Table of contents

Dear Colleagues, Ladies and Gentlemen, on behalf of the Directorate of Joint Institute for Nuclear Research (JINR) it is a pleasure for me to welcome you here to Dubna for the 16th International Workshop on High Energy Spin Physics. It provides an opportunity to present and discuss the news accumulated during last year. Another important feature of this series of workshops has always been the participation of a large number of physicists from the former Soviet Union and Eastern European countries, for which long trips have previously been limited by financial (and earlier also by bureaucratic) reasons. It thus represents an important addition to the series of large International Symposia on spin physics held in even-numbered years in different countries, including the Symposium held in Dubna in 2012.

JINR has a long-lasting tradition of experimental and theoretical studies of spin phenomena. The workshops on high energy spin physics started in Dubna in 1981 due to the initiative of L. Lapidus, an outstanding theoretical physicist. Since then, these meetings have been held in Dubna in every odd year and have become regular thanks to Anatoly Vasilievich Efremov, the chairman for many years.

Recent years have brought a lot of new experimental results, and above all the discovery and determination of quantum characteristics of the Higgs boson at the Large Hadron Collider.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

The procedure for calculation of the QCD evolution of transverse momentum dependent distributions within the covariant approach is suggested. The standard collinear QCD evolution together with the requirements of relativistic invariance and rotational symmetry of the nucleon in its rest frame represent the basic ingredients of our approach. The obtained results are compared with the predictions of some other approaches.

Recently CMS and ATLAS announced that they had measured the Higgs boson parity. In this note we show that their approach can determine this parity only under the additional assumption that an extension of Standard Model of some special type is realized in Nature.

We show that the used approach gives no information about the Higgs boson parity when assuming most other extensions of the Standard Model.

The task of the transportation of the polarized proton and deuteron beam of an energy 10-20 keV in the given magnetic field is considered. Specifically the magnetic field is produced by the system of a solenoid and some ring permanent magnets with contrary directed field. The Lorentz equations together with classic equations for vector and tensor polarizations have been solved. The results of the numerical simulation for a simple two- ring system are presented, which shows there is no essential depolarization in agrement with theoretical estimation.

The choice of magnet system for the Spin Physics Detector of the NICA Collider of LHEP JINR is given. The inverse problem of magnetostatics is solved for a magnetic field of 0.5 tesla in the aperture a) ɸ 3 m x 5 m and b) ɸ 3 m x 6 m. We also discuss the design of the magnet with a field of 0.3 T.

The paper presents the results obtained for the "warm" and SC versions of the magnetic system: currents (ampere-turns), the geometry (size) of the coil and the iron yoke, weight (on the whole and the individual elements), the magnet transportation and assembly.

The first ever polarized Drell-Yan measurement, presently being done by the COMPASS collaboration at CERN is described. Emphasis is put on the polarized target and its upgrade.

In the framework of the proposed by the author Strongly Correlated Quark Model the valence quarks are treated as vortical solitons, and the proton spin arises from the additive sum of the valence quark vorticities. The spin "crisis" is a manifestation of the irrotational character of vortical fields quarks.

Gravitational and electromagnetic (EM) field of electron is described by the Kerr-Newman (KN) black hole solution with a topological defect. Regularization of this defect by the Higgs field leads to the smooth source which shares much in common with the known MIT- and SLAC- bag models, but has the advantage, of matching gravitational and electromagnetic fields of the electron. This model is flexible, and the rotating KN bag takes the shape of a thin disk with a circular string positioned on the sharp border of the disk. We consider the lowest excitations of the KN solution and the corresponding deformations of the bag surface, setting a preliminary correspondence with electroweak sector of the SM.

In the present talk we briefly discuss the most general form of QCD Factorization, which we call Basic Factorization, and show how it is related to the conventional forms of factorization: K_T-Factorization and Collinear Factorization. When Basic Factorization is applied to hadronic scattering amplitudes, integration over momenta of the partons connecting perturbative and non-perturbative blobs runs over the whole phase space but result of the integration must be finite. This obvious requirement allows us to obtain theoretical restrictions on the fits for the involved non-perturbative contributions. In order to model non-perturbative contributions in Basic Factorization, we suggest the Resonance Model which can universally be used to describe hadronic reactions with unpolarized or polarized hadrons.

Combining the spin-dependent dispersion GDH-sum rule, the iso-vector, photo-excitation states projecting Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (or generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector.

We discuss astrophysical problems connected with gravitational lensing where current and future polarimetric observations are very important to clarify theoretical models. Namely, we consider polarization observations for exoplanet searches with gravitational microlensing, optical polarization for gravitational lens systems, polarization signatures of cosmological gravitational waves.

