\rightarrow 0$ was demonstrated. The mass of the black hole is calculated possessing the electromagnetic origin. It was shown that there are not superluminal fluctuations and principles of causality and unitarity take place., Comment: 19 pages, 4 figures, to appear in Ann. Phys. (Berlin)

A model of nonlinear electromagnetic fields with a dimensional parameter $\beta$ is proposed. From PVLAS experiment the bound on the parameter $\beta$ was obtained. Electromagnetic fields are coupled with the gravitation field and we show that the universe accelerates due to nonlinear electromagnetic fields. The magnetic universe is considered and the stochastic magnetic field is a background. After inflation the universe decelerates and approaches to the radiation era. The range of the scale factor, when the causality of the model and a classical stability take place, was obtained. The spectral index, the tensor-to-scalar ratio, and the running of the spectral index were estimated which are in approximate agreement with the PLANCK, WMAP, and BICEP2 data., Comment: 20 pages, 4 figures, to appear in IJMPA

A new model of nonlinear electromagnetic fields possessing a dimensional parameter $\beta$ is proposed. Electromagnetic fields are considered as the source of the gravitation field and accelerated expansion of the universe is driven by nonlinear electromagnetic fields. We consider the magnetic universe and the stochastic magnetic field is a source of the universe acceleration. After the universe inflation and the accelerated expansion the universe decelerates. We show the causality of the model and a classical stability at the deceleration phase. The spectral index, the tensor-to-scalar ratio, and the running of the spectral index were estimated that approximately fulfil the PLANK, WMAP, and BICEP2 data., Comment: 19 pages, 7 figures

A new model of nonlinear electrodynamics with a dimensional parameter $\beta$ coupled to gravity is considered. We show that an accelerated expansion of the universe takes place if the nonlinear electromagnetic field is the source of the gravitational field. A pure magnetic universe is investigated and the magnetic field drives the universe to accelerate. In this model, after the big bang, the universe undergoes inflation, and the accelerated expansion and then decelerates approaching Minkowski spacetime asymptotically. We demonstrate the causality of the model and a classical stability at the deceleration phase., Comment: 12 pages, 1 figure

A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter $\gamma$ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested. We have investigated the gauge covariant quantization of the nonlinear electrodynamics fields as well as the gauge fixing approach based on Dirac's brackets., Comment: 17 pages, 1 figure, minor corrections, to be published in Commun.Theor.Phys

An $arctan$-electrodynamics coupled with the gravitational field is investigated. We obtain the regular black hole solution that at $r\rightarrow \infty$ gives corrections to the Reissner-Nordstr\"om solution. The corrections to Coulomb's law at $r\rightarrow\infty$ are found. We evaluate the mass of the black hole that is a function of the dimensional parameter $\beta$ introduced in the model. The magnetically charged black hole was investigated and we have obtained the magnetic mass of the black hole and the metric function at $r\rightarrow \infty$. The regular black hole solution is obtained at $r\rightarrow 0$ with the de Sitter core. We show that there is no singularity of the Ricci scalar for electrically and magnetically charged black holes. Restrictions on the electric and magnetic fields are found that follow from the requirement of the absence of superluminal sound speed and the requirement of a classical stability., Comment: 17 pages, 4 figures, journal version

Photoproduction of $\pi\eta$-pairs from nucleons has been investigated from threshold up to incident photon energies of $\approx$~1.4~GeV. The quasi-free reactions $\gamma p\rightarrow p\pi^0\eta$, $\gamma n\rightarrow n\pi^0\eta$, $\gamma p\rightarrow n\pi^+\eta$, and $\gamma n\rightarrow p\pi^-\eta$ were for the first time measured from nucleons bound in the deuteron. The corresponding reactions from a free-proton target were also studied to investigate final-state interaction effects (for neutral pions the free-proton results could be compared to previous measurements; the $\gamma p\rightarrow n\pi^+\eta$ reaction was measured for the first time). For the $\pi^0\eta$ final state coherent production via the $\gamma d\rightarrow d\pi^0\eta$ reaction was also investigated. The experiments were performed at the tagged photon beam of the Mainz MAMI accelerator using an almost $4\pi$ coverage electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. The total cross sections for the four different final states obey the relation $\sigma(p\pi^0\eta)$ $\approx$ $\sigma(n\pi^0\eta)$ $\approx$ $2\sigma(p\pi^-\eta)$ $\approx$ $2\sigma(n\pi^+\eta)$ as expected for a dominant contribution from a $\Delta^{\star}\rightarrow\eta\Delta(1232)\rightarrow\pi\eta N$ reaction chain, which is also supported by the shapes of the invariant-mass distributions of nucleon-meson and $\pi$-$\eta$ pairs. The experimental results are compared to the predictions from an isobar reaction model., Comment: accepted for publication in Phys. Lett. B

