General formalism in collinear regime for pseudoscalar meson production in NN collisions

The spin structure of the matrix element for the pseudoscalar meson production processes in nucleon-nucleon collisions is established in the collinear kinematical regime in terms of 3 independent scalar amplitudes. This result is valid for any reaction mechanism and for any energy of the colliding and the produced particles. The complete experiment for the full reconstruction of all 3 complex amplitudes must contain two different classes of polarization experiments. The polarization transfer coefficients can be used to determine the moduli of all 3 amplitudes, whereas the spin correlation coefficients for + collisions are sensitive to the relative phases of different amplitudes. Received: 13 August 2001 / Accepted: 20 September 2001     

Vector boson in the constant electromagnetic field

The propagator and the complete sets of in-and out-solutions of the wave equation, together with the Bogoliubov coefficients relating these solutions are obtained for the vector W-boson (with the gyromagnetic ratio g=2) in a constant electromagnetic field. When only the electric field is present, the Bogoliubov coefficients are independent of the boson polarization and are the same as for the scalar boson. For the collinear electric and magnetic fields, the Bogoliubov coefficients for states with the boson spin perpendicular to the field are again the same as in the scalar case. For the W ^? spin parallel (antiparallel) to the magnetic field, the Bogoliubov coefficients and the one-loop contributions to the imaginary part of the Lagrange function are obtained from the corresponding expressions for the scalar case by the substitution m ² → m ²+2eH (m ² → m ²-2eH). For the gyromagnetic ratio g=2, the vector boson interaction with the constant electromagnetic field is described by the functions that can be expected by comparing the scalar and Dirac particle wave functions in the constant electromagnetic field.     

Covariant methods for calculating differential cross sections and polarization characteristics of reactions

A covariant method for calculating reaction amplitudes in the diagonal spin basis is presented. In this basis, amplitudes represent the spin kinematics of the interacting particles in the simplest and most adequate manner. A matrix is obtained such that differential cross sections for polarized particles and amplitude combinations that are required to calculate various polarization characteristics of reactions can be expressed in an arbitrary basis in terms of the amplitudes calculated in one basis.     

Complete experiment in eN-elastic scattering, in presence of two-photon exchange

Using a general parametrization of the spin structure of the matrix element for elastic eN-scattering, in terms of three independent complex amplitudes, we found the expressions for all polarization observables, in electron–proton elastic scattering. This allows to suggest possible methods to measure the nucleon electromagnetic form factors, in presence of two-photon exchange. We show that the measurements of the differential cross section for electron and positron nucleon elastic scattering, in the same kinematical conditions, allows to extract the nucleon electromagnetic form factors. The same is correct for the polarization method, with the measurement of the P_x,z components of the final nucleon polarization (for the scattering of longitudinally polarized electrons and positrons). An alternative way, in absence of positron beam, is to measure a definite set of T-odd polarization observables, which includes three different experiments or only T-even observables, with five independent experiments. In both cases, the ratio G_E(Q²)/G_M(Q²) is related to quantities of the order of and requires different polarization experiments with very high accuracy.     

Can spin-polarized photoemission measure spin properties in condensed matter?

Photoemitted electrons move in a vacuum; their quantum state can be completely characterized in terms of energy, momentum and spin polarization by spin-polarized photoemission experiments. A review article in this issue by Heinzmann and Dil (2012 J. Phys.: Condens. Matter 24 173001) considers whether the measured spin properties, i.e. the magnitude and direction of the spin polarization vector, can be traced back to the quantum state from which these electrons originate. The careful conclusion is that they can, which is highly relevant in view of the current interest in these experiments and their application to topological insulators, where the spin-orbit interaction produces spin-polarized surface states.     