The report shows the possibilities of studying the spin one observables in the elastic dN and dd interactions at the NICA collider of the VBLHEP JINR. The use of the colliding deuteron beams would allow us to carry out the measurements of the differential cross sections I⁰(dN, dd) of the elastic scattering of unpolarized deuterons and the differential cross sections I^pol(dN,dd) and the vector A_y(Ed,θ) and tensor A_yy(Ed,θ) and A_xx(E_d.θ) analyzing powers in elastic collisions of the vector and tensor polarized deuterons. The planned luminosity of the colliding polarized deuteron beams will provide sufficiently high elastic events counting rate. The use of the colliding beams of the polarized deuterons for the spin one >dN and dd observables research has a number of significant advantages in comparison with the experiments with the "fixed" target. The angular acceptance of the collider detector covers the full solid angle 4π radians while the wide ranges of the energies of the dN, dd interactions and the 4-momentum transfer squared are available.

A major experimental program is presently underway to determine the Sivers, Boer-Mulders and transversity distributions, vital for understanding the internal structure of the nucleon. To this end we consider the Sivers, Boer-Mulders and transversity azimuthal asymmetries of the difference cross sections of hadrons with opposite charges in SIDIS reactions with unpolarized and transversely polarized target l + N → l' + h + X, h = π^±, K^±, h^±. We show that on deuteron target these asymmetries are particularly simple and determine the sum of the valence-quark Q_v = u_v + d_v transverse momentum dependent distributions without any contributions from the strange or other sea-quark functions.

At present, data on these asymmetries are presented for the integrated asymmetries i.e. the x_B- and z_h-dependent asymmetries. If data are available in small bins in Q², so that Q²-dependence can be neglected, these expressions simplify dramatically leading to remarkably simple and powerful tests of the simplifying assumptions used in extracting these functions from the data.

Many scenarios of new physics can lead to deviations of the observables (cross sections, asymmetries) from the Standard Model predictions in e⁺e^- collision. The possibility of uniquely identifying the indirect effects of s-channel sneutrino exchange, as predicted by supersymmetric theories with R-parity violation, against other new physics scenarios in high-energy electron-positron annihilation into tau pairs at the International Linear Collider has been studied.

Adding to the nucleon-nucleon scattering database is one of the major priorities of the ANKE collaboration. Such data are necessary ingredients, not only for the understanding of nuclear forces, but also for the description of meson production and other nuclear reactions at intermediate energies.

By measuring the cross section, deuteron analysing powers, and spin-correlation parameters in the dp → {pp}_sn reaction, where {pp}_s represents the ¹S₀ state, information has been obtained on small-angle neutron-proton spin-flip charge-exchange amplitudes.

The measurements of pp elastic scattering by the COSY-EDDA have had a major impact on the partial wave analysis of this reaction above 1 GeV. However, these experiments only extended over the central region of c.m. angles, 30⁰ < θ_cm < 150⁰, that has left major ambiguities in the phase shift analysis by the SAID group. In contrast, the small angle region is accessible at ANKE-COSY, that allowed measurement of the differential cross section and the analysing power at 5⁰ < θ_cm < 30⁰ in the 0.8 — 2.8 GeV energy range.

The data on the pn elastic scattering are much more scarce than those of pp, especially in the region above 1.15 GeV. The study of the dp → {pp}_s n reaction provides the information about the pn elastic scattering at large angles. The small angle scattering was studied with the polarized proton COSY beam and an unpolarised deuterium gas target. The detection the spectator proton in the ANKE vertex silicon detector allowed to use the deuterium target as an effective neutron one. The analysing powers of the process were obtained at six beam energies from 0.8 to 2.4 GeV.

The current design of the Medium-energy Electron-Ion Collider (MEIC) project at Jefferson lab features a single 8 GeV/c figure-8 booster based on super-ferric magnets. Reducing the circumference of the booster by switching to a racetrack design may improve its performance by limiting the space charge effect and lower its cost. We consider problems of preserving proton and deuteron polarizations in a superconducting racetrack booster. We show that using magnets based on hollow high-current NbTi composite superconducting cable similar to those designed at JINR for the Nuclotron guarantees preservation of the ion polarization in a racetrack booster up to 8 GeV/c. The booster operation cycle would be a few seconds that would improve the operating efficiency of the MEIC ion complex.

New exact solution class of Born - Infeld type nonlinear scalar field model is obtained. These solutions are three-dimensional solitons propagating with speed of light. The appropriate twisted solitons are considered. Energy and absolute value of momentum for such soliton are proportional to absolute value of its angular momentum or spin in some approximation. The model of ideal gas for the twisted lightlike solitons with lowest twist parameter is considered. Explicit conditions provide that the spin of each soliton equals Planck constant. It is shown that these solitons look like photons.

