Self-consistent medium polarization in spin-polarized 3He

A microscopic calculation of the residual particle-hole (p-h) interaction in spin-polarized 3He is performed. As a starting point the Brueckner G matrix is used which is supplemented by including the phonon exchange terms self-consistently. An important ingredient in this microscopic version of the induced interaction is the treatment of the full momentum dependence of the interaction. This allows a consistent description of the Landau limit (Pauli-principle sum rule for the Landau parameters is fulfilled) but also enables a detailed study of the p-h interaction at finite momentum transfers. A comparison with correlated basis functions results shows good agreement for momentum transfers larger than the Fermi momentum.

In vivo magnetic resonance vascular imaging using laser-polarized 3He microbubbles

Laser-polarized gases (3He and 129Xe) are currently being used in magnetic resonance imaging as strong signal sources that can be safely introduced into the lung. Recently, researchers have been investigating other tissues using 129Xe. These studies use xenon dissolved in a carrier such as lipid vesicles or blood. Since helium is much less soluble than xenon in these materials, 3He has been used exclusively for imaging air spaces. However, considering that the signal of 3He is more than 10 times greater than that of 129Xe for presently attainable polarization levels, this work has focused on generating a method to introduce 3He into the vascular system. We addressed the low solubility issue by producing suspensions of 3He microbubbles. Here, we provide the first vascular images obtained with laser-polarized 3He. The potential increase in signal and absence of background should allow this technique to produce high-resolution angiographic images. In addition, quantitative measurements of blood flow velocity and tissue perfusion will be feasible.

Measurement of target single-spin asymmetry in charged kaon electroproduction on a transversely polarized 3He target

The subject of quark transverse spin and transverse momentum distribution are two current research frontier in understanding the spin structure of the nucleons. The goal of the research reported in this dissertation is to extract new information on the quark transversity distribution and the novel transverse-momentum-dependent Sivers function in the neutron. A semi-inclusive deep inelastic scattering experiment was performed at the Hall A of the Jefferson laboratory using 5.9 GeV electron beam and a transversely polarized ^{3}He target. The scattered electrons and the produced hadrons (pions, kaons, and protons) were detected in coincidence with two large magnetic spectrometers. By regularly flipping the spin direction of the transversely polarized target, the single-spin-asymmetry (SSA) of the semi-inclusive deep inelastic reaction ^{3}He^{uparrow}(e,e'h^{\pm})X was measured over the kinematic range 0.13 < x < 0.41 and 1.3 < Q^{2} < 3.1 (GeV)^{2}. The SSA contains several different azimuthal angular modulations which are convolutions of quarks distribution functions in the nucleons and the quark fragmentation functions into hadrons. It is from the extraction of the various ``moments'' of these azimuthal angular distributions (Collins moment and Sivers moment) that we obtain information on the quark transversity distribution and the novel T-odd Sivers function. In this dissertation, I first introduced the theoretical background and experimental status of nucleon spins and the physics of SSA. I will then present the experimental setup and data collection of the JLab E06-010 experiment. Details of data analysis will be discussed next with emphasis on the kaon particle identification and the Ring-Imaging Cherenkov detector which are my major responsibilities in this experiment. Finally, results on the kaon Collins and Sivers moments extracted from the Maximum Likelihood method will be presented and interpreted. I will conclude with a discussion on the future prospects for this research.

Weiterentwicklung einer Produktionsanlage und der Speicherungs- bzw. Transportkonzepte für hochpolarisiertes 3He