The new model of modified $F(R)$ gravity theory with the function $F(R) = R+(a/\gamma) \arcsin(\gamma R)$ is suggested and investigated. Constant curvature solutions corresponding to the extremum of the effective potential are obtained. We consider both the Jordan and Einstein frames, and the potential and the mass of the scalar degree of freedom are found. It was shown that the de Sitter space-time is unstable but the flat space-time is stable. We calculate the slow-roll parameters $\epsilon$, $\eta$, and the $e$-fold number of the model. Critical points of autonomous equations for the de Sitter phase and the matter dominated epoch are obtained and learned., Comment: 16 pages, 8 figures, accepted for publication in IJGMMP

We investigate a new model of nonlinear electromagnetic field coupled with the gravitation field. The black hole solution is obtained possessing the asymptotic Reissner-Nordstr\"om solution. The electric field has the finite value at the origin and there are not singularities., Comment: 8 pages, 1 figure, accepted for publication in IJGMMP

A new model of nonlinear electrodynamics with three parameters is suggested. The phenomena of vacuum birefringence takes place when there is the external constant magnetic field. We calculate the indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field. From the Bir\'{e}fringence Magn\'{e}tique du Vide (BMV) experiment one of the coefficients, $\gamma\approx 10^{-20}$ T$^{-2}$, was estimated. The canonical, symmetrical Belinfante energy-momentum tensors and dilatation current were obtained. The dilatation symmetry and the dual symmetry are broken in the model considered., Comment: 9 pages, no figures, accepted for publication in Phys.Lett.A

We propose a new model of modified $F(R)$ gravity theory with the function $F(R) = (1/\beta) \arcsin(\beta R)$. Constant curvature solutions corresponding to the flat and de Sitter spacetime are obtained. The Jordan and Einstein frames are considered; the potential and the mass of the scalar degree of freedom are found. We show that the flat spacetime is stable and the de Sitter spacetime is unstable. The slow-roll parameters $\epsilon$, $\eta$, and the $e$-fold number of the model are evaluated in the Einstein frame. The index of the scalar spectrum power-law $n_s$ and the tensor-to-scalar ratio $r$ are calculated. Critical points of autonomous equations for the de Sitter phase and the matter dominated epoch are found and studied. We obtain the approximate solution of equations of motion which is the deviation from the de Sitter phase in the Jordan frame. It is demonstrated that the model passes the matter stability test., Comment: 19 pages, 8 figures, extended version, accepted for publication in Astrophysics and Space Science

The generalized logarithmic electrodynamics with two parameters $\beta$ and $\gamma$ is considered. The indexes of refraction of light in the external magnetic field are calculated. In the case $\beta=\gamma$ we come to results obtained by P. Gaete and J. Helay\"el-Neto [7] (Eur.Phys.J. C\textbf{74}, 2816 (2014)). The bound on the values of $\beta$, $\gamma$ was obtained from the Bir\'efringence Magn\'etique du Vide (BMV) experiment. The symmetrical Belinfante energy-momentum tensor and dilatation current are found., Comment: 7 pages, no figures, changed title, corrected typo in Eq. 11

A new model of nonlinear electrodynamics with three parameters is suggested and investigated. It is shown that if the external constant magnetic field presents the phenomenon of vacuum birefringence takes place. The indexes of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field are calculated. The electric field of a point-like charge is not singular at the origin and the static electric energy is finite. We have calculated the static electric energy of point-like particles for different parameters of the model. The canonical and symmetrical Belinfante energy-momentum tensors and dilatation current are obtained. We demonstrate that the dilatation symmetry and dual symmetry are broken in the model suggested., Comment: 10 pages, 1 figure, accepted for publication in Ann. Phys. (Berlin)

A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy-momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles., Comment: 12 pages, 1 figure, substantial changes, journal version, to be published in Ann.Phys