We present progress in development of the truncated Mellin moments approach (TMMA). We show our recent results on the generalization of DGLAP evolution equations and discuss some their applications in spin physics.

We test the recently proposed "Massive" Perturbation Theory (MPT) for the description of the Γ₁^p-n data at low momentum transfers. The MPT constructed on the two grounds: the first is pQCD with only one parameter added, an effective "glueball mass" m_p ≲ M_gl ≲ 1 GeV; serving as an infrared "regulator"; the second stems out of the ghost- free Analytic Perturbation Theory comprising non-power perturbative expansion that makes it compatible with linear integral transformations. It is regular in the low-energy region and could serve as a practical means for the analysis of data below 1 GeV up to the IR-limit. We study the non-perturbative Bjorken sum rule higher twists correction by using the MPT, the integral representation for infinite sum of higher twists coefficients and the QCD-inspired model for the Q²-dependence of the generalized Gerasimov-Drell-Hearn sum rule.

Hyperon production is an excellent probe of QCD in the confinement domain, and spin observables are a powerful tool in understanding the underlying physics. For the Ω hyperon, seven polarisation parameters can be extracted from the angular distributions of its decay products with the future ANDA experiment at FAIR. Simulation studies reveal great prospects for strange and single charmed hyperon channels with ANDA. Software tools supporting these investigations are currently under development.

The integrated proton-deuteron cross section σ˜ for the case of transversal polarization p^p_y of the proton and tensor polarization P_xz of the deuteron provides a null test signal for time-reversal invariance violating but P-parity conserving effects. The corresponding experiment is planned at COSY to measure the observable σ˜. Here we consider in general case the status of the null-test observable in pd scattering, calculate σ˜ within the Glauber theory of the double-polarized pd scattering at 100 - 1000 MeV and study the contribution of the deuteron S- and D-waves for several type of the T-odd NN interactions.

New results on the transverse spin azimuthal asymmetries in semi-inclusive DIS reactions extracted by the COMPASS Collaboration from the data collected with a transversely polarised proton target are presented. A noticeable similarity between the Collins asymmetry and the dihadron asymmetry, already been observed and reported, triggered a more deep investigation on the angular correlations and the relevant kinematical variables. The resulting phenomenological analysis of the transversity induced asymmetries, presented in this talk, allows to establish quantitative relationships, providing strong indication that the underlying fragmentation mechanisms are all driven by a common physical process.

Two solenoid Siberian snakes are required to obtain ion polarization in the "spin transparency" mode of the NICA collider. The field integrals of the solenoid snakes for protons and deuterons at maximum momentum of 13.5 GeV/c are equal to 2×50 T·m and 2×160 T·m respectively. The snakes introduce strong betatron oscillation coupling. The calculations of orbital parameters of proton and deuteron beams in NICA collider with solenoid snakes are presented.

The NICA Collider with two solenoid Siberian snakes is "transparent" to the spin. The collider transparent to the spin provides a unique capability to control any polarization direction of protons and deuterons using additional weak solenoids without affecting orbital parameters of the beam. The spin tune induced by the control solenoids must significantly exceed the strength of the zero-integer spin resonance, which contains a coherent part associated with errors in the collider's magnetic structure and an incoherent part associated with the beam emittances. We present calculations of the coherent part of the resonance strength in the NICA collider for proton and deuteron beams.

Based on the factorization representation of the General Parton Distributions (GPDs) the momentum transfer dependence was determined by the analysis of the different representations of parton distribution functions (PDFs) and all possible experimental data of the electromagnetic form factors of the proton and neutron. The obtained t-dependence of the GPDs is checked by analysis of the different hadronic reactions (including exclusive and elastic hadron scattering) in a wide energy region with minimum free fitting parameters.

It is shown that the fundamental Lagrangian of Quantum Chromodynamis should be modified by the adding gluon masses to produce the mass-gap in accordance with the Källen-Lehmann spectral representation. On mass-shell renormalizability and unitarity of the resulting theory is demonstrated.

The recently completed Q_weak experiment at Jefferson Laboratory made the first direct determination of the proton's weak charge, Q^p_W, via a measurement of the parity-violating asymmetry in elastic electron-proton scattering at low four-momentum transfer. The Standard Model (SM) makes a precise prediction of Q^p_W (SM) = 0.0710 ± 0.0007. A deviation from this prediction could be an indicator of new physics. A longitudinally polarized electron beam was scattered off a liquid hydrogen target and detected in eight azimuthally symmetric fused silica detectors. The small asymmetry, A_ep = -279 ± 35 (stat) ±31 (syst) ppb, was measured by observing the difference in rates seen in the detectors when the helicity of the electron beam was rapidly reversed. The measured asymmetry is the most precise and smallest asymmetry ever measured in an p scattering experiment. Combining this asymmetry with previous parity- violating electron scattering (PVES) data, we obtained a value of Q^p_W(PVES) = 0.064 ± 0.012, which agrees well with the SM value. The results of the experiment's commissioning run, which constitutes about 4% of the total data set, are reported here. Analysis of the remainder of the data set is ongoing and will significantly reduce the statistical and systematic uncertainties; several aspects of this analysis will be highlighted.

