$\eta$ meson production of high-energy nuclear collisions at NLO

Abstract

The transverse momentum spectrum of $\eta$ meson in relativistic heavy-ion collisions is studied at the next-to-leading-order (NLO) within the perturbative QCD, where the jet quenching effect in the QGP is incorporated with the effectively medium-modified $\eta$ fragmentation functions using the higher-twist approach. We show that the theoretical simulations could give nice descriptions of PHENIX data on $\eta$ meson in both $\mathrm{p}+\mathrm{p}$ and central $\mathrm{Au}+\mathrm{Au}$ collisions at the RHIC, and also provide numerical predictions of $\eta$ spectra in central $\mathrm{Pb}+\mathrm{Pb}$ collisions with $\sqrt{s_{NN}}=2.76$~TeV at the LHC. The ratios of $\eta /{\pi }^0$ in $\mathrm{p}+\mathrm{p}$ and in central $\mathrm{Au}+\mathrm{Au}$ collisions at $200$~GeV are found to overlap in a wide $p_T$ region, which matches well the measured ratio $\eta /{\pi }^0$ by PHENIX. We demonstrate that, at the asymptotic region when $p_T\to \infty$ the ratios of $\eta /{\pi }^0$ in both $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{p}+\mathrm{p}$ are almost determined only by quark jets fragmentation and thus approach to the one in $e^{+}{e}^{-}$ scattering; in addition, the almost identical gluon (quark) contribution fractions to $\eta$ and to $\pi$ result in a rather moderate variation of $\eta /{\pi }^0$ distribution at intermediate and high $p_T$ region in $\mathrm{A}+\mathrm{A}$ relative to that in $\mathrm{p}+\mathrm{p}$; while a slightly higher $\eta /{\pi }^0$ at small $p_T$ in $\mathrm{Au}+\mathrm{Au}$ can be observed due to larger suppression of gluon contribution fraction to ${\pi }^0$ as compared to the one to $\eta$. The theoretical prediction for $\eta /{\pi }^0$ at the LHC has also been presented.

Comments: 7 pages, 8 figures, 2 typos corrected, revision for publication