Inclusive double-helicity asymmetries in neutral pion and eta meson production in $\vec{p}+\vec{p}$ collisions at $\sqrt{s}=200$ 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 $π^0$ and $η$ production in $\sqrt{s} = 200$ GeV polarized $p$$+$$p$ collisions. Comparison of the $π^0$ results with different theory expectations based on fits of other published data showed a preference for small positive values of gluon polarization, $ΔG$, in the proton in the probed Bjorken $x$ range. The effect of adding the new 2009 \pz data to a recent global analysis of polarized scattering data is also shown, resulting in a best fit value $ΔG^{[0.05,0.2]}_{\mbox{DSSV}} = 0.06^{+0.11}_{-0.15}$ in the range $0.05<x<0.2$, with the uncertainty at $Δχ^2 = 9$ 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 $ΔG^{[0.05,0.2]}_{\mbox{DSSV}}$ between $0.02$ and $0.12$, demonstrating the need for full treatment of the experimental systematic uncertainties in future global analyses.