two subsystems. The ratios of the yields obtained in PbSc and PbGl to the averaged ones are presented in panels (b)-(d) and (f)-(h) of Fig. \[fig:FIG1\_CuAu\_CY\]. Only uncorrelated systematic uncertainties are shown in the ratios. Yields obtained in the different subsystems are consistent within statistical and uncorrelated systematic uncertainties. Typical systematic uncertainties for the combined spectra, and $\eta$ $R_{AB}$ and $\eta$/ratio are listed in Table \[tab2\].

To facilitate comparison between different experiments and data sets, the data points of the meson spectra are plotted at the center of each given $p_T$ interval, which, due to the falling spectrum, does not represent the true physical value of the yield at that  [@LAFFERTY1995541]. A bin-shift correction is applied that adjusts the meson yields to their value at the bin center.

![image](FIG2_Yields_rev3_1cp.pdf){width="0.98\linewidth"}

![ Ratios of $\eta$ and $\pi^0$ yields measured as a function of $p_T$ in different centrality intervals of Cu$+$Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV. Dashed curve shows the $m_T$ scaling curve normalized to 0.5 at high momentum (see text). Error bars represent a quadratic sum of statistical and type-A systematic uncertainties for $\pi^0$ and $\eta$ yields. Error boxes represent a quadratic sum of type-B systematic uncertainties for $\pi^0$ and $\eta$ yields. []{data-label="fig:FIG2_CuAu_eta_pi0_rat"}](FIG3_eta_to_pi0_rat_rev3_1cp.pdf){width="1.0\linewidth"}

