Gluon Polarization Research Articles

Inclusive cross section and double-helicity asymmetry forπ0production at midrapidity inp+pcollisions ats=510 GeV

PHENIX measurements are presented for the cross section and double-helicity asymmetry ($A_{LL}$) in inclusive $\pi^0$ production at midrapidity from $p$$+$$p$ collisions at $\sqrt{s}=510$~GeV from data taken in 2012 and 2013 at the Relativistic Heavy Ion Collider. The next-to-leading-order perturbative-quantum-chromodynamics theory calculation is in excellent agreement with the presented cross section results. The calculation utilized parton-to-pion fragmentation functions from the recent DSS14 global analysis, which prefer a smaller gluon-to-pion fragmentation function. The $\pi^{0}A_{LL}$ results follow an increasingly positive asymmetry trend with $p_T$ and $\sqrt{s}$ with respect to the predictions and are in excellent agreement with the latest global analysis results. This analysis incorporated earlier results on $\pi^0$ and jet $A_{LL}$, and suggested a positive contribution of gluon polarization to the spin of the proton $\Delta G$ for the gluon momentum fraction range $x>0.05$. The data presented here extend to a currently unexplored region, down to $x\sim0.01$, and thus provide additional constraints on the value of $\Delta G$. The results confirm the evidence for nonzero $\Delta G$ using a different production channel in a complementary kinematic region.

Gluon Polarization in Longitudinally Polarized pp Collisions at STAR

The STAR Collaboration is performing a wide range of measurements to determine the gluon helicity distribution in the proton. Gluon-gluon and quark-gluon scattering dominate jet production in proton-proton collisions at RHIC, so the longitudinal double-spin asymmetry, [Formula: see text], for jet production places significant constraints on the gluon polarization in the proton. In recent years STAR has recorded large longitudinally polarized [Formula: see text] data sets at both [Formula: see text] GeV and [Formula: see text] GeV. The 2009 STAR inclusive jet [Formula: see text] measurements at [Formula: see text] GeV show the first experimental evidence of non-zero gluon polarization over the Bjorken-[Formula: see text] range, [Formula: see text]. Furthermore, data collected at [Formula: see text] GeV during the 2012 and 2013 RHIC runs allow access to the gluon polarization at lower [Formula: see text]. In this talk, I will present the final results of the 2009 inclusive jet [Formula: see text] measurement at [Formula: see text] GeV, the analysis status of the 2012 inclusive jet [Formula: see text] measurement at [Formula: see text] GeV, and the status of di-jet and other STAR measurements that are sensitive to gluon polarization.

Results on longitudinal spin physics at COMPASS

The COMPASS experiment at the CERN SPS has taken data on deep inelastic scattering of polarised muons on a polarised NH3 target in 2007 and 2011 and on a polarised LiD target in 2002–2004 and 2006. The new results on the longitudinal double spin asymmetry A 1 p and the spin-dependent structure function g 1 p obtained from the 2011 data set are presented. These results are used in a NLO QCD fit to the world data to obtain the polarised parton distributions. Also an update of the results on the Bjorken sum rule, connecting the integral of the non-singlet spin-dependent structure function with the ratio of the weak coupling constants, will be given.Direct access to the gluon polarisation is possible via the photon gluon fusion process in semi-inclusive deep inelastic scattering. This process is studied using the p T dependence of charged hadron asymmetries. The latest results indicate a positive gluon polarisation in the kinematic region of COMPASS

J/ψ Longitudinal Double Spin Asymmetry Measurement at Forward Rapidity in p + p Collisions at s = 510 GeV

The polarized gluon distribution, as described by the polarized parton distribution function [Formula: see text], is an important part of the spin structure of the nucleon; however the current data have very limited constraints on [Formula: see text] for [Formula: see text]. During the 2013 RHIC run, the PHENIX experiment collected 146 pb[Formula: see text] of longitudinally polarized [Formula: see text] data at [Formula: see text] GeV with an average beam polarization of 52%. At this energy, [Formula: see text] particles are predominantly produced through gluon-gluon interactions and thus the longitudinal double spin asymmetry, [Formula: see text], is sensitive to the gluon polarization inside the proton. We measure the [Formula: see text] [Formula: see text] in the rapidity range [Formula: see text] by detecting the decay [Formula: see text] pairs using the PHENIX muon detector arms. In this kinematic range, [Formula: see text] is sensitive to the polarized gluon distribution at small [Formula: see text] as well as at moderate [Formula: see text] where recent RHIC data on jet and [Formula: see text] production show possible evidence for significant gluon polarization. Compared to previous measurements in 2005 and 2006, the Run 2013 data set has roughly twenty times more statistics and will allow us to measure [Formula: see text] with a statistical uncertainty at [Formula: see text]% level. In these preceedings, the latest status of this analysis will be presented.

