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The first measurements of the invariant differential cross sections ofinclusive $\pi^0$ and $\eta$ meson production at mid-rapidity in proton-protoncollisions at $\sqrt{s}=0.9$ TeV and $\sqrt{s}=7$ TeV are reported. The $\pi^0$measurement covers the ranges $0.4<p_T<7$ GeV/$c$ and $0.3<p_T<25$ GeV/$c$ forthese two energies, respectively. The production of $\eta$ mesons was measuredat $\sqrt{s}=7$ TeV in the range $0.4<p_T<15$ GeV/$c$. Next-to-Leading Orderperturbative QCD calculations, which are consistent with the $\pi^0$ spectrumat $\sqrt{s}=0.9$ TeV, overestimate those of $\pi^0$ and $\eta$ mesons at$\sqrt{s}=7$ TeV, but agree with the measured $\eta/\pi^0$ ratio at$\sqrt{s}=7$ TeV.

Neutral pion and $\eta$ meson production in proton-proton collisions at $\sqrt{s}=0.9$ TeV and $\sqrt{s}=7$ TeV