Session DG: Mini-Symposium on the Spin Structure of the Nucleon II

The Orbital Angular Momentum Sum Rule

As an alternative to the Ji sum rule for the quark angular momentum, a sum rule for the quark orbital angular momentum, based on a twist-3 generalized parton distribution, has been suggested. We study the validity of this sum rule in the context of scalar Yukawa interactions as well as in QED for an electron.   

Studies of Transverse Momentum Dependent Parton Distributions and Bessel Weighting

We present a new technique for analysis of transverse momentum dependent parton distribution functions, based on the Bessel weighting formalism. Advantages of employing Bessel weighting are that transverse momentum weighted asymmetries provide a means to disentangle the convolutions in the cross section in a model independent way. The resulting compact expressions immediately connect to work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions. As a test case, we apply the procedure to studies of the double longitudinal spin asymmetry in SIDIS using a dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. Using a fully differential cross section for the process, the effect of four momentum conservation is analyzed using various input models for transverse momentum distributions and fragmentation functions. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations. Bessel weighting provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs.   

Dependence of Forward $\pi^{0}$ Transverse Single Spin Asymmetries on Roman Pot Triggers from $\sqrt{s}=200$ GeV $pp$ Collisions at STAR

Surprisingly substantial transverse single spin asymmetries, $A_N$, have been observed in many hadronic channels since 1976. Since then, many attempts have been made to explain the underlying mechanism, such as the Sivers effect, Collins effect, and twist-3 contributions; however, no explanation has been fully sufficient. Diffractive contributions to the cross-section may provide additional insight to the origin of the large $A_{N}$. In the most recent RHIC run of $pp$ collisions, the Forward Meson Spectrometer, an electromagnetic calorimeter covering a forward pseudorapidity range of $2.6<\eta<4$, recorded a substantial data set mostly composed of $\pi^{0}$s from which $A_{N}$ can be extracted. Furthermore, STAR installed Roman Pot silicon trackers to tag diffractive events through forward going protons. Correlations of $\pi^{0}$ events with Roman Pot triggers will for the first time address the role of the diffractive contributions to $A_{N}$. The status of the analysis of such correlations will be presented.   

Measurements of Forward $\pi^0$ $A_N$ in Polarized p-p and p-A Collisions at STAR

In 2015 the first collisions between polarized protons and nuclei occurred at the Brookhaven Relativistic Heavy Ion Collider (RHIC). This talk will present the status of analysis that compares the forward transverse single spin asymmetries $A_N$ in p-p and p-A collisions with CM energy $\sqrt{s_{NN}}=200$ GeV. Photons from $\pi^0$ decays were measured with the STAR FMS electromagnetic calorimeter that had been upgraded for this run, resulting in significantly improved stability, resolution and photon/electron identification. The STAR FMS observed $\pi^0$ photons in the forward direction relative to the polarized proton beam, in the pseudo-rapidity range 2.6 $<$ $\eta$ $<$4.0, and in the transverse momentum range 1.5 $<$ $p_T$ $<$ 7 GeV/c. At this energy and within this kinematic range, STAR has previously reported an unexpected upward trend in the $p_T$ dependence of the $\pi^0$ $A_N$ asymmetry. We will discuss the impact of previous and current measurements of nuclear modification effects in this forward region, including unique information on the nuclear dependence of $A_N$, in comparison to models with saturation effects.   

Transverse Single Spin Asymmetry of $J/\psi$ Production in Polarized $p+p$ Collisions at $\sqrt{s} = 200$ GeV

Transverse single spin asymmetries (SSAs) quantify the asymmetry of particle production relative to the transverse spin axis of a polarized hadron. SSAs have come to be recognized as a means of accessing QCD dynamics, both within initial-state hadrons and in the process of hadronization from partons. At $\sqrt{s} = 200$ GeV, heavy flavor single-spin asymmetries in proton-proton collisions provide access to gluon dynamics within the nucleon. Previous measurements of $J/\psi$ SSAs have been performed at RHIC based on PHENIX 2006, 2008 and 2012 datasets at both central and forward rapidity. In 2015, PHENIX collected an integrated luminosity of transverse polarized $p+p$ collision data at $\sqrt{s} = 200$ GeV, about 2 times as large as the datasets in 2006, 2008, and 2012 combined. The latest status of the $J/\psi$ SSA measurement for $200$ GeV $p+p$ collisions based on the PHENIX 2015 data will be presented.   

