Search

Manifestation of the heavy 3/2-spin lepton $(h^\pm)$, as possible virtual intermediate state in Feynmann diagrams, have been searched in the $e^+\,e^-\to \gamma\,\gamma$ reaction at high energies and large photon angles. The spin-vector field $\Psi_\alpha$ of the 3/2-lepton is described by the Rarita-Schwinger one and phenomenological Lagrangian of $h^\pm\, e^\pm \, \gamma$-interaction is chosen similarly to interaction of $\Delta$ isobar with nucleon and $\gamma$ quant. It is described by two constants with dimension $[M^{-1}]$ and $[M^{-2}].$ The differential cross section and polarization asymmetries have been calculated for the case when both beams are polarized longitudinally along their directions, as well transversally, in the reaction plane, and normally, perpendicularly to it. Numerical estimations are performed in wide diapason of the collision energy and parameters entering phenomenological Lagrangian., Comment: 17 pages, 7 figures

The nonresonant mechanism in the reactions $e^+\,e^-\to \pi^-\,p\,\bar{n}$ and $e^+\,e^-\to \pi^+\,n\,\bar{p}$ is investigated in frame of the one-photon exchange approximation. The description of the hadronic phase space and the invariant amplitude formalism, earlier developed for the neutral pion channel, are applied here. Some modifications are required to fulfill the invariance and to account for an additional contribution due to diagram with the pion pole. Two different variants which lead to dipole and monopole asymptotic behaviour of the pion electromagnetic form factor, are considered. The double and single distributions over the invariant variables as well the total cross section, are obtained. The results are plotted for $s=$5,\,6,\,10,\,16\, GeV$^2$. The calculations are performed for the $\pi^-\,p\,\bar{n}$ channel and the rules to proceed to the $\pi^+\,n\,\bar{p}$ channel are formulated for every distribution., Comment: 30 pages, 9 figures

The dependence of the nucleon polarization in the reaction $e^+ + e^- \to N + \bar{N} +\pi^0 $ over different invariant variables in frame of the non-resonant mechanism, has been derived. The nucleon polarization is expressed in terms of six invariant complex amplitudes, assuming the conservation of the hadron electromagnetic currents and the P-invariance of the hadron electromagnetic interaction. An inclusive experimental setup when the proton (or the antiproton) and the pion are detected in coincidence is considered. Numerical estimations were performed for the so called normal polarization in the energy range from threshold up to $s=16$ GeV$^2$, using a specific parametrization of the nucleon electromagnetic form factors and taking into account the unpolarized differential cross section of the non-resonant mechanism, as previously calculated., Comment: 18 pages, 10 figures

The general analysis of the differential cross section and various polarization observables is performed for the process $e^+ + e^- \to N + \bar N +\pi^0 $ assuming that the annihilation occurs through the exchange of one virtual photon. The dependence of the differential distributions over invariant variables is derived for the reaction $e^+ + e^- \to N + \bar N +\pi^0 $ in the so-called non-resonant mechanism, applying the conservation of the hadron electromagnetic currents and the P-invariance of the hadron electromagnetic interaction. The detection in an exclusive experimental set up where the nucleon (or antinucleon) and pion are detected in coincidence is considered. A number of single and double differential distributions have been calculated analytically and numerical estimates are given for the $p\bar p\pi^0$ and $n\bar n\pi^0$ channels, in the Born (non-resonant) approximation, in the energy range from threshold up to $s=16$ GeV$^2$., Comment: 29 pages, 9 figures

We study features of tunneling dynamics in an exactly-solvable model of N=4 supersymmetric quantum mechanics with a multi-well potential and with broken reflective symmetry. Quantum systems with a phenomenological potential of this type demonstrate the phenomenon of partial localization of under-barrier states, possibly resulting in the appearance of the so-called "resonant" tunneling, or the phenomenon of coherent tunneling destruction, referring to the complete localization. Taking the partial localization and the coherent tunneling destruction as basic examples, we indicate main advantages of using isospectral exactly-solvable Hamiltonians in studies quantum mechanical systems with two- and three-well potentials. They, in particular, are: having enough freedom of changing the potential shape in a wide range, that allows one to choose an exactly-solvable model close to characteristics of the phenomenological one; ability of changing the number of local minima and symmetry characteristics of the potential (symmetric or deformed) without changing the main part of the spectrum; engaging a smart basis of states, that dramatically decreases the dimensionality of matrices used in the diagonalization procedure of the corresponding spectral problem., Comment: 32 pages, 10 Figs; v2: 29 pages, 10 Figs, corrected version; v3: 32 pages, improved Figs, published version

