Session CG: Mini-Symposium on the Spin Structure of the Nucleon I

The Spin Structure of the nucleon

This talk will review the status of the experiments studying the spin structure of the nucleon. After a brief overview of the topics, I will focus on the program measuring the generalized Gerasimov-Drell-Hearn (GDH) sum, in the context of connecting the effective descriptions of the strong force at long distances to its fundamental partonic description at short distances. The generalized GDH sum rule is a theoretical relation valid at any distance. Consequently, it can be an Ariadne's thread to follow to understand how the transition between the partonic to hadronic descriptions happens. Measurements at intermediate and short distances have been made available in the 1990s and 2000s. Long distance results are being now finalized. With them, a large part of this experimental program will be completed. I will give the status of the measurements at long distances. I will then conclude the talk with a practical example on how the GDH data are used to connect the fundamental and effective descriptions of the strong force. Such example demonstrates how the generalized GDH program is bearing fruits.   

Drell-Yan Cross Section and Longitudinal Double Spin Asymmetry in the PHENIX Experiment at RHIC

Analysis of the Drell-Yan process in high energy polarized proton-proton collisions is a unique method for probing the proton spin structure. Measurement of the longitudinal double spin asymmetry ($A_{LL}$) in the Drell-Yan process provides clean access to the anti-quark helicity distributions without involving quark fragmentation functions. In the PHENIX experiment at RHIC, the Forward Silicon Vertex Detector (FVTX), together with forward muon spectrometers, allows us to study the Drell-Yan process by detecting the muon pairs in the forward region ($1.2<|\eta|<2.4$) while also suppressing backgrounds due to heavy-flavor production. In this talk we present the status of the Drell-Yan cross-section and $A_{LL}$ measurement for the intermediate mass region (4 GeV $< M <$ 8 GeV) using the RHIC 2013 data of proton-proton collisions at a center of mass energy of 510 GeV.   

A Measurement of Proton Structure Function $g_2$ at Low $Q^2$

Measurements of the nucleon spin-dependent structure functions at low $Q^2$ have been proven to be powerful tools in testing the validity of effective theories of Quantum Chromodynamics. The neutron spin structure functions, $g_1^n$ and $g_2^n$, and the proton spin structure function, $g_1^p$, have been measured over a wide kinematic range. However, the proton spin structure function, $g_2^p$, remains largely unmeasured. The recent Jefferson Lab Hall A experiment E08-027 is an inclusive measurement of the proton $g_2$ structure function in the low momentum transfer region of $0.02 < Q^2 < 0.20$ GeV${}^{\mathrm{2}}$. This experiment will allow us to extract the generalized longitudinal-transverse spin polarizability $\delta_{LT}$ and test the Burkhardt-Cottingham sum rule at low $Q^2$. Chiral Perturbation Theory ($\chi PT$) is expected to work in this kinematic region and this measurement of $\delta_{LT}$ will give a benchmark test to $\chi PT$ calculations. The details of the experiment will be presented in this talk, along with the preliminary results and an overview of the analysis progress.   

Proton Spin Polarizabilities with Polarized Compton Scattering at MAMI

The nucleon polarizabilities are fundamental structure observables, which describe its response to an applied electric or magnetic field. While the electric and magnetic scalar polarizabilities of the nucleon have been measured, little effort has been made to extract the spin dependent polarizabilities. These leading order spin dependent terms of the nucleon polarizabilities, $\gamma_{E_{1}E_{1}},\gamma_{M_{1}M_{1}},\gamma_{M_{1}E_{2}}$ and $\gamma_{E_{1}M_{2}}$ describe the spin response of a proton to electric and magnetic dipole and quadrupole interactions. We plan to extract these spin polarizabilities of the proton using real polarised Compton scattering off the proton at the MAMI tagged photon facility in Mainz, Germany. This requires precise measurement of the single and double polarization observables which are sensitive to these polarizabilities. The double polarization observables $\sum_{2x}$, $\sum_{2z}$ are measured via a circulary polarized photon beam and a transversely and a linearly polarized butanol target in the resonance region ($E=250-310$ MeV). This presentation will be focused on the status and analyis of an experiment completed at MAMI in 2014 and 2015 for the measurement of $\sum_{2z}$ at different energies and angles.   

Transverse Force on Quarks in Deep-Inelastic Scattering

Transverse single-spin asymmetries are not the only observable where the transverse force on quarks in DIS plays a role. For example, higher-twist effects in polarized inclusive DIS can be related to that force. Furthermore the torque due to that force is relevant when comparing the Jaffe-Manohar with the Ji definition for quark orbital angular momentum. I explain the origin of that force in semi-classical pictures and discuss connections and differences with the Aharonov-Bohm effect.   

Direct Photon Production and Gluon Polarization Measurements in Proton-Proton Collisions at PHENIX

Direct photons probe the hard scattering process in proton-proton collisions. The channel that dominates their production in these collisions is ``the inverse QCD Compton effect,'' $g + q \rightarrow \gamma + q$. Calculating this process requires no photon fragmentation function, which facilitates comparisons between theories and experiments. In $polarized$ p+p collisions, direct photons help determine the proton spin structure. At leading order, the longitudinal double-spin asymmetry $A_{LL}$ is directly proportional to the product of quark and gluon polarizations. The polarized quark distributions are known from polarized lepton-proton scattering experiments. Using them together with $A_{LL}$ measurements allows to access both the magnitude and sign of the polarized gluon distribution. The PHENIX experiment has collected data from polarized p+p collisions at RHIC at center of mass energies of 200 GeV and 500 GeV. This talk presents the status of direct photon cross section measurements and $A_{LL}$ measurements at midrapidity ($|\eta| < 0.35$) using these data.   

Partons Transverse Momentum and Orbital Angular Momentum Distributions

We discuss the two definitions of partonic orbital angular momentum given by Ji and by Jaffe and Manohar, respectively. It is by now established that the two definitions are described by the same generalized transverse momentum distribution, $F_{14}$, while they differ through their gauge link structure. They can also be both described in terms of a twist three generalized parton distribution, $G_2$ which can be measured in DVCS type experiments. Here, starting from nonlocal, $k_T$ unintegrated, off-forward matrix elements, instead of the standard OPE, we show how $G_2$ can be written as the sum of twist two, quark mass, and interaction dependent (twist three) terms, thus emphasizing the role of quark intrinsic transverse momentum and off-shellness. The twist two term in particular is given by the $k_T^2$ moment of $F_{14}$. We therefore uncover a relation/sum rule connecting the two definitions of orbital angular momentum, $F_{14}$ and $G_2$. We explore both the spin and the intrinsic transverse momentum/transverse space correlations as well as the gauge link structure behind the two decomposition frameworks, which are necessary to extract orbital angular momentum from experiment.