Der Bedarf an hyperpolarisiertem 3He in Medizin und physikalischer Grundlagenforschung ist in den letzten ca. 10-15 Jahren sowohl in Bezug auf die zu Verfügung stehende Menge, als auch auf den benötigten Grad der Kernspinpolarisation stetig gestiegen. Gleichzeitig mußten Lösungen für die polarisationserhaltende Speicherung und den Transport gefunden werden, die je nach Anwendung anzupassen waren. Als Ergebnis kann mit dieser Arbeit ein in sich geschlossenes Gesamtkonzept vorgestellt werden, daß sowohl die entsprechenden Mengen für klinische Anwendungen, als auch höchste Polarisation für physikalische Grundlagenfor-schung zur Verfügung stellen kann. Verschiedene unabhängige Polarimetriemethoden zeigten in sich konsistente Ergebnisse und konnten, neben ihrer eigenen Weiterentwicklung, zu einer verläßlichen Charakterisierung des neuen Systems und auch der Transportzellen und –boxen eingesetzt werden. Die Polarisation wird mittels „Metastabilem Optischen Pumpen“ bei einem Druck von 1 mbar erzeugt. Dabei werden ohne Gasfluß Werte von P = 84% erreicht. Im Flußbetrieb sinkt die erreichbare Polarisation auf P ≈ 77%. Das 3He kann dann weitgehend ohne Polarisationsver-luste auf mehrere bar komprimiert und zu den jeweiligen Experimenten transportiert werden. Durch konsequente Weiterentwicklung der vorgestellten Polarisationseinheit an fast allen Komponenten kann somit jetzt bei einem Fluß von 0,8 barl/h eine Polarisation von Pmax = 77% am Auslaß der Apparatur erreicht werden. Diese skaliert linear mit dem Fluß, sodaß bei 3 barl/h die Polarisation immer noch bei ca. 60% liegt. Dabei waren die im Rahmen dieser Arbeit durchgeführten Verbesserungen an den Lasern, der Optik, der Kompressionseinheit, dem Zwischenspeicher und der Gasreinigung wesentlich für das Erreichen dieser Polarisatio-nen. Neben dem Einsatz eines neuen Faserlasersystems ist die hohe Gasreinheit und die lang-lebige Kompressionseinheit ein Schlüssel für diese Leistungsfähigkeit. Seit Herbst 2001 er-zeugte das System bereits über 2000 barl hochpolarisiertes 3He und ermöglichte damit zahl-reiche interdisziplinäre Experimente und Untersuchungen. Durch Verbesserungen an als Prototypen bereits vorhandenen Transportboxen und durch weitgehende Unterdrückung der Wandrelaxation in den Transportgefäßen aufgrund neuer Erkenntnisse über deren Ursachen stellen auch polarisationserhaltende Transporte über große Strecken kein Problem mehr dar. In unbeschichteten 1 Liter Kolben aus Aluminosilikatglä-sern werden nun problemlos Speicherzeiten von T1 > 200h erreicht. Im Rahmen des europäi-schen Forschungsprojektes „Polarized Helium to Image the Lung“ wurden während 19 Liefe-rungen 70barl 3He nach Sheffield (UK) und bei 13 Transporten 100 barl nach Kopenhagen (DK) per Flugzeug transportiert. Zusammenfassend konnte gezeigt werden, daß die Problematik der Kernspinpolarisationser-zeugung von 3He, die Speicherung, der Transport und die Verwendung des polarisierten Ga-ses in klinischer Diagnostik und physikalischen Grundlagenexperimenten weitgehend gelöst ist und das Gesamtkonzept die Voraussetzungen für allgemeine Anwendungen auf diesen Gebieten geschaffen hat.

Measurement of the doubly-polarized He3→(γ→,n)pp reaction at 16.5 MeV and its implications for the GDH sum rule

We report new measurements of the double-polarized photodisintegration of 3He at an incident photon energy of 16.5 MeV, carried out at the High Intensity γ-ray Source (HIγS) facility located at Triangle Universities Nuclear Laboratory (TUNL). The spin-dependent double-differential cross sections and the contribution from the three-body channel to the Gerasimov–Drell–Hearn (GDH) integrand were extracted and compared with the state-of-the-art three-body calculations. The calculations, which include the Coulomb interaction and are in good agreement with the results of previous measurements at 12.8 and 14.7 MeV, deviate from the new cross section results at 16.5 MeV. The GDH integrand was found to be about one standard deviation larger than the maximum value predicted by the theories.

