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For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish, and their Von Neumann entropy has no dependence on the specific form of momentum distribution, as long as it is isotropic.

Heisenberg’s uncertainty principle in a formulation of uncertainties, intrinsic to any quantum system, is rigorously proven and demonstrated in various quantum systems. Nevertheless, Heisenberg’s original formulation of the uncertainty principle was given in terms of a reciprocal relation between the error of a position measurement and the thereby induced disturbance on a subsequent momentum measurement. However, a naive generalization of a Heisenberg-type error-disturbance relation for arbitrary observables is not valid. An alternative universally valid relation was derived by Ozawa in 2003. Though universally valid, Ozawa’s relation is not optimal. Recently, Branciard has derived a tight error-disturbance uncertainty relation (EDUR), describing the optimal trade-off between error and disturbance under certain conditions. Here, we report a neutron-optical experiment that records the error of a spin-component measurement, as well as the disturbance caused on another spin-component to test EDURs. We demonstrate that Heisenberg’s original EDUR is violated, and Ozawa’s and Branciard’s EDURs are valid in a wide range of experimental parameters, as well as the tightness of Branciard’s relation.

This paper aims at reproducing quantum mechanical (QM) spin and spin entanglement results using a realist, stochastic, and local approach, without the standard QM mathematical formulation. The concrete model proposed includes the description of Stern–Gerlach apparatuses and of Bell test experiments. Single particle trajectories are explicitly evaluated as a function of a few stochastic variables that they assumedly carry on. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. Notably, it is shown that the proposed model, despite being both local and realist, is able to violate the Bell–CHSH inequalities by exploiting the coincidence loophole and thus intrinsically renouncing to one of the Bell’s assumptions.

This contribution summarizes recent results from the RHIC spin program and the measurement of light quark fragmentation functions at Belle.

Transverse Spin and Transverse Momemtum Dependent (TMD) distribution study has been one of the main focuses of hadron physics in recent years. The initial exploratory Semi-Incluisve Deep-Inelastic-Scattering (SIDIS) experiments with transversely polarized proton and deuteron from HERMES and COMPASS attracted great attention and lead to very active efforts in both experiments and theory. QCD factorization has been carefully studied. A SIDIS experiment on the neutron with a polarized ³He target was performed at JLab. Recently published results will be shown. Precision TMD experiments are planned at JLab after the 12 GeV energy upgrade. The approved experiments with a new SoLID spectrometer on both the proton and neutron will be presented. Proper QCD evolution treatments beyond collinear cases become crucial for the precision study of the TMDs. Experimentally, Q² evolution and higher-twist effects are often closely related. The experience of study higher-twist effects in the cases of moments of the spin structure functions will be discussed.

Single Spin Asymmetries and Transverse Momentum Dependent (TMD) distribution study has been one of the main focuses of hadron physics in recent years. The initial exploratory Semi-Inclusive Deep-Inelastic-Scattering (SIDIS) experiments with transversely polarized proton and deuteron targets from HERMES and COMPASS attracted great attention and lead to very active efforts in both experiments and theory. A SIDIS experiment on the neutron with a polarized ³He target was performed at JLab. Recently published results as well as new preliminary results are shown. Precision TMD experiments are planned at JLab after the 12 GeV energy upgrade. Three approved experiments with a new SoLID spectrometer on both the proton and neutron will provide high precision TMD data in the valence quark region. In the long-term future, an Electron-Ion Collider (EIC) as proposed in US (MEIC@JLab and E-RHIC@BNL) will provide precision TMD data of the gluons and the sea. A new opportunity just emerged in China that a low-energy EIC (1st stage EIC@HIAF) may provide precision TMD data in the sea quark region, complementary to the proposed EIC in US.

An overview of our ongoing extractions of parton distribution functions of the nucleon is given. First JAM results on the determination of spin-dependent parton distribution functions from world data on polarized deep-inelastic scattering are presented first, and followed by a short report on the status of the JR unpolarized parton distributions. Different aspects of PDF analysis are briefly discussed, including effects of the nuclear structure of targets, target-mass corrections and higher twist contributions to the structure functions.