The triplet-like QED processes $\gamma + \ell_i \to \ell^+_j \ell^-_j + \ell_i$ with $i\neq j,$ and $i=e, \mu,$ $j=e, \mu,\tau$ has been investigated as the reactions where a dark photon, $A'$, is produced as a virtual state with subsequent decay into a $\ell^+_j \ell^-_j-$-pair. This effect arises due to the so-called kinetic mixing and is characterized by the small parameter $\epsilon$ describing the coupling strength relative to the electric charge $e$. The main advantage of searching $A'$ in these processes is that the background to the $A'$ signal is pure QED. Concerning $A'$, we consider its contribution in the Compton-type diagrams only since, in this case, the virtual dark photon has time-like nature and its propagator has the Breit-Wigner form. So, near the resonance, $A'$ can manifest itself. The contribution of $A'$ in the Borsellino diagrams is negligible since, in this case, the virtual dark photon is space-like, the $A'$ propagator does not peak and the effect is proportional, at least, to $\epsilon^2$. We calculate the distributions over the invariant mass of the produced $\ell^+_j \ell^-_j-$ pair and search for the kinematical region where the Compton-type diagrams contribution is not suppressed with respect to the Borsellino ones. The value of the parameter $\epsilon$ is estimated as a function of the dark photon mass for a given number of events., Comment: 27 pages, 13 figures, accepted for publication in Phys Rev D

The polarization effects in the one-meson radiative decay of the polarized $\tau$ lepton, $\tau^-\to\pi^-\gamma\nu_{\tau}$, have been investigated. We present the analytical results for the $t-$distribution of the partial differential widths, which responsible for different polarization phenomena, in the case of the photon energy cut: $\omega>X$. These quantities depend on the invariant mass squared $t$ of the pseudoscalar meson and photon and the photon energy cut $X.$ Our analytical formulae, in terms of the weak vector and axial-vector form factors, describing the structure-dependent part of the decay amplitude, are valid also for the decay $\tau^{\pm}\to K^{\pm}\,\nu_\tau\,\gamma$ after trivial substitutions of the corresponding constants. We demonstrate the essential decrease of the inner bremsstrahlung contribution in comparison with the structural one with increase of the photon cut energy. In numerical calculations the vector and axial-vector form factors are determined using the chiral effective theory with resonances (R$\chi$T)., Comment: 20 pages, 5 figures

The differential cross section for elastic scattering of deuterons on electrons at rest is calculated taking into account the QED radiative corrections to the leptonic part of interaction. These model-independent radiative corrections arise due to emission of the virtual and real soft and hard photons as well as to vacuum polarization. We consider an experimental setup where both final particles are recorded in coincidence and their energies are determined within some uncertainties. The kinematics, the cross section, and the radiative corrections are calculated and numerical results are presented., Comment: 18 pages, 10 figures, 3 tables. arXiv admin note: substantial text overlap with arXiv:1612.02139

The process of the triplet production on a free electron, $\gamma e^-\to e^+e^-e^-$, has been investigated as a reaction where a dark photon, $A'$, is produced as a virtual state with subsequent decay into a $e^+e^-$-pair. This effect arises due to the so-called kinetic mixing and is characterized by the small parameter $\epsilon$ describing the coupling strength relative to the electric charge e. The search of $A'$ in this process has advantage because the background to the $A'$ signal is pure QED. This QED background is described by eight Feynman diagrams taking into account the identity of final electrons. As concern $A'$, we leave its contribution in Compton-like diagrams only since, in this case, the virtual dark photon is time-like and its propagator has the Breit-Wigner form. So, near the resonance $A'$ can manifest itself. The contribution of $A'$ in Borsellino diagrams is negligible since, in this case, the virtual dark photon is space-like, the $A'$ propagator does not peak and effect is proportional at least to $\epsilon^2$. We calculate the distributions over the invariant masses of the both produced $e^+e^-$ pairs and search for the kinematical region where the Compton-like diagrams contribution is not suppressed as compared with the Borsellino one. We estimate what value of the parameter $\epsilon$, as a function of the dark photon mass, can be obtained at given number of the measured events., Comment: 24 pages, 7 figures

The emission of the hard photon by the initial state is considered. The nucleon polarization and the differential cross sections for some experimental conditions have been calculated. The case of the emission of the collinear (with respect to the direction of the electron beam momentum) photon is considered separately. The differential cross section, the nucleon polarization, the correlation coefficients for both polarized nucleons (provided the electron beam is unpolarized or longitudinally polarized), the transfer polarization from the longitudinally polarized electron beam to the nucleon have been calculated. The photon energy distribution for the reaction $e^+e^-\to h_1h_2\gamma $, where $h_1 $ and $h_2$ are some hadrons for the case of the collinear photon, emitted in the initial state, has been calculated. As $h_1h_2$ final state we considered some channels, namely: two spinless mesons (for example, $\pi^+\pi^-, K^+K^-$), two spin--one particles (for example, $\rho^+\rho^-, d\bar d$), the $\pi a_1(1260)$ and $\Delta(1232)\bar N$ channels. The photon energy distributions are calculated in terms of the form factors of the $\gamma^*\to h_1h_2$ transition ($\gamma^*$ is the virtual photon)., Comment: 24 pages, 1 figure, typos corrected, added references