The construction of the PAX installation was inspired by the idea to make a beam of polarized antiprotons available for the experiments at the HESR FAIR. A spin filtering experiment with transversally polarized protons was realized using the new PAX installation at COSY. The results of this measurement are in perfect agreement with the FILTEX experiment. Hence, filtering is a viable method to produce a stored beam of polarized antiprotons. Another experiment which can be pursued using the PAX installation is the test of Time Reversal Invariance at COSY (TRIC). The goal of the TRIC experiment is to improve the present upper limit on violation of the T-odd P-even interaction by an order of magnitude using a genuine null observable available in a double polarized pd scattering. The status of the PAX spin filtering experiments as well as present understanding of the possible systematic uncertainties in TRIC are presented in this contribution.

A feasibility of the proton beam polarimetry based on exploiting the observed large single-spin asymmetry A_N in inclusive charged pion production is evaluated for the SPASCHARM experiment at IHEP, Protvino, Russia. It is shown that, for a few hours of beam exposition time, the beam polarization could be measured at the statistical errors of ∼3-5%. The inclusive pion polarimetry at SPASCHARM does not require construction of a special polarimeter. The polarimetry will be carried out entirely by the main SPASCHARM spectrometer simultaneously with physics data taking.

In the Standard Model of Particle Physics (SM), minimal supersymmetric extension of the SM (MSSM), standard pion-nucleon field theory and other models is shown how to define the values of coupling constants and masses. Discrete dynamics, spins, constituent supersymmetric model for W and Higgs bosons considered, supersymmetric mechanism of confinement in QCD described.

I present a determination of longitudinally-polarized parton distribution functions of the proton from inclusive deep-inelastic scattering data: NNPDFpol1.0+. This determination, based on the NNPDF methodology, upgrades a previous analysis, NNPDFpol1.0, in two respects: first, it includes all new data sets which have recently become available from the COMPASS experiment at CERN and from the E93-009, EG1-DVCS and E06-014 experiments at JLAB; second, it uses the state-of-the-art unpolarized parton set NNPDF3.0 as a baseline for the reconstruction of fitted observables and for the determination of positivity constraints. I discuss the impact of both these new inputs on the uncertainty of parton distribution functions.

The major goal of the upgraded Nuclotron facility is to obtain the information on the equation-of-state for dense nuclear matter playing a key role in the under standing of the collapse supernovae and neutron stars stability. These studies can be performed either in heavy ion collisions or via the short-range few nucleon correlations. The obtained experimental results and future program with the use of polarized deuteron beam and the internal target station are discussed. The polarization studies for the NN, NA and dA reactions with the extracted deuteron beam at the BM@N setup are proposed. The further extension of the polarization program at BM@N is related with the study of the in-medium modification of the polarization for the strange and multi-strange baryons and the spin alignment for vector mesons decaying in hadronic modes.

The feasibility study for the measurements of the polarization observables in the ³He(d,p) ⁴He reaction for DSS project using a part of the BM@N setup have been performed. Deuteron beam with energy of 1.5 GeV, magnet, 12 stations GEM tracker and TOF wall were used in simulations in order to obtain momentum resolution and to prove the separation of the secondary protons and deuterons. Summarized results of the dp breakup reactions with detection of two protons in coincidence for some kinematic configurations at energies from 300 to 500 MeV obtained in Nuclotron are presented.

Production of unstable particles off nuclei allows to determine the total cross section of the unstable particle interaction with nucleons. The interaction of vector mesons V(ρ, ω, ϕ) with nucleons are defined by a set of amplitudes corresponding to the transverse polarization of the vector meson (helicity λ = ±1) meson or longitudinal one (λ = 0). Whereas the total cross section for the interaction of the transversely polarized vector meson with nucleon σ _T = σ(V_TN) can be extract from the coherent photoproduction, measurements of vector meson interaction with nucleon σ_L= σ(V_LN).

As a good tool for such investigation we proposed the photoproduction of ω mesons on the set of nuclei in the incoherent region. Such experiment can be done using the feasibility of the new experiment GlueX at Jefferson Lab, designed to study the photoproduction of mesons in a large beam energy range up to 12 GeV.