Results on longitudinal spin physics at COMPASS

The COMPASS experiment at the CERN SPS has taken data for deep inelastic scattering of polarised muons off a polarised NH3 target in 2007 and 2011 and off a polarised 6LiD target in 2002–2004 and 2006.We present our new results on the longitudinal double spin asymmetry A1p and the spin-dependent structure function g1p obtained from the 2011 data set. These results are used in a NLO QCD fit to the world data to obtain the polarised parton distributions. Also an update on our results on the Bjorken sum rule, connecting the integral of the non-singlet spin-dependent structure function with the ratio of the weak coupling constants, is given.The gluon polarisation can be accessed directly via the photon gluon fusion process in semi-inclusive deep inelastic scattering. This process is studied using the pT dependence of charged hadron asymmetries. The latest results indicate a positive gluon polarisation in the kinematic region of COMPASS.

Double Helicity Asymmetries of Forward Neutral Pions from s = 510 GeV pp Collisions at STAR

Longitudinally polarized [Formula: see text] scattering experiments provide access to gluon polarization via measurement of the double helicity asymmetry, [Formula: see text]. At the completion of the 2013 RHIC running period, a significant dataset of [Formula: see text]s corresponding to an integrated luminosity of 46 [Formula: see text] (2012) and 8 [Formula: see text] (2013) produced from polarized [Formula: see text] scattering at [Formula: see text] GeV with an average beam polarization of approximately [Formula: see text] was acquired. The [Formula: see text] kinematics were measured via isolation cones by the STAR Forward Meson Spectrometer, an electromagnetic calorimeter covering a forward pseudorapidity range of [Formula: see text]. The asymmetric [Formula: see text] subprocess becomes more dominant in this forward region than in the midrapidity region; furthermore, asymmetry measurements in the forward region are sensitive to low-[Formula: see text] gluons. Progress on [Formula: see text] determined from forward [Formula: see text] events, complementing previous midrapidity measurements, are presented.

Longitudinal double spin asymmetries in single hadron quasi-real photoproduction at high pT

We measured the longitudinal double spin asymmetries ALL for single hadron muoproduction off protons and deuterons at photon virtuality Q2<1(GeV/c)2 for transverse hadron momenta pT in the range 1 GeV/c to 4 GeV/c. They were determined using COMPASS data taken with a polarised muon beam of 160 GeV/c or 200 GeV/c impinging on polarised 6LiD or NH3 targets. The experimental asymmetries are compared to next-to-leading order pQCD calculations, and are sensitive to the gluon polarisation ΔG inside the nucleon in the range of the nucleon momentum fraction carried by gluons 0.05<xg<0.2.

Recent results on nucleon spin structure study at RHIC

Both the PHENIX and STAR experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory are running polarized proton–proton collisions at $$\sqrt s $$ = 200 and 500 GeV. The main goal of the RHIC spin physics program is to gain deeper insight into the spin structure of the nucleon. We will give an overview of recent spin results from RHIC, particularly the study of gluon polarization via jet/hadron production and sea quark polarization via W boson production in longitudinally polarized proton–proton collisions.

Reformulations of Yang–Mills theories with space–time tensor fields

We provide the reformulations of Yang–Mills theories in terms of gauge invariant metric-like variables in three and four dimensions. The reformulations are used to analyze the dimension two gluon condensate and give gauge invariant descriptions of gluon polarization. In three dimensions, we obtain a non-zero dimension two gluon condensate by one loop computation, whose value is similar to the square of photon mass in the Schwinger model. In four dimensions, we obtain a Lagrangian with the dual property, which shares the similar but different property with the dual superconductor scenario. We also make discussions on the effectiveness of one loop approximation.