On AdS/QCD correspondence and the partonic picture of deep inelastic scattering

We critically examine the question of scaling of the Deep Inelastic Scattering process in the medium Bjorken x region on a scalar boson in the framework of the AdS/QCD correspondence. To get the right polarization structure of the forward electroproduction amplitude, we show that one needs to add (at least) the scalar to scalar and scalar to vector hadronic amplitudes. This illustrates how the partonic picture may emerge from a simple scenario based on the AdS/QCD correspondence, provided one allows the conformal dimension of the hadronic field to equal 1 and use the concept of “hadron–parton duality”.     

Polarization transfer in deuteron stripping reactions

Polarization phenomena involving the spins of a and b in the A(a, b)B reaction are discussed using a complete set of irreducible tensors carrying definite spin transfer. The linear model independent equations relating the cross section and the polarization observables with these tensors are shown to be particularly appropriate for the study of spin dependent interactions, preferentially associated with particular values of spin transfer. The DWBA theory of polarization transfer in deuteron stripping reactions is thoroughly discussed and among the 17 polarization observables we distinguish those likely to be more sensitive to spin dependent distortion, to have stronger deuteron D-state effects, to exhibit the sign-rule j-dependence and other forms of j-dependence. For certain deuteron polarizations, when the spin transfer is pure $\text{s =}\text{1}\text{2}$, it is shown that deuteron stripping reactions are transparent to vector polarization transfer and the outgoing nucléon polarization independent of scattering angle and deuteron energy. DWBA calculations including contributions from spin transfer $\text{3}\text{2}$ through the deuteron D-state and spin-orbit distortion show that polarization transfer in such deuteron polarizations can be explored as a method of producing fast polarized neutrons with known polarization.     

Spin symmetry in Dirac negative-energy spectrum in density-dependent relativistic Hartree-Fock theory

The spin symmetry in the Dirac negative-energy spectrum and its origin are investigated for the first time within the density-dependent relativistic Hartree-Fock (DDRHF) theory. Taking the nucleus ¹⁶O as an example, the spin symmetry in the negative-energy spectrum is found to be a good approximation and the dominant components of the Dirac wave functions for the spin doublets are nearly identical. In comparison with the relativistic Hartree approximation where the origin of spin symmetry lies in the equality of the scalar and vector potentials, in DDRHF the cancellation between the Hartree and Fock terms is responsible for the better spin symmetry properties and determines the subtle spin-orbit splitting. These conclusions hold even in the case when significant deviations from the G -parity values of the meson-antinucleon couplings occur.     

A relativistic quark model for mesons based on numerical solutions of the Bethe-Salpeter equation

A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound $\text{spin}\text{-}\text{1}\text{2}$ quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons.Numerical solutions to the Bethe-Salpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral vector exchange interaction. The interaction function corresponds to single particle exchange, with the addition of either one or two regulating terms. It is found that the second regulator allows the internal quark momentum to be nonrelativistic, but that the spinor structure of the wave function remains highly relativistic.Only the scalar interaction can account for the observed spectrum of states. The pseudoscalar interaction yields a vector state of lower mass than the pseudoscalar state, and the vector interaction leads to a vector state which lies approximately one quark mass above the pseudoscalar state. The λ quark is taken as slightly heavier than the p and n, and the perturbation treatment of the mass difference leads to a quadratic mass formula.The decay amplitudes for π, K → μν are calculated, and it is found, independent of parameters, that $\text{?}{}_{\mathrm{\pi }}\text{≈ ?}{}_{\mathrm{K}}$ for either a scalar or vector interaction, in agreement with experiment and in contrast with the nonrelativistic model. The amplitudes for ?^o, ω, φ → e⁺e^?, μ⁺μ^? are also calculated, but in this case the ratios (again parameter independent) are in minor discrepancy with experiment.The question of the additivity of quark amplitudes is examined by calculating (with significant restrictions) the magnetic moments of the vector mesons and the amplitudes for magnetic transitions such as ω → π^oγ. The magnetic moments of the vector mesons have the same (trivial) ratios to each other as in the nonrelativistic model, but they are strongly enhanced over the sum of the quark magnetic moments. The amplitude for magnetic transitions, however, is related to the quark magnetic moments in approximately the same ratio as in the nonrelativistic model.The model is also used to obtain parameter dependent predictions for the masses and decay amplitudes. These predictions are not experimentally correct, but are generally well within an order of magnitude for a wide range of the parameters.The most significant defect discovered of the model is the presence of ghost states (the daughters of the vector mesons, with J^PC = 0^+?) with masses of about 2 BeV.     