The investigation of the partonic degrees of freedom beyond collinear approximation (3D description) has been gained increasing interest in the last decade. The Thomas Jefferson National Laboratory, after the CEBAF upgrade to 12 GeV, will become the most complete facility for the investigation of the hadron structure in the valence region by scattering of polarized electron off various polarized nucleon targets. A compendium of the planned experiments is here presented.

Psuedo-scalar meson photo production measurements have been carried out with longitudinally-polarized neutrons using the circularly and linearly polarized photon beams and the CLAS at Thomas Jefferson National Accelerator Facility (Jlab). The experiment aims to obtain a complete set of spin observables on an efficient neutron target. Preliminary E asymmetries for the exclusive reaction, γ + n(p) → π^- + p(p), selecting quasi free neutron kinematics are discussed.

Using the technique of helicity amplitudes, the electromagnetic process e⁺e^- → μ⁺μ^-(τ⁺τ^-) is theoretically studied in the one-photon approximation. The structure of the triplet states of the final (μ⁺μ^-) system is analyzed. It is shown that in the case of unpolarized electron and positron the final muons are also unpolarized, but their spins are strongly correlated. Explicit expressions for the components of the correlation tensor of the (μ⁺μ^-) system are derived. The formula for the angular correlation at the decays of final muons μ⁺ and μ^- is obtained. It is demonstrated that spin correlations of muons in the considered process have the purely quantum character, since one of the Bell-type incoherence inequalities for the correlation tensor components is always violated.

The spin structure of the process γγ → e⁺e^- is theoretically investigated. It is shown that, if the primary photons are unpolarized, the final electron and positron are unpolarized as well but their spins are strongly correlated. For the final (e⁺e^-) system, explicit expressions for the components of the correlation tensor are derived, and the relative fractions of singlet and triplet states are found. It is demonstrated that in the process γγ → e⁺e^- one of the Bell-type incoherence inequalities for the correlation tensor components is always violated and, thus, spin correlations of the electron and positron in this process have the strongly pronounced quantum character. Analogous consideration can be wholly applied as well to the two-photon processes γγ → μ⁺μ^- and γγ → τ⁺τ^-, which become possible at considerably higher energies.

Spin-physics projects at J-PARC are explained by including future possibilities. J-PARC is the most-intense hadron-beam facility in the high-energy region above multi-GeV, and spin physics will be investigated by using secondary beams of kaons, pions, neutrinos, muons, and antiproton as well as the primary-beam proton. In particle physics, spin topics are on muon $g-2$, muon and neutron electric dipole moments, and time-reversal violation experiment in a kaon decay. Here, we focus more on hadron-spin physics as for future projects. For example, generalized parton distributions (GPDs) could be investigated by using pion and proton beams, whereas they are studied by the virtual Compton scattering at lepton facilities. The GPDs are key quantities for determining the three-dimensional picture of hadrons and for finding the origin of the nucleon spin including partonic orbital-angular-momentum contributions. In addition, polarized parton distributions and various hadron spin topics should be possible by using the high-momentum beamline. The strangeness contribution to the nucleon spin could be also investigated in principle with the neutrino beam with a near detector facility.

Searches for the role of spin in gravitation dated before the firm establishment of the electron spin in 1925. Since mass and spin, or helicity in the case of zero mass, are the Casimir invariants of the Poincaré group and mass participates in universal gravitation, these searches are natural steps to pursue. In this update, we report on the progress on this topic in the last five years after our last review. We begin with how is Lorentz/Poincaré group in local physics arisen from spacetime structure as seen by photon and matter through experiments/observations. The cosmic verification of the Galileo Equivalence Principle for photons/electromagnetic wave packets (Universality of Propagation in spacetime independent of photon energy and polarization, i.e. nonbirefringence) constrains the spacetime constitutive tensor to high precision to a core metric form with an axion degree and a dilaton degree of freedom. Hughes-Drever-type experiments then constrain this core metric to agree with the matter metric. Thus comes the metric with axion and dilation. In local physics this metric gives the Lorentz/Poincaré covariance. Constraints on axion and dilaton from polarized/unpolarized laboratory/astrophysical/cosmic experiments/observations are presented. In the end, we review the theoretical progress on the issue of gyrogravitational ratio for fundamental particles and the experimental progress on the measurements of possible long range/intermediate range spin-spin, spin-monopole and spin-cosmos interactions.

