Single spin asymmetries in charged pion production from semi-inclusive deep inelastic scattering on a transversely polarized 3He Target at Q2 = 1.4-2.7 GeV2

The Collins Asymmetry in Λ Hyperon Produced SIDIS Process at Electron–Ion Colliders

We investigate Collins asymmetry in the Λ hyperon produced semi-inclusive deep inelastic scattering (SIDIS) process based on the kinematical region of Electron-ion collider in China (EicC) and Electron–ion collider (EIC) within the transverse momentum dependence (TMD) factorization framework at next-to-leading-logarithmic order. The asymmetry is contributed by the convolution of the target proton transversity distribution function and the Collins function of the final-state Λ hyperon. The TMD evolution effect of the corresponding parton distribution functions (PDFs) and fragmentation functions (FFs) is considered with the help of parametrization of the non-perturbative Sudakov form factors for the proton PDFs and Λ fragmentation functions. We apply the parametrization of the collinear proton transversity distribution function and the model results of Λ Collins function from the diquark spectator model as the inputs of the TMD evolution to numerically calculate Collins asymmetry in Λ produced SIDIS process at the kinematical configurations of EIC and EicC. It can be shown that the asymmetry is significant and can be measured at EIC and EicC. The flavor dependence of transversity distribution functions could be further constrained by studying the Λ hyperon produced SIDIS process in the future to improve our understanding of the spin structure within nucleons.

Extraction of the Sivers Function from SIDIS, Drell-Yan, and W^{±}/Z Data at Next-to-Next-to-Next-to Leading Order

We perform the global analysis of polarized semi-inclusive deep inelastic scattering (SIDIS), pion-induced polarized Drell-Yan (DY) process, and W^{±}/Z boson production data and extract the Sivers function for u, d, s and for sea quarks. We use the framework of transverse momentum dependent factorization at next-to-next-to-next-to leading order (N^{3}LO) accuracy. The Qiu-Sterman function is determined in a model independent way from the extracted Sivers function. We also evaluate the significance of the predicted sign change of the Sivers function in DY process with respect to SIDIS.

The spin structure of the nucleon

We review the present understanding of the spin structure of protons and neutrons, the fundamental building blocks of nuclei collectively known as nucleons. The field of nucleon spin provides a critical window for testing Quantum Chromodynamics (QCD), the gauge theory of the strong interactions, since it involves fundamental aspects of hadron structure which can be probed in detail in experiments, particularly deep inelastic lepton scattering on polarized targets. QCD was initially probed in high energy deep inelastic lepton scattering with unpolarized beams and targets. With time, interest shifted from testing perturbative QCD to illuminating the nucleon structure itself. In fact, the spin degrees of freedom of hadrons provide an essential and detailed verification of both perturbative and nonperturbative QCD dynamics. Nucleon spin was initially thought of coming mostly from the spin of its quark constituents, based on intuition from the parton model. However, the first experiments showed that this expectation was incorrect. It is now clear that nucleon physics is much more complex, involving quark orbital angular momenta as well as gluonic and sea quark contributions. Thus, the nucleon spin structure remains a most active aspect of QCD research, involving important advances such as the developments of generalized parton distributions (GPD) and transverse momentum distributions (TMD). Elastic and inelastic lepton-proton scattering, as well as photoabsorption experiments provide various ways to investigate non-perturbative QCD. Fundamental sum rules-such as the Bjorken sum rule for polarized photoabsorption on polarized nucleons-are also in the non-perturbative domain. This realization triggered a vigorous program to link the low energy effective hadronic description of the strong interactions to fundamental quarks and gluon degrees of freedom of QCD. This has also led to advances in lattice gauge theory simulations of QCD and to the development of holographic QCD ideas based on the AdS/CFT or gauge/gravity correspondence, a novel approach providing a well-founded semiclassical approximation to QCD. Any QCD-based model of the nucleon's spin and dynamics must also successfully account for the observed spectroscopy of hadrons. Analytic calculations of the hadron spectrum, a long sought goal of QCD research, have now being realized using light-front holography and superconformal quantum mechanics, a formalism consistent with the results from nucleon spin studies. We begin this review with a phenomenological description of nucleon structure in general and of its spin structure in particular, aimed to engage non-specialist readers. Next, we discuss the nucleon spin structure at high energy, including topics such as Dirac's front form and light-front quantization which provide a frame-independent, relativistic description of hadron structure and dynamics, the derivation of spin sum rules, and a direct connection to the QCD Lagrangian. We then discuss experimental and theoretical advances in the nonperturbative domain-in particular the development of light-front holographic QCD and superconformal quantum mechanics, their predictions for the spin content of nucleons, the computation of PDFs and of hadron masses.

Optically polarized 3He

This article reviews the physics and technology of producing large quantities of highly spin-polarized 3He nuclei using spin-exchange (SEOP) and metastability-exchange (MEOP) optical pumping. Both technical developments and deeper understanding of the physical processes involved have led to substantial improvements in the capabilities of both methods. For SEOP, the use of spectrally narrowed lasers and K-Rb mixtures has substantially increased the achievable polarization and polarizing rate. For MEOP nearly lossless compression allows for rapid production of polarized 3He and operation in high magnetic fields has likewise significantly increased the pressure at which this method can be performed, and revealed new phenomena. Both methods have benefitted from development of storage methods that allow for spin-relaxation times of hundreds of hours, and specialized precision methods for polarimetry. SEOP and MEOP are now widely applied for spin-polarized targets, neutron spin filters, magnetic resonance imaging, and precision measurements.

First Measurement of Transverse-Spin-Dependent Azimuthal Asymmetries in the Drell-Yan Process

The first measurement of transverse-spin-dependent azimuthal asymmetries in the pion-induced Drell-Yan (DY) process is reported. We use the CERN SPS 190  GeV/c π^{-} beam and a transversely polarized ammonia target. Three azimuthal asymmetries giving access to different transverse-momentum-dependent (TMD) parton distribution functions (PDFs) are extracted using dimuon events with invariant mass between 4.3  GeV/c^{2} and 8.5  GeV/c^{2}. Within the experimental uncertainties, the observed sign of the Sivers asymmetry is found to be consistent with the fundamental prediction of quantum chromodynamics (QCD) that the Sivers TMD PDFs extracted from DY have a sign opposite to the one extracted from semi-inclusive deep-inelastic scattering (SIDIS) data. We present two other asymmetries originating from the pion Boer-Mulders TMD PDFs convoluted with either the nucleon transversity or pretzelosity TMD PDFs. A recent COMPASS SIDIS measurement was obtained at a hard scale comparable to that of these DY results. This opens the way for possible tests of fundamental QCD universality predictions.

Measurement of the Transverse Single-Spin Asymmetry in p^{↑}+p→W^{±}/Z^{0} at RHIC

We present the measurement of the transverse single-spin asymmetry of weak boson production in transversely polarized proton-proton collisions at sqrt[s]=500  GeV by the STAR experiment at RHIC. The measured observable is sensitive to the Sivers function, one of the transverse-momentum-dependent parton distribution functions, which is predicted to have the opposite sign in proton-proton collisions from that observed in deep inelastic lepton-proton scattering. These data provide the first experimental investigation of the nonuniversality of the Sivers function, fundamental to our understanding of QCD.

Measurement of Azimuthal Asymmetries in Inclusive Charged Dipion Production in e^{+}e^{-} Annihilations at sqrt[s]=3.65 GeV

We present a measurement of the azimuthal asymmetries of two charged pions in the inclusive process e^{+}e^{-}→ππX, based on a data set of 62  pb^{-1} at the center-of-mass energy of 3.65 GeV collected with the BESIII detector. These asymmetries can be attributed to the Collins fragmentation function. We observe a nonzero asymmetry, which increases with increasing pion momentum. As our energy scale is close to that of the existing semi-inclusive deep inelastic scattering experimental data, 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.

Measurement of the Target-Normal Single-Spin Asymmetry in Quasielastic Scattering from the Reaction (3)He(↑)(e,e')

We report the first measurement of the target single-spin asymmetry, A(y), in quasielastic scattering from the inclusive reaction (3)He(↑)(e,e') on a (3)He gas target polarized normal to the lepton scattering plane. Assuming time-reversal invariance, this asymmetry is strictly zero for one-photon exchange. A nonzero A(y) can arise from the interference between the one- and two-photon exchange processes which is sensitive to the details of the substructure of the nucleon. An experiment recently completed at Jefferson Lab yielded asymmetries with high statistical precision at Q(2)=0.13, 0.46, and 0.97  GeV(2). These measurements demonstrate, for the first time, that the (3)He asymmetry is clearly nonzero and negative at the 4σ-9σ level. Using measured proton-to-(3)He cross-section ratios and the effective polarization approximation, neutron asymmetries of -(1-3)% were obtained. The neutron asymmetry at high Q(2) is related to moments of the generalized parton distributions (GPDs). Our measured neutron asymmetry at Q(2)=0.97  GeV(2) agrees well with a prediction based on two-photon exchange using a GPD model and thus provides a new, independent constraint on these distributions.

Sivers effect in two-hadron electroproduction

The Sivers effect in single hadron semi-inclusive deep inelastic scattering on a transversely polarized nucleon describes the modulation of the cross section with the sine of the azimuthal angle between the produced hadron's transverse momentum and the nucleon spin (P(h) and φ(S), respectively). This effect is attributed to the so-called Sivers parton distribution function of the nucleon. We employ a simple phenomenological parton model to derive the relevant cross section for two-hadron production in semi-inclusive deep inelastic scattering including the Sivers effect. We show that the Sivers effect can be observed in such a process as sine modulations involving the azimuthal angles φ(T) and φ(R) of both the total and the relative transverse momenta of the hadron pair. The existence of the modulation with respect to φ(R) is new. Finally, we employ a modified version of the lepto Monte Carlo event generator that includes the Sivers effect to estimate the size of single spin asymmetries corresponding to these modulations. We show that sin(φ(R)-φ(S)) modulations can be significant, especially if we impose asymmetric cuts on the momenta of the hadrons in the pairs.

Precision measurement of the neutron twist-3 matrix element d(2)(n): probing color forces

Double-spin asymmetries and absolute cross sections were measured at large Bjorken x  (0.25≤x≤0.90), in both the deep-inelastic and resonance regions, by scattering longitudinally polarized electrons at beam energies of 4.7 and 5.9 GeV from a transversely and longitudinally polarized (3)He target. In this dedicated experiment, the spin structure function g(2)((3)He) was determined with precision at large x, and the neutron twist-3 matrix element d(2)(n) was measured at ⟨Q(2)⟩ of 3.21 and 4.32  GeV(2)/c(2), with an absolute precision of about 10(-5). Our results are found to be in agreement with lattice QCD calculations and resolve the disagreement found with previous data at ⟨Q(2)⟩=5  GeV(2)/c(2). Combining d(2)(n) and a newly extracted twist-4 matrix element f(2)(n), the average neutron color electric and magnetic forces were extracted and found to be of opposite sign and about 30  MeV/fm in magnitude.

Indication on the process dependence of the Sivers effect

We analyze the spin asymmetry for single inclusive jet production in proton-proton collisions collected by the AnDY experiment at the Relativistic Heavy Ion Collider and the Sivers asymmetry data from semi-inclusive deep inelastic scattering experiments. In particular, we consider the role color gauge invariance plays in determining the process dependence of the Sivers effect. We find that after carefully taking into account the initial-state and final-state interactions between the active parton and the remnant of the polarized hadron, the calculated jet spin asymmetry based on the Sivers functions extracted from HERMES and COMPASS experiments is consistent with the AnDY experimental data. This provides a first indication for the process dependence of the Sivers effect in these processes. We also make predictions for both direct photon and Drell-Yan spin asymmetry, to further test the process dependence of the Sivers effect in future experiments.

Beam-target double-spin asymmetry A{LT} in charged pion production from deep inelastic scattering on a transversely polarized {3}He target at 1.4<Q{2}<2.7 GeV{2}

We report the first measurement of the double-spin asymmetry A{LT} for charged pion electroproduction in semi-inclusive deep-inelastic electron scattering on a transversely polarized {3}He target. The kinematics focused on the valence quark region, 0.16<x<0.35 with 1.4<Q{2}<2.7  GeV{2}. The corresponding neutron A{LT} asymmetries were extracted from the measured {3}He asymmetries and proton over {3}He cross section ratios using the effective polarization approximation. These new data probe the transverse momentum dependent parton distribution function g{1T}{q} and therefore provide access to quark spin-orbit correlations. Our results indicate a positive azimuthal asymmetry for π{-} production on {3}He and the neutron, while our π{+} asymmetries are consistent with zero.

Constraining quark angular momentum through semi-inclusive measurements

The determination of quark angular momentum requires the knowledge of the generalized parton distribution E in the forward limit. We assume a connection between this function and the Sivers transverse-momentum distribution, based on model calculations and theoretical considerations. Using this assumption, we show that it is possible to fit nucleon magnetic moments and semi-inclusive single-spin asymmetries at the same time. This imposes additional constraints on the Sivers function and opens a plausible way to quantifying quark angular momentum.