Unveiling the proton spin decomposition at a future electron-ion collider

We present a detailed assessment of how well a future Electron-Ion Collider could constrain helicity parton distributions in the nucleon and, therefore, unveil the role of the intrinsic spin of quarks and gluons in the proton's spin budget. Any remaining deficit in this decomposition will provide the best indirect constraint on the contribution due to the total orbital angular momenta of quarks and gluons. Specifically, all our studies are performed in the context of global QCD analyses based on realistic pseudo-data and in the light of the most recent data obtained from polarized proton-proton collisions at BNL-RHIC that have provided evidence for a significant gluon polarization in the accessible, albeit limited range of momentum fractions. We also present projections on what can be achieved on the gluon's helicity distribution by the end of BNL-RHIC operations. All estimates of current and projected uncertainties are performed with the robust Lagrange multiplier technique.

Second order gluon polarization for SU(N) theory in a linear covariant gauge

The gluon polarization functional is evaluated for a generic linear covariant gauge and for any space dimension in pure Yang-Mills SU(N) theory up to second order in a generalized perturbation theory, where the zeroth order action is freely chosen and can be determined by some variational method. Some numerical data are given for the gluon propagator in Landau gauge and compared with Feynmann gauge. A comparison is given for several variational methods that can be set up by the knowledge of the second-order polarization.

Nucleon spin structure

This paper contains three parts relating to the nucleon spin structure in a simple picture of the nucleon: (i) The polarized gluon distribution in the proton is dynamically predicted starting from a low scale by using a nonlinear quantum chromodynamics (QCD) evolution equation — the Dokshitzer–Gribov–Lipatov–Altarelli–Paris (DGLAP) equation with the parton recombination corrections, where the nucleon is almost consisted only of valence quarks. We find that the contribution of the gluon polarization to the nucleon spin structure is much larger than the predictions of most other theories. This result suggests that a significant orbital angular momentum of the gluons is required to balance the gluon spin momentum. (ii) The spin structure function [Formula: see text] of the proton is studied, where the perturbative evolution of parton distributions and nonperturbative vector meson dominance (VMD) model are used. We predict [Formula: see text] asymptotic behavior at small x from lower Q2to higher Q2. The results are compatible with the data including the early HERA estimations and COMPASS new results. (iii) The generalized Gerasimov–Drell–Hearn (GDH) sum rule is understood based on the polarized parton distributions of the proton with the higher twist contributions. A simple parameterized formula is proposed to clearly present the contributions of different components in the proton to [Formula: see text]. The results suggest a possible extended objects with size 0.2–0.3 fm inside the proton.

Precision Measurement of the Longitudinal Double-Spin Asymmetry for Inclusive Jet Production in Polarized Proton Collisions at sqrt[s]=200 GeV.

We report a new measurement of the midrapidity inclusive jet longitudinal double-spin asymmetry, A_{LL}, in polarized pp collisions at center-of-mass energy sqrt[s]=200 GeV. The STAR data place stringent constraints on polarized parton distribution functions extracted at next-to-leading order from global analyses of inclusive deep-inelastic scattering (DIS), semi-inclusive DIS, and RHIC pp data. The measured asymmetries provide evidence at the 3σ level for positive gluon polarization in the Bjorken-x region x>0.05.

Polarization energy loss in hot viscous quark–gluon plasma

The gluon polarization tensor for quark–gluon plasma with shear viscosity is derived with the viscous chromohydrodynamics. The longitudinal and transverse dielectric functions are evaluated from the gluon polarization tensor, through which the polarization energy loss suffered by a fast quark traveling through the viscous quark–gluon plasma is investigated. The numerical analysis indicates that shear viscosity significantly reduces the polarization energy loss.

Impact of gluon polarization on Higgs boson plus jet production at the LHC

In this paper we consider Higgs boson plus jet production as a process that is sensitive to the linear polarization of gluons inside the unpolarized protons of the LHC. The leading order expressions for the transverse momentum distribution of the Higgs boson plus jet pair are provided in terms of transverse momentum dependent quark and gluon distributions. This includes both angular independent and azimuthal angular dependent contributions, presented directly in the laboratory frame. Lacking experimental constraints on the linearly polarized gluon distribution, we study its effects on Higgs boson plus jet production using two different models to illustrate the generic features and maximal effects. It is found that the $\mathrm{cos}2\ensuremath{\phi}$ distribution may be the most promising observable, as it is driven by only one initial linearly polarized gluon. The potential advantages of the Higgs boson plus jet process compared to other processes sensitive to the linear polarization of gluons are discussed.