The absolute polarimeter based on the elastic p-scattering in the diffraction kinematic regions with the total momentum transfer squared coverage of 0.1 < − t < 0.3 (GeV/c)² is proposed for the polarized antiproton beam at the U-70 proton synchrotron of IHEP. It is shown that it would take ∼200-400 hours for measuring the beam polarization at the statistical errors of ΔP_B/P_B ≃10–15%. These time estimates include also the time which is necessary for the measurements of an analyzing power A_N, using a polarized target. Besides the measurements of beam polarizations, the proposed polarimeter provides an opportunity for carrying out the experimental studies of the small momentum transfers physics which would be a valuable enrichment of the SPASCHARM experiment capabilities and its physics program.

We consider the pion pole contribution and transversity effects determined by the H_T and Ē_T Generalized Parton Distributions (GPDs) which are essential in hard pseudoscalar and vector meson leptoproduction. We investigate spin effects in the ω and ρ⁰ reactions. It is shown that the pion pole contribution is very important in the w production. Such effects in the ρ⁰ channel are much smaller. Our results on spin asymmetries and spin density matrix elements in these reactions were found to be in good agreement with HERMES data.

The paper explores quantum mechanics of half-spin particle motion in the field of Reissner-Nordström (RN) naked singularity. It is shown that for any quantum mechanical Dirac particle, irrespective of availability and sign of its electrical charge, the RN naked singularity is separated by an infinitely high positive potential barrier. With like charges of a particle and the source of the RN naked singularity, near the origin there exists the second completely impenetrable potential barrier. It has been proved that in the field of the RN naked singularity, bound states of half-spin particles can exist. The conditions for appearance of such states were revealed and computations were performed to find energy eigenvalues and eigenfunctions.

The paper presents the analysis of effective potentials of Dirac equations in static Schwarzschild and Reissner-Nordström (RN) fields. It is shown that in all the explored cases the condition of a particle "fall" to appropriate event horizons is fulfilled. The exception is one of the solutions for the Reissner-Nordström extremal field, for which the existence of the stationary bound state of half-spin particles is possible inside the event horizon.

An overview of more recent and important results from the HERMES experiment are presented in this paper. HERMES collected a wealth of data using the 27.6 GeV polarized HERA lepton beam and various polarized and unpolarized gaseous targets. This unique data set opens the door to the measurements of observables sensitive to the multidimensional structure of the nucleon. Among them are semi-inclusive deep-inelastic scattering measurements of azimuthal modulations sensitive to the transverse momentum distributions, such as the leading- twist Sivers and Collins distributions and distributions sensitive to the convolutions of the twist-2 and twist-3 functions. They all provide an information on the three-momentum-dependent quark distributions. Knowledge on the quark distribution as a function of longitudinal momentum and transverse position in impact-parameter space can be accessed, e.g., through exclusive ω—meson leptoproduction, particularly through the measurement of spin density matrix elements and the measurement of azimuthal modulations on transversely polarized proton target. The measurement of Bose-Einstein correlations of hadron pairs in quasi-real leptoproduction are also presented. The transverse polarization of Λ hyperons measured again in quasi-real leptoproduction regime are presented as well. Finally, the new analysis for the search on pentaquark at HERMES are mentioned.

Experimental data on the transverse single-spin asymmetry A_N in the collisions of polarized protons with protons and nuclear targets are analyzed. The existing data are compared with predictions from the chromomagnetic polarization of quarks (CPQ) model for the processes of π^±, K^±, p and antiproton production in the inclusive reactions. The results of A_n calculations for the above processes are presented in the following kinematic region: 8.77 ≤ √s ≤ 500 GeV, 0 < x_F ≤ 0.83, 0 ≤ p_T ≤ 9 GeV/c. Predictions of the CPQ model can be used for planning of experiments SPASCHARM(IHEP), SPD(JINR), STAR and PHENIX.

The differential cross sections of the charge exchange reaction dp → (pp)n has been measured at 1.75 GeV/c momentum per nucleon for small transferred momenta using the one arm magnetic spectrometer STRELA at the Nuclotron accelerator. The ratio of the differential cross section of the charge exchange reaction dp → (pp)n to that of the np → pn elementary process is discussed in order to estimate the spin-dependent part of the np → pn charge exchange amplitude on the basis of dp → (pp)n data. The np → pn amplitude turned out to be predominantly spin-dependent.

This work dedicated to describing two-body compounded system of quarks (meson) in point form of Poincare invariant quantum mechanics with potential, which was offered by so-called Mock-meson model. Authors shows process of calculation the basis parameters of the model by the variational method and followed applications for radiative decay processes. For such calculation authors use the simplest radiative decay scheme. Comparing results with experimental data was shown how to calculate the anomalous part of quark magnetic moment.

