Inclusive cross section and double-helicity asymmetry for ${\pi }^0$ production at midrapidity in $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$

PHENIX measurements are presented for the cross section and double-helicity asymmetry ($A_{LL}$) in inclusive ${\pi }^0$ production at midrapidity from $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$ from data taken in 2012 and 2013 at the Relativistic Heavy Ion Collider. The next-to-leading-order perturbative-quantum-chromodynamics theory calculation is in excellent agreement with the presented cross section results. The calculation utilized parton-to-pion fragmentation functions from the recent DSS14 global analysis, which prefer a smaller gluon-to-pion fragmentation function. The ${\pi }^0{A}_{LL}$ results follow an increasingly positive asymmetry trend with $p_T$ and $\sqrt{s}$ with respect to the predictions and are in excellent agreement with the latest global analysis results. This analysis incorporated earlier results on ${\pi }^0$ and jet $A_{LL}$ and suggested a positive contribution of gluon polarization to the spin of the proton $\mathrm{\Delta }G$ for the gluon momentum fraction range $x>0.05$. The data presented here extend to a currently unexplored region, down to $x\sim 0.01$, and thus provide additional constraints on the value of $\mathrm{\Delta }G$.

Figure 1

The probability for two photons from ${\pi }^0$ decay to be separated by the PHENIX EMCal clustering algorithm vs ${\pi }^0$ $p_T$; obtained from geant [19] simulation for the two-photon energy asymmetry cut $\alpha <0.8$.

Figure 2

The neutral pion production cross section at midrapidity in $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$ as a function of $p_T$ and NLO pQCD calculations for theory scales $\mu =p_T/2$ (dotted line), $p_T$ (solid line) and $2p_T$ (dashed line), with $\mu$ representing equal factorization, renormalization, and fragmentation scales. Note that the error bars, representing the combined statistical and point-to-point systematic uncertainties, are smaller than the points. (bottom panel) Relative difference between the data and theory for the three theory scales. Experimental uncertainties are shown for the $\mu =p_T$ curve.

Figure 3

$A_{LL}$ vs $p_T$ for ${\pi }^0$ production at midrapidity in $p+p$ collisions at $\sqrt{s}=510\mathrm{GeV}$. Error bars are combined statistical and point-to-point systematic uncertainties. The $A_{LL}=0$ (yellow) line is uncertainty from relative luminosity. The theoretical curve with 90% C.L. band (green) is from a DSSV14 calculation [16].

Figure 4

$A_{LL}$ vs $x_T$ for ${\pi }^0$ production at midrapidity at $\sqrt{s}=200\mathrm{GeV}$ (blue) from [14] and 510 GeV (red) from this analysis. Error bars are combined statistical and point-to-point systematic uncertainties. Note that the relative luminosity uncertainties from two data samples are about the same, hence are indistinguishable in the plot in the overlapping $x_T$ range. Theoretical curves are from recent NLO global analyses [5, 6, 16], with the lower curves (blue) for $\sqrt{s}=200\mathrm{GeV}$ and the higher curves (red) for $\sqrt{s}=510\mathrm{GeV}$.