Measurements of the cos$\phi$ and cos2$\phi$ Moments of the SIDIS Cross-section at CLAS

Measurements of the cos$\phi$ and cos2$\phi$ moments of the semi-inclusive deep inelastic scattering (SIDIS) cross-section were performed. The data set used was the E1-f run from the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab which ran in 2003. The run used a 5.498 GeV longitudinally polarized electron beam and an unpolarized liquid hydrogen target. Two pion channels ($\pi^+$ and $\pi^-$) were studied over a broad kinematical range (x = 0.1 - 0.6, Q$^2$ = 1.0 - 4.5 GeV$^2$, z = 0.0 - 1.0, and P$_T$ = 0.0 - 1.0 GeV). These measurements give insights into the transverse momentum dependence of parton distribution functions (PDFs) which describe the dynamics of quarks and gluons inside of the proton. This may give access to the quark orbital angular momentum contribution to the proton spin.   

Measurement of unpolarized differential cross section of semi-inclusive deep-inelastic scattering on a $^3$He target

Jefferson Lab experiment E06-010 was performed with 5.9 GeV polarized e$^-$ beam on a transversely polarized $^3$He target. The produced hadrons at semi-inclusive deep-inelastic scattering (SIDIS) kinematics were detected in the high-resolution spectrometer (HRS) in coincidence with the scattered electrons detected by the BigBite spectrometer. The kinematic coverage focuses on the valence quark region, x = 0.1 to 0.4, at Q$^2$=1 to 3 (GeV/c)$^2$. Previous analysis effort has been focused on extracting single-spin asymmetry (SSA) and double-spin asymmetry (DSA) related to various TMDs such as Transversity, Sivers, Pretzelosity and Transverse Helicity (g$_{1T} ^q$). The extracted unpolarized differential cross section will put important constraints on the Cahn effect of SIDIS and the Boer-Mulders function. In this talk we will present new results on extracted unpolarized differential cross section of SIDIS in channels e$^-$ + $^3$He $\to$ e$^{- \prime}$+$\pi ^{\pm}$ +X. A dedicated study of the acceptance of HRS and BigBite spectrometers, as well as updated study of the efficiencies and particle contamination in the experiment allowed us to control systematic uncertainties to an acceptable level.   

First Observation of Collins Asymmetries for Charged Pions in Jets in $p^{\uparrow}p$ Collisions at STAR

The transversity distribution ($h_1\left(x\right)$), which describes the transverse polarization of quarks in transversely polarized protons, is only accessible through channels that couple $h_1\left(x\right)$ to another chiral odd distribution, such as the Collins fragmentation function ($\Delta^N D\left(z,k_T\right)$). Significant Collins asymmetries of charged pions have been observed in semi-inclusive deep inelastic scattering (SIDIS) data. These SIDIS asymmetries combined with $e^+e^-$ process asymmetries from Belle and BaBar have allowed for the extraction of $h_1\left(x\right)$ and $\Delta^N D\left(z,k_T\right)$. Uncertainties on $h_1\left(x\right)$ remain large due to the limited statistics and kinematic reach of the available data. In transversely polarized hadronic collisions, Collins asymmetries may be isolated and extracted by measuring the spin dependent azimuthal distributions of charged pions in jets. This presentation will show the first observation of midrapditiy ($\vert\eta\vert< 1$) Collins asymmetries measured in $\sqrt{s}=200$ and $500$ GeV $p^\uparrow p$ collisions. These results access higher momentum scales than the existing SIDIS data and will allow for a comprehensive study of evolution and factorization of the Collins channel.   

Measuring Intrinsic Partonic Transverse Momentum via Two-Particle Correlations in PHENIX

Investigating partonic interactions is one of the primary goals of the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC). Probing parton dynamics within the nucleon and in the process of hadronization is one of the frontiers in quantum chromodynamics, yet distinguishing initial-state effects related to nucleon structure from final-state effects related to hadronization can be a challenge in proton-proton collisions. Direct photons, coming directly from the partonic hard-scattering process, offer an excellent mechanism through which to measure the intrinsic partonic transverse momentum since the photon is independent of non-perturbative final state hadronization effects. Therefore direct photons are an optimal observable for isolating initial state effects in the proton. At leading order in proton-proton collisions, quark-gluon Compton scattering and quark-antiquark annihilation are the dominant $2\rightarrow 2$ scattering processes for the production of direct photons. By measuring the angle between the correlated direct photon and away side charged hadrons produced from the scattered parton, the intrinsic partonic transverse momentum can be quantified. The status of the analysis with data taken by the PHENIX detector in 2012 and 2013 will be presented.