We discuss the application of the analytic approach called the fractional Analytic Perturbation Theory (APT) to the QCD analysis of the non-singlet structure function xF₃(x,Q²). The inverse Mellin transform method applyed for the fit of experimental data and for estimation of the Jacobi polynomial method accuracy in extraction of values of the scale parameter Λ_QCD and the form of the xF₃ structure function. Our estimates give the accuracy of the Jacobi polynomials method for the x-shape of the structure function about 10%, and accuracy for the scale parameter Λ_QCD 4%.

Exclusive electroproduction of ω mesons on unpolarized hydrogen and deuterium targets is studied in the kinematic region of Q² > 1.0 GeV², 3.0 GeV < W < 6.3 GeV, and −t' < 0.2 GeV². The data were accumulated with the HERMES forward spectrometer during the 1996-2007 running period using the 27.6 GeV longitudinally polarized electron or positron beam of HERA. Spin-density matrix elements are presented in projections of Q² or −t'. Violation of s-channel helicity conservation is observed for some of these elements. A sizable contribution from unnatural-parity-exchange amplitudes is established for special combinations of spin-density matrix elements. The determination of the virtual-photon longitudinal-to- transverse cross-section ratio reveals that a dominant part of the cross section arises from transversely polarized photons. Good agreement is found between the HERMES proton data and results of a pQCD-inspired Goloskokov-Kroll model that includes pion-pole contributions.

The concept of z-scaling previously developed for analysis of inclusive reactions in proton-proton collisions is applied for description of processes with polarized particles. Hypothesis of self-similarity of the proton spin structure is discussed. The possibility of extracting information on spin-dependent fractal dimensions of hadrons and fragmentation process from the cross sections and asymmetries is justified. The double longitudinal spin asymmetry A_LL of jet and π⁰-meson production and the coefficient of polarization transfer D_LL measured in proton-proton collisions at √s = 200 GeV at RHIC are analyzed in the framework of z-scaling. The spin-dependent fractal dimension of proton is estimated.

The 160 GeV polarised muon beam available at CERN, with positive or negative charge, makes COMPASS a unique place for GPD studies. The first GPD related COMPASS results come from exclusive vector meson production on transversely polarised protons and deuterons. The data were taken in 2003-2010 with large solid-state polarised targets, although without detection of recoil particles. Results on various transverse target spin dependent azimuthal asymmetries are presented and their relations to GPDs are discussed. The dedicated COMPASS GPD program started in 2012 with commissioning of a new long liquid hydrogen target and new detectors such as the large recoil proton detector and the large-angle electromagnetic calorimeter. It was followed by a short pilot 'DVCS run'. The performance of the setup and first results on DVCS and exclusive π⁰ channels have been demonstrated. The full data taking for the GPD program approved within COMPASS-II proposal is planned for 2016 and 2017.

Formula for calculating the concentration profile of ions in biological membranes has been obtained. It is assumed that ions are moving in a viscous medium under the action of the electric field and a concentration gradient. The problem is that ions are coated with shells consisting of water dipoles. These dipoles copy the form of the ions and in a strong electric field they can acquire the shape of an ellipsoid which changes the effective ion radius in the membrane. Calculation of the Na⁺¹ and K⁺¹ profiles leads to a conclusion that active and passive transport of ions is closely associated with the shape of the hydrated shells. The work was performed at the Veksler and Baldin Laboratory of High Energy Physics, JINR, Dubna.

The polarized proton and antiproton beam channel is currently under development at the U-70 accelerator of IHEP, Protvino, Russia. An availability of the both, polarized protons and antiprotons provides an exciting opportunity for the comparative studies of spin effects induced by polarized protons and antiprotons in a variety of hadronic reactions. While the proton and antiproton beams are formed by essentially the same method, there is the specific in the antiproton beam shaping and properties compared to protons. In this report, we address some technical details of forming the polarized antiproton beam and describe its main properties.

A new experiment SPASCHARM for systematic study of polarization phenomena in inclusive and exclusive hadronic reactions is currently under commissioning at IHEP. The universal experimental setup will detect dozens of various resonances and stable particles produced in collisions of unpolarized beams with the polarized target, and at the next stage, using polarized beams. At the first stage with polarized target, the final states composed of light quarks (u, d, s) will be reconstructed. Hyperon polarization and spin density matrix elements of the vector mesons will be measured along with the single-spin asymmetries. The 2π-acceptance in azimuth, which is extremely useful for reduction of systematic errors in measurements of spin observables, will be implemented in the experiment. The solid angle acceptance of the setup, Δθ≈250 mrad vertically and 350 mrad horizontally in the beam fragmentation region, covers a wide range of kinematic variables p_T and x_F. This provides the opportunity for separating dependences on these two variables which is usually not possible in the setups with a small solid angle acceptance. Unlike some previous polarization experiments, the SPASCHARM will be able to simultaneously accumulate and record data on the both, charged and neutral particle production.

