Inclusive double-helicity asymmetries in neutral-pion and eta-meson production in $\overrightarrow{p}+\overrightarrow{p}$ collisions at $\sqrt{s}=200\mathrm{GeV}$

Results are presented from data recorded in 2009 by the PHENIX experiment at the Relativistic Heavy Ion Collider for the double-longitudinal spin asymmetry, $A_{LL}$, for ${\pi }^0$ and $\eta$ production in $\sqrt{s}=200\mathrm{GeV}$ polarized $p+p$ collisions. Comparison of the ${\pi }^0$ results with different theory expectations based on fits of other published data showed a preference for small positive values of gluon polarization, $\mathrm{\Delta }G$, in the proton in the probed Bjorken $x$ range. The effect of adding the new 2009 ${\pi }^0$ data to a recent global analysis of polarized scattering data is also shown, resulting in a best fit value $\mathrm{\Delta }{G}_{\text{DSSV}}^{[0.05,0.2]}=0.06_{-0.15}^{+0.11}$ in the range $0.05<x<0.2$, with the uncertainty at $\mathrm{\Delta }{\chi }^2=9$ when considering only statistical experimental uncertainties. Shifting the PHENIX data points by their systematic uncertainty leads to a variation of the best-fit value of $\mathrm{\Delta }{G}_{\text{DSSV}}^{[0.05,0.2]}$ between 0.02 and 0.12, demonstrating the need for full treatment of the experimental systematic uncertainties in future global analyses.

Figure 1

Diagram showing the three elements of pQCD factorization: parton distribution functions $f_{a,b}(x)$, partonic cross sections ${\sigma }^{a+b\to c}$, and fragmentation functions $D_c^h(z)$.

Figure 2

Cross section of the PHENIX central arms in their 2009–2010 configuration. The EMCal (PbSc and PbGl) is the primary subsystem used in this analysis. The PC3 is also used to veto charged particles. Not pictured in this view are the BBC and ZDC luminosity monitors at forward rapidity.

Figure 3

Schematic (not to scale) of the hits in the PC3 (transparent grid) and the related ${\theta }_{CV}$ from three particle classes, which leave clusters in the EMCal (solid grid behind PC3): (a) photons that convert outside of the magnetic field prior to the EMCal, and have very small ${\theta }_{CV}$, (b) charged hadrons that bend in the magnetic field, and so have moderate sized ${\theta }_{CV}$, and (c) photons that do not convert, and are randomly associated with a different particle’s PC3 hit, and therefore are likely to have large ${\theta }_{CV}$.

Figure 4

${\theta }_{CV}$ intervals used in the analysis as a function of cluster energy in the EMCal PbSc. Clusters in the red cross-hatched region are excluded from the analysis. For $E_{\text{cluster}}>1.9\mathrm{GeV}$, no distinction between the regions is possible due to the inverse relationship between bend and energy for hadronic tracks.

Figure 5

Yield of cluster pairs in the PbSc with $p_T$ of $1–1.5\mathrm{GeV}/c$ for different ${\theta }_{CV}$ requirements as a function of invariant mass (calculated assuming both clusters are photons), in the PbSc only and for $E_{\text{cluster}}<1.9\mathrm{GeV}$. The ratio of the “small” $+$ “not moderate” to the “large” $+$ “large” yield in the ${\pi }^0$ mass-peak region is consistent with the material budget of $\approx 10\%$ fractional radiation length in the magnetic-field region before the PC3.

Figure 6

Normalized ToF distributions for the lower energy cluster in cluster pairs passing all cuts except the ToF cut. The distributions are plotted for pairs with invariant mass reconstructions in the ${\pi }^0$ signal or sideband regions defined in the text.

Figure 7

(a) Efficiency of ToF cut, with the minimum energy, trigger, and off-line $z$-vertex cuts already applied, for different crossing selections defined in the text, and for a $p_T$ range of $2–4\mathrm{GeV}/c$. The energy asymmetry cut has not been applied here, and the decreased efficiency in the $\eta$ mass region is due to the larger background fraction. (b) Ratio of the histograms in (a) to the histogram with crossing selection $+3\mathrm{b}$.

Figure 8

(a) Two-photon invariant mass in the region of the ${\pi }^0$ mass for the $4<p_T<5\mathrm{GeV}/c$ bin with all cuts except the energy asymmetry cut applied, as discussed in the text. (b) Two-photon invariant mass in the region of the $\eta$ mass with all cuts including the energy asymmetry cut applied, as discussed in the text. In both plots, the red solid region shows the signal region and the blue hatched region shows the background sidebands used in the asymmetry analysis.

Figure 9

$A_{LL}$ vs $m_{\gamma \gamma }$ for the background region near the ${\pi }^0$ mass peak for three $p_T$ bins: $1–1.5\mathrm{GeV}/c$ (black circle), $2–2.5\mathrm{GeV}/c$ (red square) and $3–3.5\mathrm{GeV}/c$ (blue triangle), for a single spin pattern in odd crossings. The peak region $A_{LL}$ is not shown. No $m_{\gamma \gamma }$ dependence is found.

Figure 10

Relative difference between the measured trigger rate and the quantity in Eq. (12) plotted for all beam crossings in a fraction of the present data set.

Figure 11

$A_{LL}$ vs $p_T$ for ${\pi }^0$ mesons for the 2005 (red circle), 2006 (blue square) and 2009 (black triangle) PHENIX data sets. The 2009 relative luminosity systematic uncertainty is shown only in the inset, but it applies across the entire $p_T$ range.

Figure 12

$A_{LL}$ vs $p_T$ for $\eta$ mesons for the 2005 (red circle), 2006 (blue square) and 2009 (black triangle) PHENIX data sets.

Figure 13

Points are the combined $A_{LL}$ vs $p_T$ for ${\pi }^0$ mesons from 2005 through 2009 with the statistical uncertainty. The $p_T$ correlated systematic uncertainty given by the gray bands is the result of combining the year-to-year uncorrelated parts of the systematic uncertainties on relative luminosity and polarization. The year-to-year correlated parts are given in the legend. Plotted for comparison are several expectations based on fits to polarized scattering data, with uncertainties where available.

Figure 14

Points are the combined $A_{LL}$ vs $p_T$ for $\eta$ mesons from 2005 through 2009 with the statistical uncertainty. The $p_T$ correlated systematic uncertainty given by the gray bands is the result of combining the year-to-year uncorrelated parts of the systematic uncertainties on relative luminosity and polarization. The year-to-year correlated parts are given in the legend. Several theoretical expectations based on fits to polarized data are also shown, which use results from [25] for the fragmentation functions.

Figure 15

Change in ${\chi }^2$ as a function of $\mathrm{\Delta }{G}_{\mathrm{DSSV}08}^{[0.05,0.2]}$, when adding PHENIX 2009 ${\pi }^0$ data to the dssv08 global analysis (which includes earlier PHENIX ${\pi }^0$ data). (a) Contribution of the combined PHENIX data at $\sqrt{s}=200\mathrm{GeV}$ to the global ${\chi }^2$ of the dssv08 analysis using only statistical uncertainties. The different curves show the effect of shifting only the PHENIX data points up or down by their total systematic uncertainty, which is $p_T$ correlated. (b) The effect of shifting only the PHENIX $\sqrt{s}=200\mathrm{GeV}$ data points on the dssv08 global ${\chi }^2$.