Steady-state vectorial self-diffraction on a non-local photorefractive grating in a crystal of symmetry \overline{4}3m at symmetrical transmitting geometry

The steady-state two-wave interaction in a cubic crystal of the symmetry group 3m with the non-local photorefractive response in the absence of an external electric field is considered for the case of arbitrary interaction orientation with respect to the crystallographic coordinate system and for arbitrary intensities and polarization states of incident light waves. The self-diffraction problem is described on the basis of four coupled-wave equations in terms of the complex scalar amplitudes of components of the light waves with orthogonal linear polarization. The derived conservation laws are valid for the non-linear dependency of the photorefractive-grating amplitude on the modulation coefficient of the interference light pattern. It follows from these laws that the two non-unidirectional energy fluxes can form the total energy exchange between the two interacting light waves. A set of independent conservation laws allows us to decouple the coupled-wave equations and to obtain their analytical solution, at least, in the form of quadrature formulae. For example, such a solution is derived for the case of linearly polarized incident light waves and for the linearized dependency of the photorefractive-grating amplitude on the modulation coefficient. The explicit analytical expressions for the scalar amplitudes are obtained for the transversal electro-optic configuration of interaction. The possibility of polarization-state transformation of light waves without energy exchange between them is shown. Received: 30 July 2002 / Published online: 11 December 2002 RID="*" ID="*"Corresponding author. Fax: +7-3822/414321, E-mail: litvinov@ed.rk.tusur.ru     

Electron spin precession upon reflecting from ferromagnetic surfaces

Electrons with the polarization vector perpendicular to the magnetization of Fe, Co, and Ni films are spin analyzed after reflecting from the ferromagnet. At low primary electron energies a strong spin motion is found, namely, a precession of the polarization around the magnetization and a change of the angle between the polarization and the magnetization. This observation can be accounted for by the existence of spin-dependent gaps in the electronic band structure of the ferromagnets.     

Measurement of the polarization of positive muons produced in high-energy antineutrino interactions

The question whether scalar-type interactions contribute to weak interactions at large momentum transfer has been investigated by a measurement of the longitudinal polarization of positive muons produced in charged-current interactions of high-energy antineutrinos with iron. At an average momentum transfer <Q ²>=4 GeV² the muon spin is found to be oriented forward with respect to the muon momentum vector, with an average polarization of 1.10±0.24, consistent with positive helicity. A limit on scalar contributions of σ_{s, p}/σ_tot <7% at the 95% confidence level can be deduced. A search for violation of time reversal invariance which could manifest itself by a polarization component perpendicular to the muon production plane gave a limit of σ_tv/σ_tot <16% (95% c.l.). It is concluded that the weak leptonic charged current retains its dominant vector and axial vector structure at large momentum transfers.     

Invariant Amplitudes for Coherent Electromagnetic Pseudoscalar Production from a Spin-One Target, II: Crossing, Multipoles, and Observables

 The formal properties of the recently derived set of linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle have been further exploited. The crossing properties are discussed in detail. Since not all of the amplitudes have simple crossing behaviour, we introduce an alternative set of basic amplitudes which are either symmetric or antisymmetric under crossing. The multipole decomposition is given, and the representation of the multipoles as integrals over the invariant functions weighted with Legendre polynomials is derived. Furthermore, differential cross section and polarization observables are expressed in terms of the corresponding invariant functions. Received July 5, 1999; accepted for publication September 19, 1999     