We investigate the radiation of spin-1 particles by black holes in (1+1) dimensions within the Proca equation. The process is considered as quantum tunnelling of bosons through an event horizon. It is shown that the emission temperature for the Schwarzschild background geometry is the same as the Hawking temperature corresponding to scalar particles emission. We also obtain the radiation temperatures for the de Sitter, Rindler and Schwarzschild-de Sitter space-times. In a particular case when two horizons in Schwarzschild-de Sitter space-time coincides the Nariai temperature is recovered. The thermodynamical entropy of a black hole is calculated for Schwarzschild-de Sitter space-time having two horizons., Comment: 13 pages, 2 figures

Differential and total cross sections for the quasifree reactions $\gamma p\rightarrow\eta p$ and $\gamma n\rightarrow\eta n$ have been determined at the MAMI-C electron accelerator using a liquid deuterium target. Photons were produced via bremsstrahlung from the 1.5 GeV incident electron beam and energy-tagged with the Glasgow photon tagger. Decay photons of the neutral decay modes $\eta\rightarrow 2\gamma$ and $\eta\rightarrow 3\pi^0 \rightarrow 6\gamma$ and coincident recoil nucleons were detected in a combined setup of the Crystal Ball and the TAPS calorimeters. The $\eta$-production cross sections were measured in coincidence with recoil protons, recoil neutrons, and in an inclusive mode without a condition on recoil nucleons, which allowed a check of the internal consistency of the data. The effects from nuclear Fermi motion were removed by a kinematic reconstruction of the final-state invariant mass and possible nuclear effects on the quasifree cross section were investigated by a comparison of free and quasifree proton data. The results, which represent a significant improvement in statistical quality compared to previous measurements, agree with the known neutron-to-proton cross-section ratio in the peak of the $S_{11}(1535)$ resonance and confirm a peak in the neutron cross section, which is absent for the proton, at a center-of-mass energy $W = (1670\pm 5)$ MeV with an intrinsic width of $\Gamma\approx 30$ MeV.

An experimental study of $\omega$ photoproduction on the proton was conducted by using the Crystal Ball and TAPS multiphoton spectrometers together with the photon tagging facility at the Mainz Microtron MAMI. The $\gamma p\to\omega p$ differential cross sections are measured from threshold to the incident-photon energy $E_\gamma=1.40$ GeV ($W=1.87$ GeV for the center-of-mass energy) with 15-MeV binning in $E_\gamma$ and full production-angle coverage. The quality of the present data near threshold gives access to a variety of interesting physics aspects. As an example, an estimation of the $\omega N$ scattering length $\alpha_{\omega p}$ is provided., Comment: 8 pages, 5 figures. Published version; some typos were fixed

A new measurement of the rare, doubly radiative decay eta->pi^0 gamma gamma was conducted with the Crystal Ball and TAPS multiphoton spectrometers together with the photon tagging facility at the Mainz Microtron MAMI. New data on the dependence of the partial decay width, Gamma(eta->pi^0 gamma gamma), on the two-photon invariant mass squared, m^2(gamma gamma), as well as a new, more precise value for the decay width, Gamma(eta->pi^0 gamma gamma) = (0.33+/-0.03_tot) eV, are based on analysis of 1.2 x 10^3 eta->pi^0 gamma gamma decays from a total of 6 x 10^7 eta mesons produced in the gamma p -> eta p reaction. The present results for dGamma(eta->pi^0 gamma gamma)/dm^2(gamma gamma) are in good agreement with previous measurements and recent theoretical calculations for this dependence., Comment: 10 pages, 8 figures, 1 table

The radiation of vector particles by black holes in (1+2) dimensions is investigated within the WKB approximation. We consider the process of quantum tunnelling of bosons through an event horizon of the black hole. The emission temperature for the Schwarzschild background geometry coincides with the Hawking temperature and for the Rindler spacetime the temperature is the Unruh temperature. We also obtain the radiation temperatures for the de Sitter spacetime., Comment: 7 pages, no figures, journal version

Precise angular distributions have been measured for the first time for the photoproduction of $\pi^{0}$-mesons off neutrons bound in the deuteron. The effects from nuclear Fermi motion have been eliminated by a complete kinematic reconstruction of the final state. The influence of final-state-interaction effects has been estimated by a comparison of the reaction cross section for quasi-free protons bound in the deuteron to the results for free protons and then applied as a correction to the quasi-free neutron data. The experiment was performed at the tagged photon facility of the Mainz Microtron MAMI with the Crystal Ball and TAPS detector setup for incident photon energies between $0.45$~GeV and $1.4$~GeV. The results are compared to the predictions from reaction models and partial-wave analyses based on data from other isospin channels. The model predictions show large discrepancies among each other and the present data will provide much tighter constraints. This is demonstrated by the results of a new analysis in the framework of the Bonn-Gatchina coupled-channel analysis which included the present data., Comment: accepted for publication in Phys; Rev. Lett