Test of Lorentz symmetry with a 3 He,129 Xe clock-comparison experiment

In case of violation of CPT- and Lorentz Symmetry, the minimal Standard Model Extension (SME) of Kostelecky and coworkers predicts sidereal modulations of atomic transition frequencies as the Earth rotates relative to a Lorentz-violating background field. One method to search for these modulations is the so-called clock-comparison experiment, where the frequencies of co-located clocks are compared as they rotate with respect to the fixed stars. In this work an experiment is presented where polarized 3He and 129Xe gas samples in a glass cell serve as clocks, whose nuclear spin precession frequencies are detected with the help of highly sensitive SQUID sensors inside a magnetically shielded room. The unique feature of this experiment is the fact that the spins are precessing freely, with transverse relaxation times of up to 4.4 h for 129Xe and 14.1 h for 3He. To be sensitive to Lorentz-violating effects, the influence of external magnetic fields is canceled via the weighted difference of the 3He and 129Xe frequencies or phases. The Lorentz-violating SME parameters for the neutron are determined out of a fit on the phase difference data of 7 spin precession measurements of 12 to 16 hours length. The result of the fit gives an upper limit for the equatorial component of the neutron parameter b_n of 3.7×10^(−32) GeV at the 95% confidence level. This value is not limited by the signal-to-noise ratio, but by the strong correlations between the fit parameters. To reduce the correlations and therewith improve the sensitivity of future experiments, it will be necessary to change the time structure of the weighted phase difference, which can be realized by increasing the 129Xe relaxation time.

Messung des elektrischen Neutron-Formfaktors in der Reaktion 3 He(e,e'n)pp bei Q 2 = 1.58 (GeV/c) 2

Die elektromagnetischen Nukleon-Formfaktoren sind fundamentale Größen, welche eng mit der elektromagnetischen Struktur der Nukleonen zusammenhängen. Der Verlauf der elektrischen und magnetischen Sachs-Formfaktoren G_E und G_M gegen Q^2, das negative Quadrat des Viererimpulsübertrags im elektromagnetischen Streuprozess, steht über die Fouriertransformation in direkter Beziehung zu der räumlichen Ladungs- und Strom-Verteilung in den Nukleonen. Präzise Messungen der Formfaktoren über einen weiten Q^2-Bereich werden daher für ein quantitatives Verständnis der Nukleonstruktur benötigt.rnrnDa es keine freien Neutrontargets gibt, gestaltet sich die Messung der Neutron-Formfaktoren schwierig im Vergleich zu der Messung am Proton. Konsequenz daraus ist, dass die Genauigkeit der vorhandenen Daten von Neutron-Formfaktoren deutlich geringer ist als die von Formfaktoren des Protons; auch der vermessene Q^2-Bereich ist kleiner. Insbesondere der elektrische Sachs-Formfaktor des Neutrons G_E^n ist schwierig zu messen, da er aufgrund der verschwindenden Nettoladung des Neutrons im Verhältnis zu den übrigen Nukleon-Formfaktoren sehr klein ist. G_E^n charakterisiert die Ladungsverteilung des elektrisch neutralen Neutrons und ist damit besonders sensitiv auf die innere Struktur des Neutrons.rnrnIn der hier vorgestellten Arbeit wurde G_E^n aus Strahlhelizitätsasymmetrien in der quasielastischen Streuung vec{3He}(vec{e}, e'n)pp bei einem Impulsübertrag von Q^2 = 1.58 (GeV/c)^2 bestimmt. Die Messung fand in Mainz an der Elektronbeschleunigeranlage Mainzer Mikrotron innerhalb der A1-Kollaboration im Sommer 2008 statt. rnrnLongitudinal polarisierte Elektronen mit einer Energie von 1.508 GeV wurden an einem polarisierten ^3He-Gastarget, das als effektives, polarisiertes Neutrontarget diente, gestreut. Die gestreuten Elektronen wurden in Koinzidenz mit den herausgeschlagenen Neutronen detektiert; die Elektronen wurden in einem magnetischen Spektrometer nachgewiesen, durch den Nachweis der Neutronen in einer Matrix aus Plastikszintillatoren wurde der Beitrag der quasielastischen Streuung am Proton unterdrückt.rnrnAsymmetrien des Wirkungsquerschnitts bezüglich der Elektronhelizität sind bei Orientierung der Targetpolarisation in der Streuebene und senkrecht zum Impulsübertrag sensitiv auf G_E^n / G_M^n; mittels deren Messung kann G_E^n bestimmt werden, da der magnetische Formfaktor G_M^n mit vergleichsweise hoher Präzision bekannt ist. Zusätzliche Messungen der Asymmetrie bei einer Polarisationsorientierung parallel zum Impulsübertrag wurden genutzt, um systematische Fehler zu reduzieren.rnrnFür die Messung inklusive statistischem (stat) und systematischem (sys) Fehler ergab sich G_E^n = 0.0244 +/- 0.0057_stat +/- 0.0016_sys.

