Inclusive cross section and double helicity asymmetry for ${\pi }^0$ production in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$: Implications for the polarized gluon distribution in the proton

The PHENIX experiment presents results from the Relativistic Heavy Ion Collider 2005 run with polarized proton collisions at $\sqrt{s}=200\mathrm{GeV}$, for inclusive ${\pi }^0$ production at midrapidity. Unpolarized cross section results are given for transverse momenta $p_T=0.5$ to $20\mathrm{GeV}/c$, extending the range of published data to both lower and higher $p_T$. The cross section is described well for $p_T<1\mathrm{GeV}/c$ by an exponential in $p_T$, and, for $p_T>2\mathrm{GeV}/c$, by perturbative QCD. Double helicity asymmetries $A_{LL}$ are presented based on a factor of 5 improvement in uncertainties as compared to previously published results, due to both an improved beam polarization of 50%, and to higher integrated luminosity. These measurements are sensitive to the gluon polarization in the proton. Using one representative model of gluon polarization it is demonstrated that the gluon spin contribution to the proton spin is significantly constrained.

Figure 1

The neutral pion production cross section at $\sqrt{s}=200\mathrm{GeV}$ as a function of $p_T$ (squares) and the results of NLO pQCD calculations for theory scales $\mu =p_T/2$ (dotted line), $p_T$ (solid line) and $2p_T$ (dashed line), see text for details; note that the error bars are smaller than the points. The inset shows, in addition to ${\pi }^0$ (squares), data for $({\pi }^{+}+{\pi }^{-})/2$ (solid circles), and a fit of charged pion data to an exponential function for $p_T<0.8\mathrm{GeV}/c$ (dashed line). The bottom panel shows the relative difference between the data and theory for the three theory scales. Experimental uncertainties (excluding the 9.7% normalization uncertainty) are shown for the $\mu =p_T$ curve.

Figure 2

The double helicity asymmetry for neutral pion production at $\sqrt{s}=200\mathrm{GeV}$ as a function of $p_T$ ($\mathrm{GeV}/c$). Error bars are statistical uncertainties, with the 9.4% scale uncertainty not shown; other experimental systematic uncertainties are negligible. Four GRSV theoretical calculations based on NLO pQCD are also shown for comparison with the data (see text for details).

Figure 3

The ${\chi }^2$ distribution of the measured data plotted versus the value of the first moment of the polarized gluon distribution (solid line) in the $x_g$ range from 0.02 to 0.3 corresponding to our ${\pi }^0$ data in $p_T$ bins from 2 to $9\mathrm{GeV}/c$. Dashed and dotted lines correspond to $-9.4\%$ and $+9.4\%$ variation in $A_{LL}$ normalization related to the beam polarization uncertainty, the dominant systematic uncertainty of our data. Only statistical uncertainties were used for each curve. Arrows indicate $\Delta G$ corresponding to the different polarized gluon distributions discussed in the text.