Beam-helicity asymmetries have been measured at the MAMI accelerator in Mainz for the photoproduction of mixed-charge pion pairs in the reactions $\boldsymbol{\gamma}p\rightarrow n\pi^0\pi^+$ off free protons and $\boldsymbol{\gamma}d\rightarrow (p)p\pi^0\pi^-$ and $\boldsymbol{\gamma}d\rightarrow (n)n\pi^0\pi^+$ off quasi-free nucleons bound in the deuteron for incident photon energies up to 1.4 GeV. Circularly polarized photons were produced from bremsstrahlung of longitudinally polarized electrons and tagged with the Glasgow-Mainz magnetic spectrometer. The charged pions, recoil protons, recoil neutrons, and decay photons from $\pi^0$ mesons were detected in the 4$\pi$ electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. Using a complete kinematic reconstruction of the final state, excellent agreement was found between the results for free and quasi-free protons, suggesting that the quasi-free neutron results are also a close approximation of the free-neutron asymmetries. A comparison of the results to the predictions of the Two-Pion-MAID reaction model shows that the reaction mechanisms are still not well understood, in particular at low incident photon energies in the second nucleon-resonance region., Comment: accepted for publication in Eur. phys. J. A

We investigate the modified $F(R)$ gravity theory with the function $F(R) = (1-\sqrt{1-2\lambda R-\sigma (\lambda R)^2})/\lambda$. The action is converted into Einstein$-$Hilbert action at small values of $\lambda$ and $\sigma$. The local tests give a bound on the parameters, $\lambda(1+\sigma)\leq 2\times 10^{-6}$ cm$^2$. The Jordan and Einstein frames are considered, the potential, and the mass of the scalar field were obtained. The constant curvature solutions of the model are found. It was demonstrated that the de Sitter space is unstable but a solution with zero Ricci scalar is stable. The cosmological parameters of the model are evaluated. Critical points of autonomous equations are obtained and described., Comment: 21 pages, 10 figures, added references, journal version, accepted for publication in Astrophys. Space Sci

The modified Dirac equations describing massless and massive spin-1/2 particles violating the Lorentz invariance are considered. The equation for massless fermions with varying speed is formulated in the 16-component first-order form. The projection matrix, which is the density matrix, extracting solutions to the equation has been obtained. Exact solutions to the equation and energy spectrum for a massive neutrino are obtained in the presence of background matter. We have considered as subluminal as well as superluminal propagations of neutrinos. The bounds on the Lorentz invariance violation parameter from astrophysical observations by IceCube, OPERA, MINOS collaborations and by the SN1987A supernova are obtained for superluminal neutrinos., Comment: 16 pages, no figures, minor corrections

Quasi-free photoproduction of $\eta$-mesons has been measured off nucleons bound in $^3$He nuclei for incident photon energies from the threshold region up to 1.4 GeV. The experiment was performed at the tagged photon facility of the Mainz MAMI accelerator with an almost $4\pi$ covering electromagnetic calorimeter, combining the TAPS and Crystal Ball detectors. The $\eta$-mesons were detected in coincidence with the recoil nucleons. This allowed a comparison of the production cross section off quasi-free protons and quasi-free neutrons and a full kinematic reconstruction of the final state, eliminating effects from nuclear Fermi motion. In the $S_{11}$(1535) resonance peak, the data agree with the neutron/proton cross section ratio extracted from measurements with deuteron targets. More importantly, the prominent structure observed in photoproduction off quasi-free neutrons bound in the deuteron is also clearly observed. Its parameters (width, strength) are consistent with the expectations from the deuteron results. On an absolute scale the cross sections for both quasi-free protons and neutrons are suppressed with respect to the deuteron target pointing to significant nuclear final state interaction effects., Comment: accepted for publication in Eur. Phys. J. A