Proton structure and the PHENIX experiment

We briefly summarize the important and critical roles that PHENIX Experiment has played in determining the proton's internal structure in terms of quarks and gluons, and their dynamics. Some pioneering measurements by PHENIX Experiment on the motion and polarization of quarks and gluons, as well as their correlations inside a fast moving proton are presented. Some future opportunities and potentials of PHENIX Experiment are also discussed.

Spin physics highlights from STAR

As the world’s only polarized proton collider, the Relativistic Heavy Ion Collider (RHIC) at Brookhaven plays an important role in understanding the spin structure of the proton. The STAR detector, with its large acceptance for calorimetry and tracking, has been used to study polarized proton collisions for more than a decade with a range of jet, meson, and boson probes. We will discuss jets, neutral pions, and W bosons as probes of the proton’s helicity structure. Here STAR measurements have significant impact on global fits of sea quark polarizations and have provided the first firm evidence of non-zero gluon polarization within the proton. We will discuss W/Z bosons, jets, pions, and pion-jet correlations as probes of the transverse spin structure of the proton, and we will use the example of a proposed dijet measurement with an upgraded STAR detector to peer into the future.

Future Prospects of di-jet Production Constraining Δg(x) at Low x in Polarized p + p Collisions at RHIC

One of the main objectives of the high-energy spin physics program at RHIC at BNL is the precise determination of the polarized gluon distribution function, Δg(x). Polarized [Formula: see text] collisions at [Formula: see text] GeV and at [Formula: see text] GeV at RHIC provide an unique way to probe the proton spin structure. Inclusive measurements, such as inclusive jet and hadron production, have so far been the prime focus of various results at [Formula: see text] GeV constraining Δg(x) for 0.05 &lt; x &lt; 0.2. A recent global analysis provides for the first time evidence of a non-zero value of the gluon polarization [Formula: see text]. First results of di-jet production at [Formula: see text] GeV by the STAR collaboration will allow a better constraint of the underlying event kinematics. Extending the current program to smaller values of x is a key goal for the future high-energy spin physics program at RHIC. Forward di-jet production measurements at STAR beyond the current acceptance from -1 &lt; η &lt; +2 to +2.5 &lt; η &lt; +4, in particular those carried out at [Formula: see text] GeV, provides access to low x values at the level of 10-3 where current uncertainties of Δg(x) remain very large. Those measurements will eventually be complemented by a future Electron-Ion Collider facility probing Δg(x) in polarized [Formula: see text] collisions.

Statistical description of the proton spin with a large gluon helicity distribution

The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering (DIS) experimental results. It enables us to improve the description of the data by means of a new determination of the parton distributions. We will see that a large gluon polarization emerges, giving a significant contribution to the proton spin.

Recent results of gluon and sea quark polarization measurements in polarized proton-proton collisions at STAR

The STAR experiment at RHIC is carrying out a comprehensive high-energy spin physics program to understand the internal structure and dynamics of the proton in polarized proton-proton collisions at = 200 GeV and = 500/510 GeV. STAR has the capability, with nearly full azimuthal coverage, to reconstruct leptons, hadrons and jets in the mid-rapidity region (|η| < 1). The results for inclusive jet longitudinal double spin asymmetries taken during the 2009 RHIC run indicate the first non-zero gluon contribution (Δg(x,Q2)/g(x,Q2)) to the proton spin for 0.05 < x < 1 (Bjorken-x: momentum fraction of partons). Recent longitudinal single-spin asymmetry measurements of W+/− bosons at = 500/510 GeV in polarized proton-proton collisions provide a direct probe of the polarized anti-u and anti-d quark distributions (Δū(x, Q2), Δd̄(x, Q2)). These results better constrain the polarized gluon and sea quark distributions of the proton in the RHIC sensitive kinematic region. Future measurements with continuing high energy polarized proton-proton run at RHIC and detector upgrade will explore the gluonic contribution to the proton spin in extended range.