@Adare:2012wg].

The $\eta/\pi^0$ ratios ($R_{\eta/\pi^0}$) as a function of $p_T$ for different Cu$+$Au centrality intervals are presented in the Fig. \[fig:FIG2\_CuAu\_eta\_pi0\_rat\]. Within uncertainties the measured $R_{\eta/\pi^0}$ are centrality independent in the whole $p_T$ range of measurements. A constant fit to the MB data in the 4$<{\mbox{$p_T$}\xspace}<$20region results in $\eta/{\mbox{$\pi^0$}\xspace}= 0.50 \pm 0.01_{\rm stat} 
\pm 0.02_{\rm sys}$, and the various centrality bins are consistent with this value. The dashed curve in Fig. \[fig:FIG2\_CuAu\_eta\_pi0\_rat\] shows this asymptotically constant fit modified according to $m_T$-scaling. Similar results were obtained in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions as well as in $e^{+}e^{-}$ collisions in a wide range of collision energies $\sqrt{s_{_{NN}}}=3$–1800 GeV [@Busser:1974yj; @Adler:2006bv]. This suggests that QGP medium produced in Cu$+$Au collisions either does not affect the jet fragmentation into light mesons or it affects the and $\eta$ the same way.

Nuclear modification factors of $\pi^0$ and $\eta$ mesons as functions of $p_T$ are shown in Fig. \[fig:FIG3\_CuAu\_pi0\_eta\_RAA\] for different Cu$+$Au centrality intervals. The reference $\pi^0$ meson production cross section in $p$+$p$ collisions was obtained from the 2005 PHENIX $p$+$p$ measurement [@Adare:2007dg]. For $\eta$ meson $R_{AB}$ estimation, the 2006 PHENIX $p$+$p$ measurements were used [@Adare:2010cy]. The $R_{AB}$-s of $\pi^0$ and $\eta$ mesons are consistent within 