Search for a spin-dependent short-range force between nucleons with a 3 He, 129 Xe clock-comparison experiment

Light pseudoscalar bosons, such as the axion that was originally proposed as a solution of the strong CP problem, would cause a new spin-dependent short-range interaction. In this thesis, an experiment is presented to search for axion mediated short-range interaction between a nucleon and the spin of a polarized bound neutron. This interaction cause a shift in the precession frequency of nuclear spin-polarized gases in the presence of an unpolarized mass. To get rid of magnetic field drifts co-located, nuclear spin polarized 3He and 129Xe atoms were used. The free nuclear spin precession frequencies were measured in a homogeneous magnetic guiding field of about 350nT using LTc SQUID detectors. The whole setup was housed in a magnetically shielded room at the Physikalisch Technische Bundesanstalt (PTB) in Berlin. With this setup long nuclear spin-coherence times, respectively, transverse relaxation times of 5h for 129Xe and 53h for 3He could be achieved. The results of the last run in September 2010 are presented which give new upper limits on the scalar-pseudoscalar coupling of axion-like particles in the axion-mass window from 10^(-2) eV to 10^(-6) eV. The laboratory upper bounds were improved by up to 4 orders of magnitude.

An accurate combined 3 He,Cs magnetometer with fT sensitivity for the nEDM experiment at PSI

Diese Arbeit beschreibt die Entwicklung, Konstruktion und Untersuchung eines Magnetometers zur exakten und präzisen Messung schwacher Magnetfelder. Diese Art von Magnetometer eignet sich zur Anwendung in physikalischen hochpräzisions Experimenten wie zum Beispiel der Suche nach dem elektrischen Dipolmomentrndes Neutrons. Die Messmethode beruht auf der gleichzeitigen Detektion der freien Spin Präzession Kern-Spin polarisierten 3He Gases durch mehrere optisch gepumpte Cäsium Magnetometer. Es wird gezeigt, dass Cäsium Magnetometer eine zuverlässige und vielseitige Methode zur Messung der 3He Larmor Frequenz und eine komfortable Alternative zur Benutzung von SQUIDs für diesen Zweck darstellen. Ein Prototyp dieses Magnetometers wurde gebaut und seine Funktion in der magnetisch abgeschirmten Messkabine der Physikalisch Technischen Bundesanstalt untersucht. Die Sensitivität des Magnetometers in Abhängigkeitrnvon der Messdauer wurde experimentell untersucht. Es wird gezeigt, dass für kurze Messperioden (< 500s) Cramér-Rao limitierte Messungen möglich sind während die Sensitivität bei längeren Messungen durch die Stabilität des angelegten Magnetfeldes limitiert ist. Messungen eines 1 muT Magnetfeldes mit einer relative Genauigkeit von besser als 5x10^(-8) in 100s werden präsentiert. Es wird gezeigt, dass die Messgenauigkeit des Magnetometers durch die Zahl der zur Detektion der 3He Spin Präzession eingesetzten Cäsium Magnetometer skaliert werden kann. Prinzipiell ist dadurch eine Anpassung der Messgenauigkeit an jegliche experimentellen Bedürfnisse möglich. Es wird eine gradiometrische Messmethode vorgestellt, die es erlaubt den Einfluss periodischerrnmagnetischer Störungen auf dieMessung zu unterdrücken. Der Zusammenhang zwischen der Sensitivität des kombinierten Magnetometers und den Betriebsparametern der Cäsium Magnetometer die zur Spin Detektion verwendet werden wird theoretisch untersucht und anwendungsspezifische Vor- und Nachteile verschiedener Betriebsartenwerden diskutiert. Diese Zusammenhänge werden in einer Formel zusammengefasst die es erlaubt, die erwartete Sensitivität des Magnetometers zu berechnen. Diese Vorhersagen befinden sich in perfekter Übereinstimmung mit den experimentellen Daten. Die intrinsische Sensitivität des Magnetometer Prototyps wird auf Basis dieser Formel theoretisch bestimmt. Ausserdem wird die erwartete Sensitivität für die Anwendung im Rahmen des Experiments der nächsten Generation zur Bestimmung des elektrischenrnDipolmoments des Neutrons am Paul Scherrer Institut abgeschätzt. Des weiteren wird eine bequeme experimentelle Methode zur Messung des Polarisationsgrades und des Rabi Flip-Winkels der 3He Kernspin Polarisation vorgestellt. Letztere Messung ist sehr wichtig für die Anwendung in hochpräzisions Experimenten.

