Inclusive cross section and double helicity asymmetry for ${\pi }^0$ production in $p+p$ collisions at $\sqrt{s}=62.4\mathrm{GeV}$

The PHENIX experiment presents results from the RHIC 2006 run with polarized $p+p$ collisions at $\sqrt{s}=62.4\mathrm{GeV}$, for inclusive ${\pi }^0$ production at midrapidity. Unpolarized cross section results are measured for transverse momenta $p_T=0.5$ to $7\mathrm{GeV}/c$. Next-to-leading order perturbative quantum chromodynamics calculations are compared with the data, and while the calculations are consistent with the measurements, next-to-leading logarithmic corrections improve the agreement. Double helicity asymmetries $A_{LL}$ are presented for $p_T=1$ to $4\mathrm{GeV}/c$ and probe the higher range of Bjorken $x$ of the gluon ($x_g$) with better statistical precision than our previous measurements at $\sqrt{s}=200\mathrm{GeV}$. These measurements are sensitive to the gluon polarization in the proton for $0.06<x_g<0.4$.

Figure 1

The fraction of the inclusive ${\pi }^0$ yield which satisfied the BBC trigger condition.

Figure 2

Collision $z$-vertex distribution in the PHENIX IR measured by ZDCs in a Vernier scan at $\sqrt{s}=200\mathrm{GeV}$ (points) and calculations from convolution of colliding bunch intensity profiles along $z$-axis and including the hourglass effect for ${\beta }^{*}=1\mathrm{m}$, for bunches with typical length of 1 m and transverse size of 0.3 mm (histograms); (a) beams are head-on; (b) one beam is 0.9 mm displaced relative to the other beam in the horizontal direction (illustrates the hourglass effect) and (c) one beam is 0.9 mm displaced relative to the other beam in the vertical direction. The calculations include the bunch crossing angle with a vertical projection of 0.15 mrad.

Figure 3

(a) The neutral pion production cross section at $\sqrt{s}=62.4\mathrm{GeV}$ as a function of $p_T$ (circles) and the results of NLO (solid) and NLL (dashed) pQCD calculations for the theory scale $\mu =p_T$. (b) The relative difference between the data and NLO pQCD calculations for the three theory scales $\mu =p_T/2$ (upper line), $p_T$ (middle line) and $2p_T$ (lower line); experimental uncertainties (excluding the 11% normalization uncertainty) are shown for the $\mu =p_T$ curve. (c) The same as b) but for NLL pQCD calculations.

Figure 4

(a) The neutral pion production cross section at $\sqrt{s}=62.4\mathrm{GeV}$ and $\sqrt{s}=200\mathrm{GeV}$ as a function of $x_T$, scaled by $(\sqrt{s}/\mathrm{GeV}{)}^n$ with $n=6.38$; the solid line is a parametrization of $\sqrt{s}=200\mathrm{GeV}$ data. (b) The parameter $n$ in (6) obtained from the ratio of invariant cross section at $\sqrt{s}=62.4\mathrm{GeV}$ and $\sqrt{s}=200\mathrm{GeV}$, at each $x_T$ of $\sqrt{s}=62.4\mathrm{GeV}$ data; error bars show the statistical and systematic uncertainties of the $\sqrt{s}=62.4\mathrm{GeV}$ and $\sqrt{s}=200\mathrm{GeV}$ data. The shaded band reflects the $11\%\oplus 9.7\%$ normalization uncertainty in the $\sqrt{s}=62.4$ and 200 GeV cross section measurements, correspondingly.

Figure 5

The double helicity asymmetry for neutral pion production at $\sqrt{s}=62.4\mathrm{GeV}$ as a function of $p_T(\mathrm{GeV}/c)$. Error bars are statistical uncertainties, with the 14% overall polarization uncertainty not shown; other experimental systematic uncertainties are negligible. Four GRSV theoretical calculations based on NLO pQCD (solid curves) and on NLL pQCD (dashed curves) are also shown for comparison with the data (see text for details). Note that the $\Delta G=0$ curves for NLO and NLL overlap.

Figure 6

The double helicity asymmetry for neutral pion production at $\sqrt{s}=62.4\mathrm{GeV}$ and 200 GeV as a function of $x_T$. Error bars are statistical uncertainties, with the 14% (9.4%) overall polarization uncertainty for $\sqrt{s}=62.4\mathrm{GeV}$ (200 GeV) data not shown. Two GRSV theoretical calculations based on NLO pQCD are also shown for comparison with the data (see text for details.)