The differential cross section for elastic scattering of protons on electrons at rest is calculated taking into account the QED radiative corrections to the leptonic part of interaction. These model-independent radiative corrections arise due to emission of the virtual and real soft and hard photons as well as to vacuum polarization. We analyze an experimental setup when both the final particles are recorded in coincidence and their energies are determined within some uncertainties. The kinematics, the cross section, and the radiative corrections are calculated and numerical results are presented., Comment: 27 pages, 10 figures. The title of the article has been changed. Improved the quality of figures. An article without an appendix is approved for publication in the Phys.Rev.C

Polarized and unpolarized observables in the process of the triplet photoproduction on a free electron, $\gamma +e\to e+e+e$, have been calculated in the laboratory system. These observables are calculated in the approximation when the Borsellino and $\gamma -e$ diagrams are taken into account. Using the method of the invariant integration over the produced electron-positron pair variables, the different distributions were obtained in the analytical form. We obtain the double distribution over the $q^2$ (the square of the four-momentum transfer to the recoil electron) and $Q^2$ (the created $e^+e^-$-pair invariant mass squared) variables, and single distributions over $q^2$ or $Q^2$ variables. We consider the following cases: unpolarized particles, the photon beam is linearly polarized and circularly polarized photon beam interacts with a polarized electron target. The influence of the $\gamma -e$ terms on the calculated observables has been investigated. The possibility to use this process for the measurement of the circular polarization of the high-energy photon beam is also considered. The numerical estimations of various polarization observables have been done., Comment: 34 pages,11 figures, new version with minor changes

Various distributions over the angles of the emitted photon, especially over the azimuthal angle, in the one-meson radiative decay of the polarized $\tau$ lepton, $\tau^-\to\pi^-\gamma\nu_{\tau}$, have been investigated. In connection with this, the photon phase space is discussed in more detail since in the case of the polarized $\tau$ lepton it is not trivial. The decay matrix element contains both the inner bremsstrahlung and the resonance (structural) contributions. The azimuthal dependence of some observables have been calculated. They are the asymmetry of the differential decay width caused by the $\tau$ lepton polarization, the Stokes parameters of the emitted photon itself and the correlation parameters describing the influence of $\tau$-lepton polarization on the photon Stokes parameters. The numerical estimation was done in the $\tau$ lepton rest frame for arbitrary direction of the $\tau$ lepton polarization 3-vector. The vector and axial-vector form factors describing the structure-dependent part of the decay amplitude are determined using the chiral effective theory with resonances (R$\chi$T). It was found that the features of the azimuthal distributions allows to separate various terms in the spin-dependent contribution. The so-called up-down and right-left asymmetries are also calculated., Comment: 29pages, 12 figures. To be published in JETP

The polarization effects in the one-meson radiative decay of the polarized $\tau$ lepton, $\tau^-\to\pi^-\gamma\nu_{\tau}$, are investigated. The inner bremsstrahlung and structural amplitudes are taken into account. The asymmetry of the differential decay width caused by the $\tau$ lepton polarization and the Stokes parameters of the emitted photon itself, are calculated depending on the polarization of the decaying $\tau$ lepton. The numerical estimation of these physical quantities was done for arbitrary direction of the $\tau$ lepton polarization 3-vector in the rest frame. The vector and axial-vector form factors describing the structure-dependent part of the decay amplitude are determined using the chiral effective theory with resonances (R$\chi$T)., Comment: 37 pages,7 figures

The possibility in principle of the determining high energy photon circular polarization by the measurement of the created electron polarization in the process of triplet photoproduction $\gamma +e^-\rightarrow e^+e^- +e^-$ is investigated. The respective event number which depend on polarization states of photon and created electron does not decrease with the growth of the photon energy, and this circumstance can ensure the high efficiency in such kind of experiments. We study different double and single distributions of the created electron (or positron), which allow to probe the photon circular polarization and to measure its magnitude (the Stock's parameter $\xi_2$), using the technique of the Sudakov's variables. Some experimental setups with different rules for event selection are studied and corresponding numerical estimations are presented., Comment: 26 pages, 20 figures, submitted to JETP