The photoproduction of $\eta$-mesons off nucleons bound in $^2$H and $^3$He has been measured in coincidence with recoil protons and recoil neutrons for incident photon energies from threshold up to 1.4 GeV. The experiments were performed at the Mainz MAMI accelerator, using the Glasgow tagged photon facility. Decay photons from the $\eta\rightarrow 2\gamma$ and $\eta\rightarrow 3\pi^0$ decays and the recoil nucleons were detected with an almost $4\pi$ electromagnetic calorimeter combining the Crystal Ball and TAPS detectors. The data from both targets are of excellent statistical quality and show a narrow structure in the excitation function of $\gamma n\rightarrow n\eta$. The results from the two measurements are consistent taking into account the expected effects from nuclear Fermi motion. The best estimates for position and intrinsic width of the structure are $W$ = (1670$\pm$5) MeV and $\Gamma$ =(30$\pm$15) MeV. For the first time precise results for the angular dependence of this structure have been extracted., Comment: Accepted for publication in Phys. Rev. Lett

A novel theory of $F(R)$ gravity with the Lagrangian density ${\cal L}=[R-(b/\beta)\arctan\left(\beta R\right)]/(2\kappa^2)$ is analyzed. Constant curvature solutions of the model are found, and the potential of the scalar field and the mass of a scalar degree of freedom in Einstein's frame are derived. The cosmological parameters of the model are calculated, which are in agreement with the PLANCK data. Critical points for the de Sitter phase and the matter dominated epoch of autonomous equations are obtained and studied., Comment: 8 pages, 8 figures, minor corrections, journal version

We report the first large-acceptance measurement of polarization transfer from a polarized photon beam to a recoiling nucleon, pioneering a novel polarimetry technique with wide application to future nuclear and hadronic physics experiments. The commissioning measurement of polarization transfer in the $^{1}H$($\vec{\gamma}$,$\vec{p}$)$\pi^{0}$ reaction in the range $0.4

The Dalitz decay eta -> e^+ e^- gamma has been measured in the gamma p -> eta p reaction with the Crystal Ball and TAPS multiphoton spectrometers, together with the photon tagging facility at the Mainz Microtron MAMI. The experimental statistic used in this work is one order of magnitude greater than in any previous measurement of eta -> e^+ e^- gamma. The value obtained for the slope parameter 1/Lambda^2 of the eta transition form factor, 1/Lambda^2 = (1.95 +/- 0.15_stat +/- 0.10_syst) [1/GeV^2], is in good agreement with recent measurements conducted in eta -> e^+ e^- gamma and eta -> mu^+ mu^- gamma decays, as well as with recent form-factor calculations. The uncertainty obtained in the value of 1/Lambda^2 is lower compared to results from previous measurements of the eta -> e^+ e^- gamma decay., Comment: 11 pages, 10 figures, 1 table

Measurements of $\gamma p \rightarrow K^{+} \Lambda$ and $\gamma p \rightarrow K^{+} \Sigma^0$ cross-sections have been obtained with the photon tagging facility and the Crystal Ball calorimeter at MAMI-C. The measurement uses a novel $K^+$ meson identification technique in which the weak decay products are characterized using the energy and timing characteristics of the energy deposit in the calorimeter, a method that has the potential to be applied at many other facilities. The fine center-of-mass energy ($W$) resolution and statistical accuracy of the new data results in a significant impact on partial wave analyses aiming to better establish the excitation spectrum of the nucleon. The new analyses disfavor a strong role for quark-diquark dynamics in the nucleon., Comment: 7 pages, 8 figures

The g p -> K^0 Sigma^+ reaction has been measured from threshold to Eg=1.45 GeV (W_cm=1.9 GeV) using the Crystal Ball and TAPS multiphoton spectrometers together with the photon tagging facility at the Mainz Microtron MAMI. In the present experiment, this reaction was searched for in the 3pi^0 p final state, by assuming K^0_S -> pi^0 pi^0 and Sigma^+ -> pi^0 p. The experimental results include total and differential cross sections as well as the polarization of the recoil hyperon. The new data significantly improve empirical knowledge about the g p -> K^0 Sigma^+ reaction in the measured energy range. The results are compared to previous measurements and model predictions. It is demonstrated that adding the present g p -> K^0 Sigma^+ results to existing data allowed a better description of this reaction with various models., Comment: 12 pages, 10 figures, 4 tables