We propose an approach to obtain gauge-invariant maximally path-dependent operator definition of the gluon transverse-momentum dependent distribution function (gTMD). We demonstrate that the evolution equations for the gTMD can be derived from the shape- variation integral-differential equations formulated in the coordinate space.

The Sivers asymmetry in J/ψ production in scattering of muons off transversely polarized protons μ⁺ + p^↑→μ⁺ + J/ψ + X is measured in two z-bins (inclusive and exclusive production) in the COMPASS 2010 data. Only J/ψ's decaying into muons are detected. About 2 230 and 4450 J/ψ events in the lower and the higher z-bins are found. The Sivers asymmetry is extracted using a simple double-ratio method and is found to be compatible with zero in the lower z bin and to have a slight preference for negative values in the higher z bin.

HERMES has taken a wealth of deep-inelastic scattering data using the 27.6 GeV polarized lepton beam at HERA and various pure gas targets, both unpolarized and polarized, which opened the door to several unique results. Among them are the first evidences for the naive-T-odd Sivers and Collins effects. An overview of recent HERMES results on measurement of azimuthal asymmetries in semi-inclusive production of pions, charged kaons and (anti)protons is presented.

Tuning effect in particle masses manifests itself in integer relations between masses of leptons, quarks, meson and baryons. It includes also dimensionless relation between such well-known SM-parameters as masses of the muon and Z-boson, m_μ/M_Z=115.9·10⁻⁵ coinciding with the QED radiative correction α/2π=115.9·10⁻⁵ considered for the electron mass m_e by V. Belokurov and D. Shirkov. Integer presentation of particle masses (n=1,13,16,17,18,115) for values m_μ, f_π, m_π, ΔM_Δ, neutron mass and (n=3x16, n=3x18) for constituent quarks M"_q=m_p,m_ω/2=780 MeV and M_q=3ΔM_Δ=m_Ξ/3=441 MeV were found with the period δ=16m_e. More accurate relations with δ were found from precise ratio m_n/m_e=1838.6836605(11). The shift δm_n=161.65(6) keV of neutron mass from 115δ-m_e accounts integer ratio δm_N/δm_n=8(1.0001(1)) with nucleon mass splitting. With fundamental boson masses the parameters M_q=3ΔM_Δ=m_Ξ/3=441 MeV and M"_q =m_ρ/2=388.8(2) MeV are in ratios M_Z/M_q=L^Z=206.8 and M_W/M"_q =L^W=207.3 coinciding with lepton ratio L=m_μ/m_e=13·16-1=207.

The reaction p + CH₂→ forward charge particle + X is used for this aim traditionally. Analyzing power of this reaction falls off as 1/p, where p is the laboratory momentum. At the proton momenta of order 8 GeV/c, which are expected at the JLab experiment, the low analyzing power creates problems for off-line analysis of data. On the other hand, it is well known that the reaction p+p → p+p has the much more analyzing power. So, the calorimeter is predestinated for suppression of inelastic events in this reaction. In the report it is shown that the problem is solved quite well.

The current status of the muon g-2 problem is briefly discussed. We briefly discuss the latest results on the muon g-2 measured in experiment and obtained theoretically within the standard model. Special attention is for the hadronic corrections and in particular the corrections due to the light by light scattering mechanism. For latter we present the results found in the leading in 1/N_c approximation with the nonlocal chiral quark model.

The Sivers effect describes the correlation between the spin of the nucleon and the orbital motion of partons. It can be measured via Semi-Inclusive Deep Inelastic Scattering of lepton on a transversely polarised proton and deuteron targets by determining the azimuthal asymmetry related to the modulation in the Sivers angle ϕ_Siv. In the paper a method of obtaining the Sivers asymmetry for gluons is presented. It is based on the model of lepton nucleon interactions via three single-photon-exchange processes: photon-gluon fusion (PGF), QCD Compton (QCDC) and leading process (LP). A method of simultaneous extraction of the Sivers asymmetries of the three processes with the use of Monte Carlo (MC) and neural networks (NN) approach is presented. The method has been applied to COMPASS data taken with 160GeV/c muon beam scattered off transversely polarised deuteron and transversely polarised proton target. For each target a data sample of events containing at least two hadrons with large transverse momentum has been selected. Finally the results for gluon Sivers asymmetry were obtained to be: A^d_g = −0.14 ± 0.15(stat.) ± 0.06(syst.) at 〈x_g〉 = 0.13 and A^p_g = −0.26 ± 0.09(stat.) ± 0.08(syst.) at 〈x_g〉 = 0.15.