Self-gravitating wave fields in a Gödel space

The properties of self-gravitating wave fields with integral spin (scalar and vector), compatible with a Gödel type space, are investigated. The simultaneous systems of Einstein's gravitational field equations and the equations corresponding to wave fields in Gödel's metric are solved. For the scalar field, the solutions are obtained for different types of interaction Lagrangians for the gravitational and scalar fields. It is shown that for a massive vector field the relations obtained between the constants lead, within the scope of the strong gravitation theory, to the classical expression for the spin of elementary particles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 59–63, October, 1981.The authors are grateful to the participants of the theoretical seminar conducted by D. Ivanenko for discussing the results of this work.     

Quantum Vacuum and the Structure of Empty Space–Time

We have considered the possibility of formation of a massless particles with spin 1 in the region of negative energies, within the framework of the Weyl-type equation for neutrinos. It is proved that the represented approach allows to get a stable structural formation in the ground state, which can be interpreted as a fundamental massless particle. The structure and properties of this vector boson are studied in detail. The problem of entangling two vector bosons with projections of spins +1 and −1 and, accordingly, the formation of a zero-spin boson is studied within the framework of a complex stochastic matrix equations of the Langevin type. The paper discusses the structure of the Bose particle of a scalar field and the space–time properties of an empty space (quantum vacuum).

     

The Newton-Wigner and Wightman localization of the photon

A quantum theory of the photon is developed in a natural manner. Newton-Wigner and Wightman demonstrated that the photon could not be strictly localized according to natural criteria. These investigations involved the identification of an elementary system with a uirrep of the Poincare group. We identify a particle with the localized measurement of the states satisfying the uirrep. In the case of zero mass and unit spin, the photon is identified with those components of the state that can be localized. A c-number four-vector potential and Lorentz condition are derived from the relativistic wave equation. The Wightman localization is demonstrated for the three independent space components of the vector potential, and the photon is identified with these components. A position operator and probability density follow immediately from the localization. A consequence of the subjective definition of a photon is that the transformations of the vector potential are unitary, and hence the unitary scalar product can be obtained for the four-vector potential. A Hilbert space is defined for the three space components of the vector potential. A position operator and probability density are derived from the scalar product, which compare directly with those obtained from the localization and the non-relativistic theory. As the longitudinal and scalar polarizations do not contribute to the measured transition probability, they are considered virtual. Lastly, a conserved four-vector current is derived from the scalar product. The possibility of observing a strict localization of the photon in the laboratory is suggested.     

核子中夸克的极化

根据强子张量和向前的虚光子康普顿散射振幅之间的关系,用虚光子总吸收截面表达了核子的自旋结构函数和它的第一矩. 在夸克模型中计算了小动量转移区的虚光子的总吸收截面,进而得到了第一矩的理论结果,导出了质子中夸克的极化. 合理地解释了EMC和SLAC的实验结果.     

Electron spin polarization in field emission: Calculation of the effects due to external fields

In field emission experiments with spin polarized electrons a magnetic field is superposed on the electric emission field to define the preferred spin direction. The motion of the polarization vector in these fields was calculated for rays emanating from individual points of the emitter by integrating the equation of motion and taking into account relativistic terms. There is a slight shift of the polarization vector from its initial direction. If the initial polarization is aligned with the magnetic field and the emission tip is sufficiently well centred in the magnetic field, the tilting of the polarization vector for a beam of electrons starting not too far from the tip apex is less than 10°.     

J/gy suppression as evidence for high densities in nuclear collisions

It is shown that the scattering amplitudes of some degenerate massive string states can be expressed in terms of that of higher spin states at the same mass level. This phenomenon is discussed from σ-model point of view and demonstrated explicitly by using massive Ward identities generated by zero-norm states atD=26. The subtlety of the scalar propagating state is briefly pointed out. We also compare our on-shell gauge symmetry derived from σ-model with off-shell gauge symmetry of covariant string field theory.