Beam-helicity asymmetries have been measured at the MAMI accelerator in Mainz for the photoproduction of neutral pion pairs in the reactions $\vec{\gamma}p\rightarrow p\pi^0\pi^0$ and $\vec{\gamma}d\rightarrow (n)p\pi^0\pi^0$, $\vec{\gamma}d\rightarrow (p)n\pi^0\pi^0$ off free protons and off quasi-free nucleons bound in the deuteron for incident photon energies up to 1.4 GeV. Circularly polarized photons were produced from bremsstrahlung of longitudinally polarized electrons and tagged with the Glasgow magnetic spectrometer. Decay photons from the $\pi^0$ mesons, recoil protons, and recoil neutrons were detected in the 4$\pi$ covering electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. After kinematic reconstruction of the final state, excellent agreement was found between the results for free and quasi-free protons. This demonstrates that the free-nucleon behavior of such observables can be extracted from measurements with quasi-free nucleons, which is the only possibility for the neutron. Contrary to expectations, the measured asymmetries are very similar for reactions off protons and neutrons. The results are compared to the predictions from the Two-Pion-MAID reaction model and (for the proton) also to the Bonn-Gatchina coupled channel analysis., Comment: accepted for publication in Phys. Lett. B

The wave equation for spin-0 massless particles with the Lorentz violating term leading to varying speed of particles is considered. This equation is represented as the first-order 6$\times$6 matrix equation. Solutions of the equation in the form of projection matrix are obtained. The Schr\"{o}dinger form of the equation is obtained and the quantum-mechanical Hamiltonian is found., Comment: 9 pages, no figures, to appear in EPL

A precision measurement of the differential cross sections $d\sigma/d\Omega$ and the linearly polarized photon asymmetry $\Sigma \equiv (d\sigma_\perp - d\sigma_\parallel) \slash (d\sigma_\perp + d\sigma_\parallel)$ for the $\vec{\gamma} p \rightarrow \pi^0p$ reaction in the near-threshold region has been performed with a tagged photon beam and almost $4\pi$ detector at the Mainz Microtron. The Glasgow-Mainz photon tagging facility along with the Crystal Ball/TAPS multi-photon detector system and a cryogenic liquid hydrogen target were used. These data allowed for a precise determination of the energy dependence of the real parts of the $S$- and all three $P$-wave amplitudes for the first time and provide the most stringent test to date of the predictions of Chiral Perturbation Theory and its energy region of agreement with experiment., Comment: 5 pages, 2 figures

The second-order modified Dirac equation leading to the modified dispersion relation due to the Lorentz invariance violation corrections is suggested. The equation is formulated in the 16-component first- order form. I have obtained the projection matrix extracting solutions of the equation with definite spin projections which can be considered as the density matrix for pure spin states. Exact solutions of the equation are found for particles in the external constant and uniform magnetic field. The synchrotron radiation radius within the novel modified Dirac equation is estimated., Comment: 11 pages, corrected typo in Eq.(10)

The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the density matrix is obtained. The Schr\"{o}dinger form of equations is presented and the quantum-mechanical Hamiltonian is found. Exact solutions of the wave equation are obtained for particles in the constant and uniform external magnetic field. The change of the synchrotron radiation radius due to quantum gravity corrections is calculated., Comment: 15 pages, no figures, extended journal version, accepted in MPLA

A modified theory of gravity with the function $F(R) = R\exp(\alpha R)$ instead of Ricci scalar $R$ in the Einstein$-$Hilbert action is considered and analyzed. The action of the model is converted into Einstein$-$Hilbert action at small value of the parameter $\alpha$. From local tests we obtain a bound on the parameter $\alpha\leq 10^{-6}$ cm$^2$. The Jordan and Einstein frames are investigated and the potential of the scalar field in Einstein's frame is found. The mass of a scalar degree of freedom as a function of curvature is obtained. The static solutions of the model are found corresponding to the Schwarzschild$-$de Sitter space. We show that the de Sitter space is unstable but a solution with zero curvature is stable. The cosmological parameters of the model are calculated. It was demonstrated that the model passes the matter stability test., Comment: 20 pages, 9 figures, changed title, extended version, added a section, figures and references, to be published in IJMPA

The gamma p --> pi0 pi0 p reaction has been measured from threshold to 1.4 GeV using the Crystal Ball and TAPS photon spectrometers together with the photon tagging facility at the Mainz Microtron. The experimental results include total and differential cross sections as well as specific angular distributions, which were used to extract partial-wave amplitudes. In particular, the energy region below the D13(1520) resonance was studied., Comment: 12 pages, 13 figures, corrected version, published in PRC

