Transverse Spin Structure Research Articles

Magnetodielectric effect in Z-type hexaferrite

The authors report on the magnetodielectric (MD) effect of Z-type hexaferrite Sr3Co2Fe24O41 at various temperatures and frequencies. A fairly large negative MD effect was observed with a peak near room temperature and a maximum at low frequencies. Analysis suggests that the MD effect shows a quadratic dependence on magnetization. The results were discussed by considering the magnetic field induced change of transverse conical spin structure and spin-phonon coupling. This work is helpful for understanding the MD effect in materials with complicated spin structures.

COMPASS RESULTS ON TMD OBSERVABLES

The study of the transverse spin and transverse momentum structure of the nucleon is an important part of the scientific program of COMPASS, a fixed target experiment taking data at the CERN SPS since 2002. In these ten years COMPASS has produced a number of interesting results by measuring the forward going hadrons produced in deep inelastic scattering of a 160 GeV muon beam off polarized deuteron and proton targets. The COMPASS contribution to the understanding of the transverse structure of the nucleon, and the possible future contributions, are briefly reviewed here.

Transverse (spin) structure of hadrons

Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when the target and/or quark are transversely polarized. Connections between this deformation and transverse single-spin asymmetries as well as with quark–gluon correlations are discussed. The sign of transverse deformation of impact parameter dependent parton distributions in a transversely polarized target can be related to the sign of the contribution from that quark flavor to the nucleon anomalous magnetic moment. Therefore, the signs of the Sivers function for u and d quarks, as well as the signs of quark–gluon correlations embodied in the polarized structure function g2 can be understood in terms of the proton and neutron anomalous magnetic moments.

COMPASS results on the nucleon spin structure

A review of the COMPASS results on the longitudinal and transverse spin structure of nucleon is presented. The gluon contribution to the spin of nucleon, measured by several methods, is found to be small. The solid evidence for Sivers and Collins asymmetries is observed.

Tensor form factors of nucleon in QCD

We extract the isovector tensor nucleon form factors, which play an important role in understanding the transverse spin structure of the nucleon when related to the quark helicity-flip generalized parton distributions via their first moments. We employ the light-cone QCD sum rules to leading order in QCD and include distribution amplitudes up to twist 6 in order to calculate the three tensor form factors HT, ET and H˜T. Our results agree well with those from other approaches in the low and high momentum-transfer regions.

Experimental Studies of the Nucleon Spin Structure: from the Past to the Future

Twenty two years ago the "proton spin crisis" has been declared after the European Muon Collaboration at CERN had found that total quark spin constitutes only a small fraction of the proton spin. This result is now confirmed, a large gluon polarisation in the proton seems unlikely and measurements of the parton angular momenta have started only recently. Therefore the "proton spin puzzle" is still alive. A review of the longitudinal and transverse nucleon spin structure is presented. Future of the experimental spin physics is discussed.

Spin Structure Functions

Spin-dependent observables have been a powerful tool to probe the internal structure of the nucleon and to understand the dynamics of the strong interaction. Experiments involving spin degrees of freedom have often brought out surprises and puzzles. The so-called "spin crisis" in the 1980s revealed the limitation of naive quark-parton models and led to intensive worldwide efforts, both experimental and theoretical, to understand the nucleon spin structure. With high intensity and high polarization of both the electron beam and targets, Jefferson Lab has the world's highest polarized luminosity and the best figure-of-merit for precision spin structure measurements. It has made a strong impact in this subfield of research. This chapter will highlight Jefferson Lab's unique contributions in the measurements of valence quark spin distributions, in the moments of spin structure functions at low to intermediate Q2, and in the transverse spin structure.

The spin structure of the proton from lattice QCD

This proceeding discusses recent achievements in lattice QCD calculations of the longitudinal and transverse spin structure of the nucleon. Starting from the latest lattice results on moments of generalized parton distributions, we focus on the decomposition of the proton spin 1/2 in terms of quark (and gluon) spin and orbital angular momentum contributions. Recent results on the transverse nucleon spin structure obtained from lattice studies of transverse momentum distributions will be discussed and illustrated in the form of spin densities of quarks in the proton. We compare the results with expectations from phenomenological and model studies, and point out the most important systematic uncertainties and remaining challenges in the lattice approach.

Single spin asymmetries for identified hadrons at COMPASS

COMPASS is a fixed target experiment at CERN SPS, dedicated to the study of the nucleon spin structure and hadron spectroscopy. The transverse spin structure of the nucleon is investigated by measuring semi-inclusive deep inelastic scattering (SIDIS) of a 160 GeV/c longitudinally polarized muon beam off transversely polarised targets. Particle Identification (PID) is performed with a Ring Imaging CHerenkov detector (RICH) that has been upgraded in 2005. COMPASS took data using transversely polarised 6LiD target from 2002 to 2004 and with a transversely polarised NH3 target in 2007.In this talk the Collins and Sivers asymmetries on polarised proton for charged pions and kaons will be shown for the first time and compared with the same results on polarised deuteron for COMPASS.

