Examination of the universal behavior of the $\eta$-to-${\pi }^0$ ratio in heavy-ion collisions

We demonstrate that the $p_T$ dependence of the $\eta /{\pi }^0$ ratio at midrapidity is universal within a few percent for high-energy $p+p, p+A$, and $d+A$ collisions, over a broad range of collision energies. The $\eta /{\pi }^0$ ratio increases with $p_T$ up to 4 to 5 GeV/$c$ where it saturates at a nearly constant value of $0.487\pm 0.024$. Above $p_T=5$ GeV/$c$, the same constant value is also observed in $A+A$ collisions independent of collision system, energy, and centrality. At lower $p_T$, where accurate $\eta /{\pi }^0$ data are absent for $A+A$ collisions, we estimate possible deviations from the universal behavior, which could arise due to the rapid radial hydrodynamic expansion of the $A+A$ collision system. For $A+A$ collisions at the BNL Relativistic Heavy Ion Collider we find that possible deviations are limited to the $p_T$ range from 0.4 to 3 GeV/$c$ and remain less than 20% for the most central collisions.

Figure 1

The $\eta /{\pi }^0$ ratio of $p+p$ and $p+A$ collisions. Also plotted are the $\eta /{\pi }^0$ ratios determined by $m_T$ scaling and from a pythia calculation.

Figure 2

Data for the $\eta /{\pi }^0$ ratio from $p+p$ and $p+A$ collisions compared to three different methods to describe the data with a universal shape: empirical fit A, empirical fit B, and GPR.

Figure 3

Result of combining the three empirical methods into one universal estimate of $\eta /{\pi }^0$ as a function of $p_T$. Also shown for reference are the estimates based on the $m_T$-scaling hypothesis and the result of a pythia calculation, both from Fig. 1.

Figure 4

Values of $R^{\infty }=\eta /{\pi }^0(p_T\to \infty )$ as a function of $\sqrt{s_{NN}}$ for the minimum bias $p+p, p+A$, and $\mathrm{A}+\mathrm{B}$ data sets. Statistical errors are shown as bars, and systematic uncertainties are shown as bands. Also shown is a band representing $0.487\pm 0.024$, the result of the empirical fit B to the combined $p+p$ and $p+A$ data. Note that the $\mathrm{A}+\mathrm{B}$ data at 200 GeV are offset in $\sqrt{s_{NN}}$ to avoid overlap of data sets.

Figure 5

Values of $R^{\infty }=\eta /{\pi }^0(p_T\to \infty )$ as a function of $d{N}_{\mathrm{ch}}/d\eta$. The presentation is identical to Fig. 4; however, for $\mathrm{A}+\mathrm{B}$ collisions results from different centrality classes are shown rather than results for the minimum bias sample.

Figure 6

Schematic comparison of $\pi , K$, and $p$ spectra from $\mathrm{Au}+\mathrm{Au}$ and $p+p$ collisions at $\sqrt{s_{NN}}=200$ GeV. All spectra are approximately normalized to their rapidity density at midrapidity. Different particle types are separated by factors of 10 for clarity.

Figure 7

Double ratio, obtained by ${\left(R_{AA}^K\right)}_{C_i}/{\left(R_{AA}^{\pi }\right)}_{C_i}$.

Figure 8

Double ratio (the flow ratio) for $K^{\pm }/{\pi }^{\pm }$ and $\eta /{\pi }^0$ in $\mathrm{Pb}+\mathrm{Pb}$ collisions at 2.76 TeV.

Figure 9

Estimate of the effect of radial flow on $\eta /{\pi }^0$ for 0%–20% and 60%–92% $\mathrm{Au}+\mathrm{Au}$ collisions at 200 GeV and 0%–10% $\mathrm{Pb}+\mathrm{Pb}$ collisions at 2.76 TeV. Details are discussed in the text.

Figure 10

Estimate of the effect of radial flow on $\eta /{\pi }^0$ for 0%–20% and 60%–92% $\mathrm{Au}+\mathrm{Au}$ collisions at 200 GeV and 0%–10% $\mathrm{Pb}+\mathrm{Pb}$ collisions at 2.76 TeV. Data sets of comparable systems are also shown. Details are discussed in the text.

Figure 11

Ratio of photons from the decay of the two mesons. The grid band corresponds to the $\eta /\pi$ ratio in Fig. 10. The dashed line corresponds to the distribution of $\eta$ using the $m_T$-scaling method by fitting with the data of $p+p$ at 200 GeV.