A modified theory of gravity with the function $F(R) = (1-\sqrt{1-2\lambda R})/\lambda$ is suggested and analyzed. At small value of the parameter $\lambda$ introduced the action is converted into Einstein$-$Hilbert action. The theory is consistent with local tests which gives a bound on the value of the parameter $\lambda\leq 2\times 10^{-6}$ cm$^2$. I have considered the Jordan frame as well as the Einstein frame in which the potential of the scalar field was obtained. The static Schwarzschild$-$de Sitter solutions of the model are obtained and analyzed. It was demonstrated that the de Sitter space is unstable but a solution with zero Ricci scalar is stable. It is shown that there is no matter instability in the proposed model., Comment: RevTex, 5 pages, one figure, minor corrections, references added, journal version, accepted in IJTP

Coherent photoproduction of $\eta$-mesons off $^3$He, i.e. the reaction $\gamma ^3{He}\rightarrow \eta ^3{He}$, has been investigated in the near-threshold region. The experiment was performed at the Glasgow tagged photon facility of the Mainz MAMI accelerator with the combined Crystal Ball - TAPS detector. Angular distributions and the total cross section were measured using the $\eta\rightarrow \gamma\gamma$ and $\eta\rightarrow 3\pi^0\rightarrow 6\gamma$ decay channels. The observed extremely sharp rise of the cross section at threshold and the behavior of the angular distributions are evidence for a strong $\eta {^3{He}}$ final state interaction, pointing to the existence of a resonant state. The search for further evidence of this state in the excitation function of $\pi^0$-proton back-to-back emission in the $\gamma ^3{He}\rightarrow \pi^0 pX$ reaction revealed a very complicated structure of the background and could not support previous conclusions., Comment: accepted for publication in Phys. Lett. B

We postulate the second-order derivative equation with four parameters for spin-1/2 fermions possessing two mass states. For some choice of parameters fermions propagate with the superluminal speed. Thus, the novel tachyonic equation is suggested. The relativistic 20-component first-order wave equation is formulated and projection operators extracting states with definite energy and spin projections are obtained. The Lagrangian formulation of the first-order equation is presented and the electric current and energy-momentum tensor are found. The minimal and non-minimal electromagnetic interactions of fermions are considered and Schr\"{o}dinger's form of the equation and the quantum-mechanical Hamiltonian are obtained. The canonical quantization of the field in the first-order formalism is performed and we find the vacuum expectation of chronological pairing of operators., Comment: 21 pages, minor corrections, journal version, accepted in IJMPA

The generalized Maxwell equations with arbitrary gauge parameter are considered in the $11\times 11$-matrix form. The gauge invariance of such a model is broken due to the presence of a scalar field. The canonical and symmetrical Belinfante energy-momentum tensors are found. The dilatation current is obtained and we demonstrate that the theory possesses the dilatation symmetry. The matrix Schr\"{o}dinger form of equations is derived. The non-minimal interaction in curved space-time is introduced and equations are considered in Friedmann - Robertson - Walker background. We obtain some solutions of equations for the vector field., Comment: 17 pages, typos corrected, extended version, references added

The total cross section for gamma p -> 3pi0 p has been measured for the first time from threshold to 1.4 GeV using the tagged photon beam of the Mainz Microtron. The equipment utilized the Crystal Ball multiphoton spectrometer, the TAPS forward detector and a particle identification detector. The gamma p -> 3pi0 p total cross section has two broad enhancements at sqrt{s}~1.5 GeV and 1.7 GeV. We obtained the ratio of the total cross sections gamma p -> 3pi0 p to gamma p -> eta p equal to 0.014 \pm 0.001 at sqrt{s}~1.5 GeV., Comment: submitted to Physical Review C

We find the canonical and Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken and the divergence of the dilatation current is proportional to the topological mass of the gauge field. It was demonstrated that the gauge field possesses the `scale dimensionality' d=1/2. Maxwell - Chern - Simons topologically massive gauge field theory in 2+1 dimensions is formulated in the first-order formalism. It is shown that 6x6-matrices of the relativistic wave equation obey the Duffin - Kemmer - Petiau algebra. The Hermitianizing matrix of the relativistic wave equation is given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin are obtained. The 5x5-matrix Schrodinger form of the equation is derived after the exclusion of non-dynamical components, and the quantum-mechanical Hamiltonian is obtained. Projection operators extracting physical states in the Schrodinger picture are found., Comment: 18 pages, correction in Ref. [5]