Neutral pion cross section and spin asymmetries at intermediate pseudorapidity in polarized proton collisions at $\sqrt{s}=200\mathrm{GeV}$

The differential cross section and spin asymmetries for neutral pions produced within the intermediate pseudorapidity range $0.8<\eta <2.0$ in polarized proton-proton collisions at $\sqrt{s}=200\mathrm{GeV}$ are presented. Neutral pions were detected using the end cap electromagnetic calorimeter in the STAR detector at RHIC. The cross section was measured over a transverse momentum range of $5<p_T<16\mathrm{GeV}/c$ and is found to agree with a next-to-leading order perturbative QCD calculation. The longitudinal double-spin asymmetry $A_{LL}$ is measured in the same pseudorapidity range and spans a range of Bjorken-$x$ down to $x\approx 0.01$. The measured $A_{LL}$ is consistent with model predictions for varying degrees of gluon polarization. The parity-violating asymmetry $A_L$ is also measured and found to be consistent with zero. The transverse single-spin asymmetry $A_N$ is measured over a previously unexplored kinematic range in Feynman-$x$ and $p_T$. Such measurements may aid our understanding of the onset and kinematic dependence of the large asymmetries observed at more forward pseudorapidity ($\eta \approx 3$) and their underlying mechanisms. The $A_N$ results presented are consistent with a twist-3 model prediction of a small asymmetry over the present kinematic range.

Figure 1

Distributions of $x_1$ and $x_2$ in two different bins of reconstructed ${\pi }^0{p}_T$ for events at $\sqrt{s}=200\mathrm{GeV}$ over $0.8<\eta <2$. The distributions were made using Monte Carlo simulations based on PYTHIA [19, 20], utilizing unpolarized parton distribution functions.

Figure 2

Comparison of data to Monte Carlo for the distributions of two-photon invariant mass (left) and energy for the higher (center) and lower (right) energy photon. Distributions are shown with a reconstructed transverse momentum range of $7<p_T<8\mathrm{GeV}/c$. For the photon-energy distributions, a two-photon mass requirement of $0.1<M_{\gamma \gamma }<0.2\mathrm{GeV}/c^2$ is applied. The Monte Carlo distributions have been normalized to the number of counts in the data distributions.

Figure 3

Invariant mass distribution for the two-photon system with $7<p_T<8\mathrm{GeV}/c$. Also included on the plot are the template functions for the signal and two backgrounds (scaled and shifted according to the fit results), the residual between the data and the sum of the templates, and a gray-shaded area indicating the peak region.

Figure 4

Signal fractions calculated within the “peak region” of $0.1<M_{\gamma \gamma }<0.2\mathrm{GeV}/c^2$. Fractions for the full data set as well as the subsets of longitudinal and transverse polarizations are shown as a function of $p_T$ (left), and the fractions for the transversely polarized data are shown as a function of $x_F$ integrated over $5<p_T<12\mathrm{GeV}/c$ (right). Uncertainties on the signal fractions arise from those of the template forms determined from Monte Carlo and from their application to the data. The size of the uncertainties is influenced by the number of events in the available data and Monte Carlo and the quality of fits to Monte Carlo and data. The same Monte Carlo sample is used to extract the signal fractions for the three data sets.

Figure 5

Upper panel: The ${\pi }^0$ cross section (blue markers) is shown compared with an NLO pQCD calculation [1] with three options for the scale parameter. Statistical uncertainties are shown by the error bars which are indistinguishable from the markers in all bins. Systematic uncertainties are shown by the error boxes. The lower panel presents the ratio of the data to the $p_T$-scale theory curve, as well as the ratio of the $2p_T$-scale and $p_T/2$-scale theory curves to the $p_T$-scale curve.

Figure 6

The ${\pi }^0$ cross section at various ranges of pseudorapidity as measured by STAR. Error bars indicate the total uncertainty. The closed blue circles are the results of this analysis, while the other points are previously published results that use the STAR barrel electromagnetic calorimeter (open orange circles) [7] and the forward pion detectors (closed black stars and open red stars) [12, 13].

Figure 7

The $A_{LL}$ results (blue markers) are presented with the DSSV prediction [17] and the GRSV prediction [44] using the best fit to polarized DIS ($\mathrm{\Delta }g=\mathrm{std}$) and the maximum and minimum allowed values for gluon polarization. Statistical uncertainties are shown by the error bars, whereas systematic uncertainties are indicated by the error boxes. The 6% scale uncertainty is due to beam polarization uncertainty.

Figure 8

The $A_N$ results are plotted versus $x_F$ integrated over $5<p_T<12\mathrm{GeV}/c$ (left panel) and versus $p_T$ integrated over $0.06<|x_F|<0.27$ (right panel). Statistical uncertainties are shown by error bars, whereas systematic uncertainties are indicated by error boxes. Negative $x_F$ results are depicted with open circles and open error boxes, while positive $x_F$ results are exhibited with closed circles and closed systematic error boxes. The $A_N$ results are presented with model predictions based on the twist-3 mechanism in the collinear factorization framework [34]. The 4% scale uncertainty is due to beam polarization uncertainty.

Figure 9

The present $A_N$ results (blue circles) are compared with previously published values of $A_N$ [9, 23] as a function of $x_F$ (top panel). The average $p_T$ values within each $x_F$ bin are compared for the various measurements (bottom panel).