We discuss the role of gluon poles and the gauge invariance for the hadron tensors of Drell-Yan and direct photon production processes with the transversely polarized hadron. These hadron tensors are needed to construct the corresponding single spin asymmetries. For the Drell-Yan process, we perform our analysis within both the Feynman and axial-type (contour) gauges for gluons. In both the Feynman and contour gauges, we demonstrate that the gauge invariance leads to the need of the new (non-standard) diagrams. Moreover, in the Feynman gauge, we argue the absence of gluon poles in the correlators 〈̄ψγ⊥A⁺ ψ〉 related traditionally to dT(x,x)/dx. As a result, these terms disappear from the final QED gauge invariant Drell-Yan hadron tensor. For the direct photon production, by using the contour gauge for gluon fields, we find that there are new twist-3 terms present in the hadron tensor of the considering process in addition to the standard twist-3 terms.

In this talk, I present the recent measurement of the Collins fragmentation function based on a set of 62 pb^-1e⁺e^- annihilation data at √s = 3.65 GeV collected with the BESIII detector at the BEPCII storage rings. In this work, the azimuthal asymmetries of two charged pions in the inclusive process e⁺e^- → ππX are explored. These asymmetries can be attributed to the Collins fragmentation function, which describes the behavior of a hadron produced from a transversely polarized quark. The corresponding four-momentum transfer of the virtual photon, Q², is close to the energy scale of the existing semi-inclusive DIS experimental data. We observe a nonzero asymmetry, which increases with increasing pion momentum and also indicates a larger spin-dependent Collins effect than at higher energy scale. The dependence of the asymmetry on the transverse momentum of hadrons to the reference axis is also investigated. The measured asymmetries are important inputs for the global analysis of extracting the quark transversity distribution inside the nucleon, and are valuable to explore the energy evolution of the spin-dependent fragmentation function.

Status of the JINR polarized ion source development is described. The source is under tests at the test-bench of LHEP, JINR. A charge-exchange plasma ionizer has been tested initially without a storage cell in the ionization region. An unpolarized deuterium ion beam with peak current of 160 mA, 23 keV energy, pulse duration of 100 μs and repetition rate of 1 Hz has been extracted from the ionizer. With a free polarized atomic hydrogen beam injected into the ionizer a polarized proton beam with peak current of 1.4 mA has been obtained. The nearest plans for the source development include tests of the ionizer with the storage cell and tuning of the high frequency transition units installed in their operating position with a Breit-Rabi polarimeter.

After more than a decade of RHIC running as a polarized proton collider, we summarize recent achievements of the RHIC spin program and their impact on our understanding of the nucleon's spin structure, i.e. the individual parton (quarks and gluons) contributions to the helicity structure of the nucleon, and to understand the origin of the transverse spin phenomena. Open questions are identified and a suite of future measurements with polarized beams at RHIC to address them is laid out.

The large-scale cosmic ray anisotropy has been studied in the equatorial coordinate system in the PAMELA experiment. The method to obtain dipole anisotropy characteristics as well as some its modernizations is discussed in detail.

The present contribution is dedicated to the investigation of the background conditions for cosmic ray ion ionization state measurements in MONICA experiment [1]. The future experiment MONICA is aimed to study the cosmic ray ion fluxes from H till Ni in energy range 10-300 MeV/n by multilayer semiconductor telescope-spectrometer installed onboard satellite. The satellite orbit parameters (circular, altitude is about 600 km, polar) were chosen for the realization of the unique method for the measurement of the charge state of the ions with energies >10 MeV/n by using the Earth magnetic field as a separator of ion charge. The analysis of the background particle fluxes is presented taking into account the recent data of the satellite experiments and known AE-8, AP-8 models and elaborated the recommendations to improve the background conditions for the MONICA experiment.

Here we discuss a method for a study of the heavy nuclei cosmic ray composition. The method is based on a charge separation with the PAMELA calorimeter. The work is in progress now. The ability is presented to carry out measurements up to Fe and Ni. As a result we expect to get important data about the abundance of the chemical elements in the cosmic rays.

The azimuthal asymmetries in the cross sections of charged-hadron production in the muon SIDIS reactions off the longitudinally polarised deuterons are determined using the COMPASS data of 2006 and combined data of 2002-2006. The asymmetries are presented as functions of the hadron azimuthal angle ϕ in two ways: first, for hadrons integrated over the kinematic variables and, second, as a function of one of the kinematic variables x, z or p^h_T while integrating over two other. In each case asymmetries were fitted by functions included the ϕ-independent terms and terms amplitude of which are modulated with ø as predicted by the theory: sin ϕ, sin 2ϕ, sin 3ϕ and cos ϕ. Results for amplitudes are presented and discussed.