Azimuthal Spin Asymmetries in Hadronic Processes

Mulders, P.J.G. [Promotor

Wilson Lines off the Light-cone in TMD PDFs

Transverse Momentum Dependent (TMD) parton distribution functions (PDFs) also take into account the transverse momentum ($p_T$) of the partons. The $p_T$-integrated analogues can be linked directly to quark and gluon matrix elements using the operator product expansion in QCD, involving operators of definite twist. TMDs also involve operators of higher twist, which are not suppressed by powers of the hard scale, however. Taking into account gauge links that no longer are along the light-cone, one finds that new distribution functions arise. They appear at leading order in the description of azimuthal asymmetries in high-energy scattering processes. In analogy to the collinear operator expansion, we define a universal set of TMDs of definite rank and point out the importance for phenomenology.Comment: 12 pages, presented by the first author at the Light-Cone Conference 2013, May 20-24, 2013, Skiathos, Greece. To be published in Few Body System

The Construction of Gauge-Links in Arbitrary Hard Processes

Transverse momentum dependent parton distribution and fragmentation functions are described by hadronic matrix elements of bilocal products of field operators off the light-cone. These bilocal products contain gauge-links, as required by gauge-invariance. The gauge-links are path-ordered exponentials connecting the field operators along a certain integration path. This integration path is process-dependent, depending specifically on the short-distance partonic subprocess. In this paper we present the technical details needed in the calculation of the gauge-links and a calculational scheme is provided to obtain the gauge-invariant distribution and fragmentation correlators corresponding to a given partonic subprocess

Gauge Link Structure in Quark-Quark Correlators in hard processes

Distribution functions in hard processes can be described by quark-quark correlators, nonlocal matrix elements of quark fields. Color gauge invariance requires inclusion of appropriate gauge links in these correlators. For transverse momentum dependent distribution functions, in particular important for describing T-odd effects in hard processes, we find that new link structures containing loops can appear in abelian and non-abelian theories. In transverse moments, e.g. measured in azimuthal asymmetries, these loops may enhance the contribution of gluonic poles. Some explicit results for the link structure are given in high-energy leptoproduction and hadron-hadron scattering.Comment: 9 pages, 9 figure

Transverse-Momentum Distributions and Spherical Symmetry

Transverse-momentum dependent parton distributions (TMDs) are studied in the framework of quark models. In particular, quark model relations among TMDs are reviewed and their physical origin is discussed in terms of rotational-symmetry properties of the nucleon state in its rest frame.Comment: 8 pages, 2 figures, prepared for the workshop "30 years of strong interactions", Spa, Belgium, 6-8 April 201

Left-right asymmetry for pion and kaon production in the semi-inclusive deep inelastic scattering process

We analyze the left-right asymmetry in the semi-inclusive deep inelastic scattering (SIDIS) process without introducing any weighting functions. With the current theoretical understanding, we find that the Sivers effect plays a key role in our analysis. We use the latest parametrization of the Sivers and fragmentation functions to reanalyze the $\pi^\pm$ production process and find that the results are sensitive to the parametrization. We also extend our calculation on the $K^{\pm}$ production, which can help us know more about the Sivers distribution of the sea quarks and the unfavored fragmentation processes. HERMES kinematics with a proton target, COMPASS kinematics with a proton, deuteron, and neutron target (the information on the neutron target can be effectively extracted from the $^3$He target), and JLab kinematics (both 6 GeV and 12 GeV) with a proton and neutron target are considered in our paper.Comment: 7 latex pages, 11 figures, final version for publication, with references update

Sivers and Collins Single Spin Asymmetries

The Sivers and Collins asymmetries are the most prominent Single Spin Asymmetries (SSA)in Semi-Inclusive Deeply Inelastic Scattering (SIDIS)with transverse target polarization. In this talk we present our understanding of these phenomena.Comment: 9 pages, 23 eps figures. Talk at XII Workshop on High Energy Spin Physics (DSPIN-07), Dubna, Sept. 3-7, 2007 and at ASI - SYMMETRIES AND SPIN (SPIN-Praha-2007), Prague, July 8 - 14, 200

Azimuthal asymmetries in lepton-pair production at a fixed-target experiment using the LHC beams (AFTER)

A multi-purpose fixed-target experiment using the proton and lead-ion beams of the LHC was recently proposed by Brodsky, Fleuret, Hadjidakis and Lansberg, and here we concentrate our study on some issues related to the spin physics part of this project (referred to as AFTER). We study the nucleon spin structure through $pp$ and $pd$ processes with a fixed-target experiment using the LHC proton beams, for the kinematical region with 7 TeV proton beams at the energy in center-of-mass frame of two nucleons $\sqrt{s}=115$ GeV. We calculate and estimate the $\cos2\phi$ azimuthal asymmetries of unpolarized $pp$ and $pd$ dilepton production processes in the Drell--Yan continuum region and at the $Z$-pole. We also calculate the $\sin(2\phi-\phi_S)$, $\sin(2\phi+\phi_S)$ and $\sin2\phi$ azimuthal asymmetries of $pp$ and $pd$ dilepton production processes with the target proton and deuteron longitudinally or transversally polarized in the Drell--Yan continuum region and around $Z$ resonances region. We conclude that it is feasible to measure these azimuthal asymmetries, consequently the three-dimensional or transverse momentum dependent parton distribution functions (3dPDFs or TMDs), at this new AFTER facility.Comment: 15 pages, 40 figures. Version accepted for publication in EPJ

Transverse Momentum Dependent Parton Distribution/Fragmentation Functions at an Electron-Ion Collider

We present a summary of a recent workshop held at Duke University on Partonic Transverse Momentum in Hadrons: Quark Spin-Orbit Correlations and Quark-Gluon Interactions. The transverse momentum dependent parton distribution functions (TMDs), parton-to-hadron fragmentation functions, and multi-parton correlation functions, were discussed extensively at the Duke workshop. In this paper, we summarize first the theoretical issues concerning the study of partonic structure of hadrons at a future electron-ion collider (EIC) with emphasis on the TMDs. We then present simulation results on experimental studies of TMDs through measurements of single spin asymmetries (SSA) from semi-inclusive deep-inelastic scattering (SIDIS) processes with an EIC, and discuss the requirement of the detector for SIDIS measurements. The dynamics of parton correlations in the nucleon is further explored via a study of SSA in D (`D) production at large transverse momenta with the aim of accessing the unexplored tri-gluon correlation functions. The workshop participants identified the SSA measurements in SIDIS as a golden program to study TMDs in both the sea and valence quark regions and to study the role of gluons, with the Sivers asymmetry measurements as examples. Such measurements will lead to major advancement in our understanding of TMDs in the valence quark region, and more importantly also allow for the investigation of TMDs in the sea quark region along with a study of their evolution.Comment: 44 pages 23 figures, summary of Duke EIC workshop on TMDs accepted by EPJ