Measurements of double-helicity asymmetries in inclusive $J/ψ$ production in longitudinally polarized $p+p$ collisions at $\sqrt{s}=510$ GeV

TL;DR

This study measures the double helicity asymmetry $A_{LL}^{J/ψ}$ in inclusive $J/ψ$ production from longitudinally polarized $p+p$ collisions at $\sqrt{s}=510$ GeV with the PHENIX detector, using forward rapidity $J/ψ\to μ^+μ^-$ in $1.2<|η|<2.4$. The measurement, based on ~150 pb$^{-1}$, samples gluons from two distinct Bjorken $x$ ranges, enabling sensitivity to gluon polarization at $x \sim 2\times 10^{-3}$ and $x \sim 0.05$. The result, $A_{LL}^{J/ψ}=0.012\pm0.010\,(stat)\pm0.003\,(syst)$, is consistent with small but positive gluon polarization and, via comparison and NNPDF-based reweighting, suggests a more positive $\Delta g$ in the small-$x$ region, thereby helping to constrain the gluon spin contribution in global fits. The work demonstrates the viability of heavy-quark production as a probe of gluon polarization and tests of QCD factorization and NRQCD in polarized collisions.

Abstract

We report the double helicity asymmetry, $A_{LL}^{J/ψ}$, in inclusive $J/ψ$ production at forward rapidity as a function of transverse momentum $p_T$ and rapidity $|y|$. The data analyzed were taken during $\sqrt{s}=510$ GeV longitudinally polarized $p$$+$$p$ collisions at the Relativistic Heavy Ion Collider (RHIC) in the 2013 run using the PHENIX detector. At this collision energy, $J/ψ$ particles are predominantly produced through gluon-gluon scatterings, thus $A_{LL}^{J/ψ}$ is sensitive to the gluon polarization inside the proton. We measured $A_{LL}^{J/ψ}$ by detecting the decay daughter muon pairs $μ^+ μ^-$ within the PHENIX muon spectrometers in the rapidity range $1.2<|y|<2.2$. In this kinematic range, we measured the $A_{LL}^{J/ψ}$ to be $0.012 \pm 0.010$~(stat)~$\pm$~$0.003$(syst). The $A_{LL}^{J/ψ}$ can be expressed to be proportional to the product of the gluon polarization distributions at two distinct ranges of Bjorken $x$: one at moderate range $x \approx 0.05$ where recent RHIC data of jet and $π^0$ double helicity spin asymmetries have shown evidence for significant gluon polarization, and the other one covering the poorly known small-$x$ region $x \approx 2\times 10^{-3}$. Thus our new results could be used to further constrain the gluon polarization for $x< 0.05$.

Figures (4)

• Figure 1: Bjorken $x$ distribution of gluons in the $gg \rightarrow J/\psi + X \rightarrow \mu^+ \mu^- + X$ process from a pythia simulation with $J/\psi$ generated within $1.2<|y|<2.2$ and the decayed muon within $1.2<|\eta|<2.4$ for the north arm and $1.2<|\eta|<2.2$ for the south arm. Top panel shows the $p_T$ binning and the bottom panel shows the $|y|$ binning. All the distributions are arbitrarily normalized to have unit area.
• Figure 2: Dimuon invariant mass spectrum and the GPR fitting for the background fraction $f_{\rm Bkg}$ extraction. The black circles are the PHENIX unlike-sign dimuon data after event and track selection. The blue triangles are the GPR background estimation. The red boxes are the data remaining after subtraction of the background. The green dashed line represents the $J/\psi$ shape; the blue dot-dashed line represents the $\psi^{\prime}$ shape; and the red solid line the summation of $J/\psi$ and $\psi^{\prime}$. Green shaded region indicates the sideband area used for the calculation of $A_{LL}^{\rm Bkg}$ in Eq. \ref{['eq:ALL_phys']}. The data in the region between the two red vertical lines are the data used to calculate $A_{LL}^{\rm Incl}$ in Eq. \ref{['eq:ALL_phys']}.
• Figure 3: $A_{LL}^{J/\psi}$ as a function of $p_T$ (top panel) and $|y|$ (bottom panel). The black error bars show the statistical uncertainty. The red boxes show only the Type A systematic uncertainties. There are additionally a 4 $\times 10^{-4}$ global systematic uncertainty from the relative luminosity determination and a 6.5 % global scaling systematic uncertainty from the polarization magnitude determination for all $p_T$ or $|y|$ bins. The blue curve with shaded band is our $A_{LL}^{J/\psi}$ estimation using pythia6 Sjostrand:PYTHIA simulation with NNPDF data sets under the assumption of $\hat{a}^{gg \rightarrow \hbox{$J/\psi$}\xspace + X}_{LL}$$= 1$. The solid blue curve is the central value and the blue shaded band is the $\pm~2~\sigma$ uncertainty range. See details in the text.
• Figure 4: Blue dashed line is gluon polarization in NNPDFpol1.1; uncertainty band for it was obtained from 100 replicas of NNPDFpol1.1 using the replica method in Gao:2013bia. Red solid curve is the gluon polarization from NNPDFpol1.1 re-weighted using 2013 PHENIX $J/\psi$$A_{LL}$ data under the assumption that $\hat{a}^{gg \rightarrow \hbox{$J/\psi$}\xspace + X}_{LL}$ = 1.