New search for the Neutron Electric Dipole Moment using ultracold neutrons at the Spallation Neutron Source

This document introduces the planned new search for the neutron Electric Dipole Moment at the Spallation Neutron Source at the Oak Ridge National Laboratory. A spin precession measurement is to be carried out using Ultracold neutrons diluted in a superfluid Helium bath at T = 0.5 K, where spin polarized 3He atoms act as detector of the neutron spin polarization. This manuscript describes some of the key aspects of the planned experiment with the contributions from Caltech to the development of the project.

Techniques used in the design of magnet coils for Nuclear Magnetic Resonance were adapted to the geometry of the experiment. Described is an initial design approach using a pair of coils tuned to shield outer conductive elements from resistive heat loads, while inducing an oscillating field in the measurement volume. A small prototype was constructed to test the model of the field at room temperature.

A large scale test of the high voltage system was carried out in a collaborative effort at the Los Alamos National Laboratory. The application and amplification of high voltage to polished steel electrodes immersed in a superfluid Helium bath was studied, as well as the electrical breakdown properties of the electrodes at low temperatures. A suite of Monte Carlo simulation software tools to model the interaction of neutrons, 3He atoms, and their spins with the experimental magnetic and electric fields was developed and implemented to further the study of expected systematic effects of the measurement, with particular focus on the false Electric Dipole Moment induced by a Geometric Phase akin to Berry’s phase.

An analysis framework was developed and implemented using unbinned likelihood to fit the time modulated signal expected from the measurement data. A collaborative Monte Carlo data set was used to test the analysis methods.

Diffusion of laser polarized gases in MRI

The use of Magnetic Resonance Imaging (MRI) as a diagnostic tool is increasingly employing functional contrast agents to study or contrast entire mechanisms. Contrast agents in MRI can be classified in two categories. One type of contrast agents alters the NMR signal of the protons in its surrounding, e.g. lowers the T1 relaxation time. The other type enhances the Nuclear Magnetic Resonance (NMR) signal of specific nuclei. For hyperpolarized gases the NMR signal is improved up to several orders of magnitude. However, gases have a high diffusivity which strongly influences the NMR signal strength, hence the resolution and appearance of the images. The most interesting question in spatially resolved experiments is of course the achievable resolution and contrast by controlling the diffusivity of the gas. The influence of such diffusive processes scales with the diffusion coefficient, the strength of the magnetic field gradients and the timings used in the experiment. Diffusion may not only limit the MRI resolution, but also distort the line shape of MR images for samples, which contain boundaries or diffusion barriers within the sampled space. In addition, due to the large polarization in gaseous 3He and 129Xe, spin diffusion (different from particle diffusion) could play a role in MRI experiments. It is demonstrated that for low temperatures some corrections to the NMR measured diffusion coefficient have to be done, which depend on quantum exchange effects for indistinguishable particles. Physically, if these effects can not change the spin current, they can do it indirectly by modifying the velocity distribution of the different spin states separately, so that the subsequent collisions between atoms and therefore the diffusion coefficient can eventually be affected. A detailed study of the hyperpolarized gas diffusion coefficient is presented, demonstrating the absence of spin diffusion (different from particle diffusion) influence in MRI at clinical conditions. A novel procedure is proposed to control the diffusion coefficient of gases in MRI by admixture of inert buffer gases. The experimental measured diffusion agrees with theoretical simulations. Therefore, the molecular mass and concentration enter as additional parameters into the equations that describe structural contrast. This allows for setting a structural threshold up to which structures contribute to the image. For MRI of the lung this allows for images of very small structural elements (alveoli) only, or in the other extreme, all airways can be displayed with minimal signal loss due to diffusion.

Measurement Of Longitudinal Spin Asymmetries For Weak Boson Production In Polarized Proton-proton Collisions At Rhic.