Magnetic Ordering in Relation to the Room-Temperature Magnetoelectric Effect ofSr3Co2Fe24O41

The origin of a room-temperature magnetoelectric (ME) effect has been examined by means of neutron powder diffraction measurements for a Z-type hexaferrite Sr(3)Co(2)Fe(24)O(41). The temperature and magnetic-field dependence of the electric polarization P and several magnetic Bragg reflections show that a commensurate magnetic order with a (0,0,1) propagation vector has an intimate connection with the ME effect. The room-temperature ME effect can be understood in terms of the appearance of P which is induced by a transverse conical spin structure through the inverse Dzyaloshinskii-Moriya mechanism in analogy with Y-type hexaferrites.

Transverse spin structure of the nucleon through target single-spin asymmetry in semi-inclusive deep-inelastic (e, e’ $ \pi^{\pm}_{}$ ) reaction at Jefferson Lab

Jefferson Lab (JLab) 12 GeV energy upgrade provides a golden opportunity to perform precision studies of the transverse spin and transverse-momentum-dependent structure in the valence quark region for both the proton and the neutron. In this paper, we focus our discussion on a recently approved experiment on the neutron as an example of the precision studies planned at JLab. The new experiment will perform precision measurements of target Single Spin Asymmetries (SSA) from semi-inclusive electro-production of charged pions from a 40-cm long transversely polarized $^3$He target in Deep-Inelastic-Scattering kinematics using 11 and 8.8 GeV electron beams. This new coincidence experiment in Hall A will employ a newly proposed solenoid spectrometer (SoLID). The large acceptance spectrometer and the high polarized luminosity will provide precise 4-D ($x$, $z$, $P_T$ and $Q^2$) data on the Collins, Sivers, and pretzelocity asymmetries for the neutron through the azimuthal angular dependence. The full 2$\pi$ azimuthal angular coverage in the lab is essential in controlling the systematic uncertainties. The results from this experiment, when combined with the proton Collins asymmetry measurement and the Collins fragmentation function determined from the e$^+$e$^-$ collision data, will allow for a quark flavor separation in order to achieve a determination of the tensor charge of the d quark to a 10% accuracy. The extracted Sivers and pretzelocity asymmetries will provide important information to understand the correlations between the quark orbital angular momentum and the nucleon spin and between the quark spin and nucleon spin.

Highlights from the COMPASS experiment

The Compass experiment at CERN is studying the nucleon spin structure with a 160 GeV polarized muon beam and polarized targets as well as hadron structure with 190 GeV pion, kaon and proton beams. The paper gives an overview of the results for the helicity and transverse spin structure of the nucleon. A first result from the spectroscopy experiments, the observation of a resonance with exotic JPC = 1−+ quantum numbers at 1660 MeV is also presented. The paper ends with an outlook to future measurements.

The transverse spin structure of the pion at short distances

We study the form factors of the quark tensor currents in the pion at large squared momentum transfer Q2. It turns out that certain form factors can be evaluated using collinear factorization, whereas others receive important contributions from the end-point regions of the longitudinal quark momenta in the pion. We derive simple analytic expressions for the dominant terms at high Q2 and illustrate them numerically.

Finite-temperature dynamical structure factor of the Heisenberg-Ising chain

We consider the spin-1/2 Heisenberg $XXZ$ chain in the regime of large Ising-type anisotropy $\ensuremath{\Delta}$. By a combination of duality and Jordan-Wigner transformations we derive a mapping to weakly interacting spinless fermions, which represent domain walls between the two degenerate ground states. We develop a perturbative expansion in $1/\ensuremath{\Delta}$ for the transverse dynamical spin structure factor at finite temperatures and in an applied transverse magnetic field. We present a unified description for both the low-energy temperature-activated response and the temperature evolution of the $T=0$ two-spinon continuum. We find that the two-spinon continuum narrows in energy with increasing temperature. At the same time spectral weight is transferred from the two-spinon continuum to the low-energy intraband scattering continuum, which is strongly peaked around the position of the (single) spinon dispersion (``Villain mode'').

Transverse Spin Structure of the Nucleon from COMPASS

The measurement of transverse spin effects in semi-inclusive deep-inelastic scattering is an important part of the COMPASS physics program. In the years 2002-2004 data were taken by scattering a 160 GeV muon beam on a transversely polarized deuteron target. In 2007, additional data were collected on a transversely polarized proton target. New results for the Collins and Sivers asymmetries from the analysis of the proton data are presented.

