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Production of $\pi^0$ and $\eta$ mesons has been measured at midrapidity inCu$+$Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV. Measurements were performedin $\pi^0(\eta)\rightarrow\gamma\gamma$ decay channel in the 1(2)-20 GeV/$c$transverse momentum range. A strong suppression is observed for $\pi^0$ and$\eta$ meson production at high transverse momentum in central Cu$+$Aucollisions relative to the $p$$+$$p$ results scaled by the number ofnucleon-nucleon collisions. In central collisions the suppression is similar toAu$+$Au with comparable nuclear overlap. The $\eta/\pi^0$ ratio measured as afunction of transverse momentum is consistent with $m_T$-scalingparameterization down to $p_T=$2 GeV/$c$, its asymptotic value is constant andconsistent with Au$+$Au and $p$$+$$p$ and does not show any significantdependence on collision centrality. Similar results were obtained inhadron-hadron, hadron-nucleus, and nucleus-nucleus collisions as well as in$e^+e^-$ collisions in a range of collision energies $\sqrt{s_{_{NN}}}=$3--1800GeV. This suggests that the quark-gluon-plasma medium produced in Cu$+$Cucollisions either does not affect the jet fragmentation into light mesons or itaffects the $\pi^0$ and $\eta$ the same way.

Production of $\pi^0$ and $\eta$ mesons in Cu$+$Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV