Single Spin Asymmetries Research Articles

Single spin asymmetry AULsin(ϕh−ϕR) in dihadron semi-inclusive DIS

In this paper, we study the single longitudinal spin asymmetry ${A}_{UL}^{\mathrm{sin}({\ensuremath{\phi}}_{h}\ensuremath{-}{\ensuremath{\phi}}_{R})}$ of dihadron production in semi-inclusive deep inelastic scattering (SIDIS) via helicity-dependent dihadron fragmentation function (DiFF), which describes the correlation of the longitudinal polarization of a fragmenting quark with the transverse momenta of the produced hadron pair. Recently, experimental searching for this azimuthal asymmetry in dihadron SIDIS by the COMPASS Collaboration yielded a very small signal. Here we calculate this unknown T-odd DiFF ${G}_{1}^{\ensuremath{\perp}}$ using a spectator model to access the asymmetry and clarify why the signal is very small. The transverse momentum dependent factorization method, in which the transverse momentum of the final state hadron pair leaves unintegrated, has been applied. We estimate the $\mathrm{sin}({\ensuremath{\phi}}_{h}\ensuremath{-}{\ensuremath{\phi}}_{R})$ asymmetry at the kinematics of COMPASS experiments and compare with the data. What's more, the predictions on the same asymmetry are also made at the electron ion collider.

Recent results on cold-QCD from RHIC

Polarized proton-proton collisions at the Relativistic Heavy Ion Collider (RHIC) provide unique opportunities to study the spin structure of the nucleon. We will highlight recent results on the nucleon spin structure from the STAR and PHENIX experiments at RHIC: (1) A sizable gluon polarization in the proton is measured with longitudinal double spin asymmetries of jet and hadron production; (2) Longitudinal single spin asymmetries in W boson production improve constraints on the sea quark polarization. The new spin asymmetry results for W boson confirmed the SU(2) flavor asymmetry of the light sea quark polarization in the proton; (3) Transverse spin effects in hadronic systems offer new implications on parton distribution functions in the collinear and transverse momentum dependent frameworks. We will also discuss near term plans for the STAR forward detector upgrade and prospects for proton-proton and protonion collisions in the years beyond 2021 at STAR.

Overview of recent HERMES results

The HERMES experiment has collected a wealth of data using the 27.6 GeV polarized HERA lepton beam and various polarized and unpolarized gaseous targets. This allows for a series of unique measurements of observables sensitive to the multidimensional (spin) structure of the nucleon, in particular semi-inclusive deep-inelastic scattering (SIDIS) measurements.In this contribution, transverse single-spin asymmetry, longitudinal single- and double-spin asymmetries in SIDIS will be presented. The azimuthally uniform double-spin asymmetries using longitudinally polarized nucleons constrain the flavour dependence of the quark-spin contribution to the nucleon spin. For a first time, such asymmetries are explored differential in three dimensions in Bjorken-x and the in the hadron kinematics z and Ph± (which respectively represent the energy fraction and transverse momentum of the final-state hadron) simultaneously. This approach increases the quark-flavour sensitivity and allows to probe the transverse-momentum dependence of the helicity distribution. The measurement of hadron charge-difference asymmetries allows, under certain simplifying assumptions, the direct extraction of valence quark polarisations.The azimuthal modulation of this double-spin as well as of the single-(beam)spin asymmetry probe novel quark-gluon-quark correlations through twist-3 distribution and fragmentation functions. Also here, asymmetries are explored in several dimensions. Furthermore, in case of the beam-spin asymmetry, results for electro-produced protons and antiprotons have become available. The beam-spin asymmetries for pions are compared to similar measurements for pions at CLAS and unidentified hadrons at COMPASS.

Single-spin asymmetries in p^uparrow p rightarrow J/psi +X within a TMD approach: role of the color octet mechanism

We calculate the transverse single-spin asymmetry (SSA) for J/psi production in proton-proton collisions, within non-relativistic QCD, employing the transverse momentum dependent, generalized parton model, which includes both spin and intrinsic motion effects. In particular, we study the role of the color octet mechanism in accessing the gluon Sivers function. In doing that, we also show, within this approach, how the singularities coming from color octet terms in the low-P_T region can be handled, leading to finite cross sections. Predictions for both unpolarized cross sections and SSAs are given and compared against PHENIX data. Estimates for LHCb in the fixed target mode are also presented.

Lepton mass effects for beam-normal single-spin asymmetry in elastic muon-proton scattering

We estimate the beam-normal single-spin asymmetry in elastic lepton-proton scattering without employing the ultrarelativistic approximation. Our calculation is relevant for analyses of muon scattering at energies of few hundred MeV and below -- when effects of the muon mass become essential. At such energies, the transverse polarization of the muon beam is expected to contribute significantly to the systematic uncertainty of precision measurements of elastic muon-proton scattering. We evaluate such systematics using an example of the MUSE experiment at PSI. The muon asymmetry is estimated at about 0.1\% in kinematics of MUSE and it is the largest for scattering into a backward hemisphere.

Single-spin asymmetries at two loops

We find a novel mechanism for generating transverse single-spin asymmetry (SSA) in semi-inclusive deep inelastic scattering, distinct from the known ones which involve the Sivers and Collins functions, or their collinear twist-three counterparts. It is demonstrated that a phase needed for SSA can be produced purely within a parton-level cross section starting at two loops. We identify the complete set of two-loop diagrams for SSA, and discuss their gauge invariance and collinear factorization which features the $g_T$ distribution function. In the $k_T$ factorization framework, many more sources for SSA exist, and contributions from all possible two-parton transverse-momentum-dependent parton distribution functions are presented up to two loops and twist three.

Revisiting model relations between T -odd transverse-momentum-dependent parton distributions and generalized parton distributions

We revisit the connection between generalized parton distributions in impact parameter space and T-odd effects in single spin asymmetries of the semi-inclusive deep inelastic process. We show that nontrivial relations can be established only under very specific conditions, typically realized only in models that describe hadrons as two-body bound systems and involving a helicity-conserving coupling between the gauge boson and the spectator system. Examples of these models are the the scalar-diquark spectator model or the quark-target model for the nucleon, and relativistic models for the pion at the lowest order in the Fock-space expansion.

Nuclear Dependence of the Transverse Single-Spin Asymmetry in the Production of Charged Hadrons at Forward Rapidity in Polarized p+p, p+Al, and p+Au Collisions at sqrt[s_{NN}]=200 GeV.

We report on the nuclear dependence of transverse single-spin asymmetries (TSSAs) in the production of positively charged hadrons in polarized p^{↑}+p, p^{↑}+Al, and p^{↑}+Au collisions at sqrt[s_{NN}]=200 GeV. The measurements have been performed at forward rapidity (1.4<η<2.4) over the range of transverse momentum (1.8<p_{T}<7.0 GeV/c) and Feynman x (0.1<x_{F}<0.2). We observed positive asymmetries for positively charged hadrons in p^{↑}+p collisions, and significantly reduced asymmetries in p^{↑}+A collisions. These results reveal a nuclear dependence of TSSAs for charged-hadron production in a regime where perturbative techniques are applicable. These results provide new opportunities to use p^{↑}+A collisions as a tool to investigate the rich phenomena behind TSSAs in hadronic collisions and to use TSSAs as a new handle in studying small-system collisions.

QCD evolution of the orbital angular momentum of quarks and gluons: Genuine twist-three part

We present the numerical solution of the one-loop QCD evolution equation for the genuine twist-three part of the orbital angular momentum (OAM) distributions of quarks and gluons inside a longitudinally polarized nucleon. This is based on the observation that the evolution is identical to that of the Efremov-Teryaev-Qiu-Sterman function for transverse single spin asymmetry. Together with the known evolution of the Wandzura-Wilczek part, the one-loop evolution of OAM distributions is now practically under control. We also study, for the first time, the scale dependence of the potential angular momentum defined as the difference between the Ji and Jaffe-Manohar definitions of OAM.

Measurement of the single-spin asymmetry [formula omitted] in quasi-elastic 3He↑(e,e′n) scattering at 0.4 < Q2 < 1.0 GeV/c2

Due to the lack of free neutron targets, studies of the structure of the neutron are typically made by scattering electrons from either 2H or 3He targets. In order to extract useful neutron information from a 3He target, one must understand how the neutron in a 3He system differs from a free neutron by taking into account nuclear effects such as final state interactions and meson exchange currents. The target single spin asymmetry Ay0 is an ideal probe of such effects, as any deviation from zero indicates effects beyond plane wave impulse approximation. New measurements of the target single spin asymmetry Ay0 at Q2 of 0.46 and 0.96 (GeV/c)2 were made at Jefferson Lab using the quasi-elastic He↑3(e,e′n) reaction. Our measured asymmetry decreases rapidly, from >20% at Q2=0.46 (GeV/c)2 to nearly zero at Q2=0.96 (GeV/c)2, demonstrating the fall-off of the reaction mechanism effects as Q2 increases. We also observed a small ϵ-dependent increase in Ay0 compared to previous measurements, particularly at moderate Q2. This indicates that upcoming high Q2 measurements from the Jefferson Lab 12 GeV program can cleanly probe neutron structure from polarized 3He using plane wave impulse approximation.

Introduction to the Transverse-Momentum-Weighted Technique in the Twist-3 Collinear Factorization Approach

The twist-3 collinear factorization framework has drawn much attention in recent decades as a successful approach in describing the data for single spin asymmetries (SSAs). Many SSAs data have been experimentally accumulated in a variety of energies since the first measurement was done in the late 1970s and it is expected that the future experiments like Electron-Ion-Collider will provide us with more data. In order to perform a consistent and precise description of the data taken in different kinematic regimes, the scale evolution of the collinear twist-3 functions and the perturbative higher-order hard part coefficients are mandatory. In this paper, we introduce the techniques for next-to-leading order (NLO) calculation of transverse-momentum-weighted SSAs, which can be served as a useful tool to derive the QCD evolution equation for twist-3 functions and to verify the QCD collinear factorization for twist-3 observables at NLO, as well as obtain the finite NLO hard part coefficients.

Single spin asymmetry in transverse polarized proton production and $\Lambda$ production in semi-inclusive DIS at twist-3

We study the single spin asymmetry in the transversely polarized proton production and the $\Lambda$ hyperon production in semi-inclusive deep inelastic scattering with a $\sin \phi_{S_h}$ modulation, in which $\phi_{S_h}$ is the azimuthal angle of the transverse spin of the final hadron. The theoretical interpretation for the asymmetry is presented as the convolution of the twist-3 quark transverse-momentum-dependent distributions and twist-2 fragmentation functions. We investigate the role of the twist-3 distribution functions $ h(x,\mathbf{p}_{T}^{2})$ , $ f^{\perp}(x,\mathbf{p}_{T}^{2})$ and $ g^{\perp}(x,\mathbf{p}_{T}^{2})$ and the twist-2 fragmentation functions $ H_{1}(x,\mathbf{k}_{T}^{2})$ , $ D_{1T}^\perp(x,\mathbf{k}_T^2)$ and $ G_{1T}(x,\mathbf{k}_T^2)$ in this asymmetry. Using the spectator models, we compute these distribution functions and fragmentation functions and estimate their contribution to the $ \sin \phi_{S_{h}}$ asymmetry for the proton production as well as for the $\Lambda$ production at JLab with a 12GeV electron beam. The asymmetry at the COMPASS kinematics is also predicted. By comparing different sources for the asymmetry, we conclude that sizable $\sin \phi_{S_{h}}$ asymmetry for the transversely polarized proton production might be accessible in the SIDIS at the kinematics of JLab and COMPASS.

Lepton-Jet Correlations in Deep Inelastic Scattering at the Electron-Ion Collider.

We propose the lepton-jet correlation in deep inelastic scattering as a unique tool for the tomography of nucleons and nuclei at the electron-ion collider (EIC). The azimuthal angular correlation between the final state lepton and jet depends on the transverse momentum dependent quark distributions. We take the example of single transverse spin asymmetries to show the sensitivity to the quark Sivers function. When the correlation is studied in lepton-nucleus collisions, transverse momentum broadening effects can be used to explore cold nuclear matter effects. These features make lepton-jet correlations an important new hard probe at the EIC.

Single spin asymmetry in forward pA collisions: Phenomenology at RHIC

We confront the theoretical result of single spin asymmetry (SSA) $A_N$ in forward $pA$ collisions $p^\uparrow A \to hX$ including the gluon saturation effect with the recent preliminary experimental data from the PHENIX and STAR collaborations at RHIC. While we find overall reasonable agreement with the STAR data, our results indicate that the strong nuclear suppression of the asymmetry $A_N\sim A^{-1/3}$ observed by the PHENIX collaboration cannot be explained within the present understanding of this problem.

On the Double Spin Asymmetries in the Elastic Scattering of Electrons off Protons

Based on the obtained differential cross sections for the scattering of longitudinally polarized electrons, taking into account the polarization of the proton target or the longitudinal polarization of the recoil protons, the next single spin asymmetries are studied: breaking T-parity asymmetry in the spin of the target proton $${{A}^{{( \bot )}}}$$ , and the degree of longitudinal polarization of recoil protons $${{P}_{p}}$$ . Double spin asymmetries are also obtained and analyzed: asymmetry $${{A}_{{ep}}}$$ with respect to the correlation of the incident electron helicity and the spin of the target proton, and right-left asymmetry $${{D}_{p}}$$ of the degree of longitudinal polarization of the recoil proton. It is shown that these asymmetries make it possible to measure the ratios of the proton form factors $${{{{G}_{{Ep}}}} \mathord{\left/ {\vphantom {{{{G}_{{Ep}}}} {{{G}_{{Mp}}}}}} \right. \kern-0em} {{{G}_{{Mp}}}}}$$ and $${{{{G}_{{Mp}}}} \mathord{\left/ {\vphantom {{{{G}_{{Mp}}}} {{{G}_{{1p}}}}}} \right. \kern-0em} {{{G}_{{1p}}}}}$$ .

Measurement of the longitudinal spin asymmetries for weak boson production in proton-proton collisions at s=510 GeV

We report new STAR measurements of the single-spin asymmetries $A_L$ for $W^+$ and $W^-$ bosons produced in polarized proton--proton collisions at $\sqrt{s}$ = 510 GeV as a function of the decay-positron and decay-electron pseudorapidity. The data were obtained in 2013 and correspond to an integrated luminosity of 250 pb$^{-1}$. The results are combined with previous results obtained with 86 pb$^{-1}$. A comparison with theoretical expectations based on polarized lepton-nucleon deep-inelastic scattering and prior polarized proton--proton data suggests a difference between the $\bar{u}$ and $\bar{d}$ quark helicity distributions for $0.05 < x < 0.25$. In addition, we report new results for the double-spin asymmetries $A_{LL}$ for $W^\pm$, as well as $A_L$ for $Z/\gamma^*$ production and subsequent decay into electron--positron pairs.