Magnetic and ferroelectric properties of multiferroicRMn2O5

The magnetic and ferroelectric properties of multiferroicRMn2O5 (R = Y,Tb, Ho, Er, Tm) are reviewed based on recent neutron diffraction and dielectricmeasurements. Successive phase transitions of magnetic and dielectric ordering were foundto occur simultaneously in this system. The characteristic magnetic ordering ofthe system exhibits an incommensurate–commensurate phase transition, andagain transitions to an incommensurate phase. Special attention is given to themagnetic structure in order to discuss the mechanism for the introduction offerroelectric polarization. For all the compounds examined, the spin configuration forMn4+ and Mn3+ ions in the commensurate magnetic phase, where spontaneous electric polarization occurs,was determined to be a transverse spiral spin structure propagating along thec-axis. By contrast, the alignment of the induced 4f moment ofR3+ ions showed variation, depending on the character of each of the elements. Correspondingresponses to external fields such as a magnetic field, hydrostatic pressure etc at lowtemperature are strongly dependent on the rare earth element present in theRMn2O5 system. The so-called colossal magnetoelectric effect in this system can be easilyinterpreted by the phase transition from the magnetic incommensurate and weakferroelectric phase to the commensurate and ferroelectric phase.

Spin Structure of the Pion

We present the first calculation of the transverse spin structure of the pion in lattice QCD. Our simulations are based on two flavors of nonperturbatively improved Wilson fermions, with pion masses as low as 400 MeV in volumes up to (2.1 fm)(3) and lattice spacings below 0.1 fm. We find a characteristic asymmetry in the spatial distribution of transversely polarized quarks. This asymmetry is very similar in magnitude to the analogous asymmetry we previously obtained for quarks in the nucleon. Our results support the hypothesis that all Boer-Mulders functions are alike.

Low-Magnetic-Field Control of Electric Polarization Vector in a Helimagnet

The mutual control of the electric and magnetic properties of a solid is currently of great interest because of the possible application for novel electronic devices. We report on the low-magnetic-field (for example, B values of +/-30 milliteslas) control of the polarization (P) vector in a hexaferrite, Ba2Mg2Fe12O22, which shows the helimagnetic spin structure with the propagation vector k0 parallel to [001]. The B-induced transverse conical spin structure carries the P vector directing perpendicular to both B and k0, in accord with the recently proposed spin-current model. Then, the oscillating or multidirectionally rotating B produces the cyclic displacement current via the flexible handling of the magnetic cone axis.

Transverse spin structure of hadrons from lattice QCD

This paper presents recent lattice QCD calculations of transverse spin densities of quarks in hadrons. 2 2 This contribution is based on Refs. [M. Göckeler, et al., Phys. Rev. Lett. 98 (2007) 222001; D. Brömmel, et al., [QCDSF Collaboration]. arXiv:hep-lat/0708.2249]. Based on our simulation results for the tensor generalized form factors, we find substantial correlations between spin and coordinate degrees of freedom in the nucleon and the pion. They lead to strongly distorted transverse spin densities of quarks in the nucleon and a surprisingly non-trivial transverse spin structure of the pion. Following recent arguments by Burkardt [M. Burkardt, Phys. Rev. D 72 (2005) 094020], our results imply that the Boer–Mulders function h 1 ⊥ , describing correlations of the transverse spin and intrinsic transverse momentum of quarks, is large and negative for up-quarks in the proton and the π + . This supports the recent hypothesis that all Boer–Mulders functions are alike [ arXiv:0705.1573], and also provides additional motivation for future studies of azimuthal asymmetries in π p Drell-Yan production at, e.g., COMPASS.

Spiral Spin Structure in the Commensurate Magnetic Phase of Multiferroic RMn2O5

Crystal and magnetic structure analyses have been performed for single crystals of multiferroic materials R Mn 2 O 5 ( R = Y, Ho, Er) using the neutron diffraction technique. For all the compounds, the magnetic structure in the commensurate magnetic phase, where spontaneous electric polarization occurs, was determined to be a transverse spiral spin structure propagating along the c -axis. The results demonstrate that the spin configuration for Mn 4+ and Mn 3+ ions is essentially the same in all three materials, suggesting that the ferroelectricity of the commensurate magnetic phase originates from the spin configurations of Mn ions. By contrast, the alignment of the induced 4 f -moment of Ho 3+ ions is quite different from that of Er 3+ ions, which might give a rich variety of magnetic field response for magnetic and dielectric properties in the R Mn 2 O 5 system.