The Stern-Gerlach experiment and the origin of electron spin are described in historical context. SPIN 2014 occurs on the fortieth anniversary of the first International High Energy Spin Physics Symposium at Argonne in 1974. A brief history of the international spin conference series is presented.

The spin-gravity interactions imply the new manifestation of the equivalence principle leading to the absence of gravitoelectric and anomalous gravitomagnetic moments for fermions. This property is still valid in the presence of the space-time torsion due to the covariance arguments. The experimental bounds for the torsion, which may be extracted from modern co-magnetometer experiments, are discussed.

A beam channel of polarized protons and antiprotons produced from decays of $\mathrm{\Lambda }$- and anti-$\mathrm{\Lambda }$-hyperons for the SPASCHARM experiment is to be built at IHEP U-70 accelerator in Protvino, Russia. The methods for tagging and measuring polarization of the beam (anti)protons are discussed in this report. The fast on-line beam tagging exploits the correlations between polarization and kinematics of (anti)protons originated from (anti)$\mathrm{\Lambda }$-decays. In the intermediate focus of primary target, decay (anti)protons of different transverse polarizations are spatially dispersed transversely with respect to the beam axis. The tagging system, consisting of fast beam detectors with good spatial resolution, measures the momentum and trajectory of each beam particle, including its position at the intermediate focus, thus allowing instant (on-line) assignment of the transverse polarization value to each (anti)proton. This system is also extremely useful for the beam channel tuning. While being fast and convenient, the polarization tagging fully relies on computing of particle transportation in the beam channel. In order to verify the real beam polarization and operating of the tagging system and beam channel, the independent absolute beam polarimetry is to be used. It is based on measuring the spin asymmetries in elastic scattering of beam (anti)protons in Coulomb-Nuclear Interference (CNI) and diffractive kinematic regions. It is estimated that less than one week of data taking would allow measuring an absolute beam polarization at the statistical accuracy of $\sim$4–5%.

Imperfection and vertical intrinsic depolarizing resonances have been overcome by the two partial Siberian snakes in the Alternative Gradient Synchrotron(AGS). The relatively weak but numerous horizontal resonances are the main source of polarization loss in the AGS. A pair of horizontal tune jump quads have been used to overcome these weak resonances. The locations of the two quads have to be chosen such that the disturbance to the beam optics is minimum. The emittance growth has to be mitigated for this method to work. In addition, this technique needs very accurate jump timing. Using two partial Siberian snakes, with vertical tune inside the spin tune gap and 80% polarization at AGS injection, polarized proton beam had reached $1.5\times 10^{11}$ proton per bunch with 65% polarization. With the tune jump timing optimized and emittance preserved, more than 70% polarization with 2$\times 10^{11}$ protons per bunch has been achieved.

Chemically doping with trityl radicals was performed in fully deuterated polyethylene. The behavior of paramagnetic centers has been investigated by ESR X-band spectrometer. The highest deuteron polarization was 8% at 2.5 T and 1 K with a spin concentration of $3\times 10^{19}$ spins/g.

A new experiment SPASCHARM for systematic study of polarization phenomena in the inclusive and exclusive hadronic reactions in the energy range of IHEP accelerator U-70 (12–50GeV) is currently under development. 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 proton and antiproton beams. At the beginning, the final states consisting of light quarks ($u$, $d$, $s$) will be reconstructed, and later on the charmonium states will be studied. Measurements are planned for a variety of beams: ${\pi }^{\pm },K^{\pm },p$, antiprotons. Hyperon polarization and spin density matrix elements of the vector mesons will be measured along with the single-spin asymmetry (SSA). The 2$\pi$-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, $\mathrm{\Delta }\theta \approx 250$ 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.

A short review of the XV Workshop on High Energy Spin Physics (Dubna, Russia, October 8–12, 2013) is presented.