Single-spin asymmetry in dihadron production in SIDIS off longitudinally polarized nucleon targets

We study the single longitudinal-spin asymmetry of dihadron production in semi-inclusive deep inelastic scattering process. We consider the collinear picture in which the transverse momentum of the final-state hadron pair is integrated out, such that the $\sin \phi_R$ azimuthal asymmetry arises from the coupling $h_L\, H_{1}^{\sphericalangle}$ as well as the coupling $g_1 \,\widetilde{G}^{\sphericalangle}$. We calculate the unknown twist-3 dihadron fragmentation function $\widetilde{G}^{\sphericalangle}$ using a spectator model which is successful in describing the dihadron production in the unpolarized process. Using the spectator model results for the quark distributions and dihadron fragmentation functions, we estimate the $\sin \phi_R$ asymmetry of dihadron production in SIDIS at the kinematics of COMPASS and compare it with the COMPASS preliminary data. In addition, the prediction on the $\sin \phi_R$ asymmetry at the typical kinematics of the future Electron Ion Collider is also presented. In order to test the reliability of the spectator model estimate, we compare the model result for the distribution $h_L$ with the Wandzura-Wilczek approximation for that distribution, and compare $H_{1}^{\sphericalangle}$ with the existing parametrization. Although the asymmetry is dominated by the $h_L H_{1}^{\sphericalangle}$ term, we find that the contribution from the $g_1\, \widetilde{G}^{\sphericalangle}$ term should also be taken into account in certain kinematical region.

Unraveling the gluon Sivers function in hadronic collisions at RHIC

We study the transverse single-spin asymmetries for $p^\uparrow p\to \pi\, X$ and $p^\uparrow p\to \gamma\, X$ within the so-called color gauge invariant generalized parton model (CGI-GPM) which, in addition to spin and transverse momentum effects, includes initial and final state interactions with the polarized proton remnants. We compute all relevant contributions, focusing in particular on the process dependence of the gluon Sivers function, which, for these processes, can always be expressed as a linear combination of two independent, universal terms. This study extends and completes a previous one, where only quark initiated partonic processes were considered. We then perform a combined phenomenological analysis of RHIC data on transverse single-spin asymmetries in $p^\uparrow p\to \pi\, X$ and $p^\uparrow p\to D\, X$, putting the first preliminary constraints on these two gluon Sivers functions. We show how their size can be estimated by means of these data, and use our results to provide predictions for the process $p^\uparrow p\to J/\psi\,X$, comparing them with data, and $p^\uparrow p\to \gamma\, X$, for which experimental information will soon become available. Corresponding estimates within the simpler GPM approach, without initial and final state interactions and with a single universal gluon Sivers function, are also given, showing that a clear discrimination between these two models is, for the moment, not possible.

Computing the gluon Sivers function at small-x

We compute the gluon Sivers function f1T⊥g(x,k⊥) of the transversely polarized nucleon at small-x by exploiting the known connection between the dipole gluon Sivers function and the Odderon. We numerically solve the evolution equation for the Odderon both in the linear and nonlinear regimes. While we find that the x and k⊥ dependences of the Sivers function do not factorize as a result of the quantum evolution, factorization breaking is not numerically significant, and is much milder than what one expects in the case of unpolarized TMDs. We also point out the possibility that, due to the presence of a node in the Sivers function, single spin asymmetry for open charm production in semi-inclusive deep inelastic scattering flips signs as the transverse momentum of D-mesons is varied. This can be tested at the future Electron–Ion Collider.

Transverse single spin asymmetry for very forward π0 production in polarized proton-proton collisions at √s = 510 GeV

Transverse single spin asymmetry, AN, of very forward π0 production from polarized p + p collisions provides new information toward an understanding of its production mechanism. AN of forward π0 in the pseudorapidity region of 3 &lt; η &lt; 4 has been described by the partonic structure of the proton in the perturbative QCD framework. However, recent data indicates a potential contribution from not only partonic but also diffractive interactions. In order to provide a new insight on the origin of the AN, we measured the very forward π0 production in the pseudorapidity region of 6 &lt; η from √s = 510 GeV polarized p + p collisions at RHIC in 2017. We report our measurement of the very forward π0 over the transverse momentum range of 0 &lt; pT &lt; 1 GeV/c and the preliminary result.