We report measurements of single- and double-spin asymmetries for W^{±} and Z/γ^{*} boson production in longitudinally polarized p+p collisions at sqrt[s]=510  GeV by the STAR experiment at RHIC. The asymmetries for W^{±} were measured as a function of the decay lepton pseudorapidity, which provides a theoretically clean probe of the proton's polarized quark distributions at the scale of the W mass. The results are compared to theoretical predictions, constrained by polarized deep inelastic scattering measurements, and show a preference for a sizable, positive up antiquark polarization in the range 0.05

Polarized Light (lambda 400-2000 nm) on Third-Degree Burns in Diabetic Rats: Immunohistochemical Study

Aim: The aim of this study was to evaluate with light microscopy the healing process of third-degree burns on diabetic rats treated with polarized light (lambda 400-2000 nm, 20 or 40 J/cm(2)/session, 40 mW/cm(2), 2.4 J/cm(2)/min, 5.5-cm beam diameter). Background: Uncontrolled diabetes mellitus causes severe disruption of the body's metabolism, including healing. Polarized light sources have been shown to be effective in improving healing in many situations. Animals and Methods: Diabetes mellitus was induced with streptozotocin (60 mg/kg) in 45 male Wistar albino rats, and a third-degree burn (1.5 by 1.5 cm) was created on the dorsum of each animal under general anesthesia. The animals were randomly distributed into three groups: control, 20 J/cm(2), and 40 J/cm(2). Each group was then divided into three subgroups based on time of death (7, 14, 21 d). Phototherapy (20 or 40 J/cm(2) per session) was carried out immediately after the burning and repeated daily until the day before death. Following animal death, specimens were removed, embedded in paraffin, sectioned, and stained with hematoxylin and eosin (HE) or Sirius Red or immunomarked with CK AE1/AE3 antibody. Qualitative and semiquantitative analyses were performed under light microscopy. The results were statistically analyzed. Results: The animals treated with 20 J/cm(2) showed significant differences with regard to revascularization and re-epithelialization. Although the 40 J/cm(2) group showed stimulation of fibroblastic proliferation as an isolated feature, no other difference from the control was observed. Conclusion: Our results suggest that the use of polarized light at 20 J/cm(2) effectively improves the healing of third-degree burns on diabetic animals at both early and late stages of repair.

Cross Section and Parity-Violating Spin Asymmetries of W(+/-) Boson Production in Polarized p plus p Collisions at root s=500 Gev

Large parity-violating longitudinal single-spin asymmetries A(L)(e+) = 0.86(-0.14)(+0.30) and Ae(L)(e-) = 0.88(-0.71)(+0.12) are observed for inclusive high transverse momentum electrons and positrons in polarized p + p collisions at a center-of-mass energy of root s = 500 GeV with the PHENIX detector at RHIC. These e(+/-) come mainly from the decay of W(+/-) and Z(0) bosons, and their asymmetries directly demonstrate parity violation in the couplings of the W(+/-) to the light quarks. The observed electron and positron yields were used to estimate W(+/-) boson production cross sections for the e(+/-) channels of sigma(pp -> W(+)X) X BR(W(+) -> e(+) nu(e)) = 144.1 +/- 21.2(stat)(-10.3)(+3.4)(syst) +/- 21.6(norm) pb, and sigma(pp -> W(-)X) X BR(W(-) -> e(-) (nu) over bar (e)) = 3.17 +/- 12.1(stat)(-8.2)(+10.1)(syst) +/- 4.8(norm) pb.

Measurement of transverse single-spin asymmetries for J/psi production in polarized p plus p collisions at root s=200 GeV

We report the first measurement of transverse single-spin asymmetries in J/psi production from transversely polarized p + p collisions at root s = 200 GeV with data taken by the PHENIX experiment in 2006 and 2008. The measurement was performed over the rapidity ranges 1.2 < vertical bar y vertical bar < 2.2 and vertical bar y vertical bar < 0.35 for transverse momenta up to 6 GeV/c. J/psi production at the Relativistic Heavy Ion Collider is dominated by processes involving initial-state gluons, and transverse single-spin asymmetries of the J/psi can provide access to gluon dynamics within the nucleon. Such asymmetries may also shed light on the long-standing question in QCD of the J/psi production mechanism. Asymmetries were obtained as a function of J/psi transverse momentum and Feynman-x, with a value of -0.086 +/- 0.026(stat) +/- 0.003(syst) in the forward region. This result suggests possible nonzero trigluon correlation functions in transversely polarized protons and, if well defined in this reaction, a nonzero gluon Sivers distribution function.