Inspired by new trends in atomtronics, cold atoms devices and Bose-Einstein condensate dynamics, we apply a general technique of N=4 extended Supersymmetric Quantum Mechanics to isospectral Hamiltonians with triple-well potentials, i.e. symmetric and asymmetric. Expressions of quantum-mechanical propagators, which take into account all states of the spectrum, are obtained, within the N = 4 SQM approach, in the closed form. For the initial Hamiltonian of a harmonic oscillator, we obtain the explicit expressions of potentials, wavefunctions and propagators. The obtained results are applied to tunneling dynamics of localized states in triple-well potentials and for studying its features. In particular, we observe a Josephson-type tunneling transition of a wave packet, the effect of its partial trapping and a non-monotonic dependence of tunneling dynamics on the shape of a three-well potential. We investigate, among others, the possibility of controlling tunneling transport by changing parameters of the central well, and we briefly discuss potential applications of this aspect to atomtronic devices., Comment: Latex, 28 pages, 7 Figs, 2 Tables; minor presentation changes, journal version

The model--independent QED radiative corrections to polarization observables in elastic scattering of unpolarized and longitudinally--polarized electron beam by the deuteron target have been calculated in leptonic variables. The experimental setup when the deuteron target is arbitrarily polarized is considered and the procedure for applying derived results to the vector or tensor polarization of the recoil deuteron is discussed. The basis of the calculations consists of the account for all essential Feynman diagrams which results in the form of the Drell-Yan representation for the cross-section and use of the covariant parametrization of the deuteron polarization state. The numerical estimates of the radiative corrections are given for the case when event selection allows the undetected particles (photons and electron-positron pairs) and the restriction on the lost invariant mass is used., Comment: 43 pages,3 figures. To be published in ZhTEF. revised 14.02.2012. arXiv admin note: text overlap with arXiv:nucl-ex/0002003 by other authors

In this paper we propose a self--consistent approach to the description of temporal dynamics of localized states. This approach is based on exactly solvable quantum mechanical models with multi-well potentials and their propagators. States of Hamiltonians with multi-well potentials form a suitable basis for the expansion of wave packets with different shapes and localization degrees. We also consider properties of the tunneling wave packets, taking into account all states of Hamiltonians with symmetric and asymmetric potentials, as well as their dependence on the degree of localization and deformations of potentials. The study of the dynamics of initially localized states shows that application of the two-state approximation for the description of tunneling is considerably limited, especially for systems, which have several states in the under-barrier region, as for example in modern superconducting quantum interference devices and traps for cold atoms.

We derived analytic formulae for the polarization single--spin asymmetries (SSA) in the Bethe--Heitler process $e^- + p \to e^- + \gamma + p$. The asymmetries arise due to one-loop QED radiative corrections to the leptonic part of the interaction and present a systematic correction for the studies of virtual Compton Scattering on a proton through interference with the Bethe-Heitler amplitude. Considered are SSA with either longitudinally polarized electron beam or a polarized proton target. The computed effect appears to be small, not exceeding 0.1 per cent for kinematics of current virtual Compton scattering experiments., Comment: 8 pages, 9 figures

We discuss an inclusive approach to the measurement of the e+e- --> pi+ pi- cross--section by the radiative return method without photon tagging. The essential part of this approach is the choice of rules for event selection which provide rejection of events with 3 (or more) pions and decrease the final--state radiation background. The radiative corrections to the initial--state radiation process are computed for DAPhNE conditions, using the quasi--real electron approximation for both, the cross--section and the underlying kinematics. The two cases of restricted and unrestricted pion phase space are considered. Some numerical calculations illustrate our analytical results., Comment: 25 pages, 4 figures, latex

Deep-inelastic events for the scattering of the longitudinally polarized electron by polarized proton with tagged collinear photon radiated from initial-state electron are considered. The corresponding cross-section is derived in the Born approximation. The model-independent radiative corrections to the Born cross-section are also calculated. Obtained result is applied to the case of elastic scattering., Comment: 14 pages, 2 figures, submitted to JETP

The hadronic invariant mass distribution for the process of electron-positron annihilation into a pair of charged pions accompanied by a photon radiated from the initial state has been studied for the region of DA$\Phi$NE energies. The Born cross-section and the electromagnetic radiative corrections to it are calculated for realistic conditions of the KLOE detector. The dependence on the physical parameters which define the event selection is obtained., Comment: 15 pages, Latex, 21 references, no figures

The electron current tensor for the scattering of heavy photon on longitudinally polarized electron accompanied with additional hard electron-positron pair has been considered. The contribution of collinear and semicollinear kinematics is computed. The full analysis of both, spin-dependent and spin-independend parts of electron current tensor, is performed. The obtained result allows to calculate the corresponding contribution into the second order radiative correction to cross-sections of different processes with the next-to-leading accuracy., Comment: 19p,2Fig. (Submitted to Journ.of Physics G)

The initial-state radiative events in electron-positron annihilation into hadrons at DAFNE have been considered. The coresponding cross-section with the full first order radiative correction has been calculated. The analytical calculations take into account the realistic angular acceptance and energy cut of DAFNE photon detector., Comment: 6p. (Submitted to JETP Lett.)