Measurement of neutral mesons in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ and scaling properties of hadron production

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the invariant differential cross section for production of $K_S^0$, $\omega$, ${\eta }^{\prime }$, and $\varphi$ mesons in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$. Measurements of $\omega$ and $\varphi$ production in different decay channels give consistent results. New results for the $\omega$ are in agreement with previously published data and extend the measured $p_T$ coverage. The spectral shapes of all hadron transverse momentum distributions measured by PHENIX are well described by a Tsallis distribution functional form with only two parameters, $n$ and $T$, determining the high-$p_T$ and characterizing the low-$p_T$ regions of the spectra, respectively. The values of these parameters are very similar for all analyzed meson spectra, but with a lower parameter $T$ extracted for protons. The integrated invariant cross sections calculated from the fitted distributions are found to be consistent with existing measurements and with statistical model predictions.

Figure 1

Schematic view of the PHENIX central spectrometers and particle decay modes analyzed in this paper.

Figure 2

Invariant mass distribution for $\gamma \gamma$ pairs in the range $4<p_T(\mathrm{GeV}/c)<6$. The inset shows an enlargement of the region around the $\eta$ mass.

Figure 3

Invariant mass distribution for ${\pi }^0\gamma$ (left panel) and ${\pi }^0{\pi }^0$ (right panel) decays at $4<p_T(\mathrm{GeV}/c)<6$.

Figure 4

Invariant mass distribution for ${\pi }^0{\pi }^{+}{\pi }^{-}$ (left panel) and $\eta {\pi }^{+}{\pi }^{-}$ (right panel) triplets in the momentum range $4<p_T(\mathrm{GeV}/c)<6$. The inset shows the invariant mass distribution after the background removal explained in Sec. 3b.

Figure 5

Invariant mass distribution for $K^{+}{K}^{-}$ accumulated without particle identification (left panel) and with one $K$-meson identification (right panel) in the momentum range $4<p_T(\mathrm{GeV}/c)<6$. The inset shows the invariant mass distribution after the background removal explained in Sec. 3b.

Figure 6

Invariant mass distribution for $e^{+}e-$ pairs in the momentum range $0.5<p_T(\mathrm{GeV}/c)<0.75$. The inset shows the invariant mass distribution after the background removal explained in Sec. 3b.

Figure 7

Invariant mass resolution of the PHENIX detector for different decay modes measured in the momentum range $4<p_T(\mathrm{GeV}/c)<6$, except for the $e^{+}{e}^{-}$ mode that is measured in the range $0.5<p_T(\mathrm{GeV}/c)<0.75$. The lines indicate the expected detector mass resolution.

Figure 8

Detector acceptance as a function of transverse momentum for different particles measured with the PHENIX experiment. The scaling factors allow clear comparison of the $p_T$ dependence of the efficiency of rare and common decay channels. The band in the left panel shows the largest relative systematic uncertainty among all curves.

Figure 9

Efficiencies of the ERT $4\times 4$ and ERT $2\times 2$ triggers for single $\gamma$ clusters and electrons as a function of energy (left panel). Trigger efficiencies for different meson decays as determined from Monte Carlo simulation (right panel). The band shows the largest relative systematic uncertainty among all curves. The scaling factors are used for visual clarity.

Figure 10

Invariant mass distribution for $e^{+}{e}^{-}$ pairs, where one track is identified as an electron and the second track is any track (dashed line), the same for pairs which open up in the plane perpendicular to the detector magnetic field (solid line), and among those pairs, the ones in which the second track fails the electron identification cut (filled histogram).

Figure 11

Invariant differential cross section of neutral mesons measured in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ in various decay modes. The lines are fits to the spectra as described further in the text.

Figure 12

Invariant differential cross sections of different particles measured in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ in various decay modes. The spectra published in this paper are shown with closed symbols, and previously published results are shown with open symbols. The curves are the fit results discussed in the text.

Figure 13

The $p_T$ spectra of various hadrons measured by PHENIX fitted to the power law fit (dashed lines) and Tsallis fit (solid lines). See text for more details.

Figure 14

Particle mass dependence of the fit parameters. Power law parameters $\nu$ and $n$ are plotted in the upper panel. Vertical bars denote the combined statistical and systematic uncertainties. The solid lines are linear fits. The dashed lines denote the uncertainty within which the linear fit can be inclined. The lower panel shows the same for the fit parameter $T$. The proton measurement (open circle) is not used in the fits.

Figure 15

Data-to-fit ratio for different particles used in the analysis. The systematic uncertainties are the combined uncertainties of type B and type C, excluding the common 9.7% trigger uncertainty.

Figure 16

Particle spectra plotted vs $m_T$ and arbitrarily normalized at $p_T=10\mathrm{GeV}/c$. Open symbols are mesons and full symbols are baryons measured by PHENIX (circles) and STAR (stars). The lines are the Hagedorn fits by Eq. (9) to mesons (solid) and baryons (dashed) with parameters $n$ and $T$ fixed to average values. Error bars are statistical and point-by-point systematic only.

Figure 17

Comparison of the integrated parameters of the particle spectra. The upper panel shows the ratio of the published result divided by the result of the constrained Tsallis fit for $⟨p_T⟩$ ($⟨p_T^2⟩$ for the $J/\psi$ and the same for ${\psi }^{\prime }$ integrated in the $p_T$ range below $5\mathrm{GeV}/c$). The lower panel shows the ratio for $d\sigma /dy$. The statistical and systematic uncertainties shown at each point are from the published data only. The band around $y=1$ shows the uncertainty of the values extracted from the Tsallis function. The trigger efficiency scale uncertainties of 9.7% for PHENIX and 12% for STAR are not plotted. There are no points outside the plot boundaries. The vertical dashed line separates mesons and baryons.

Figure 18

Ratio of integrated yields predicted by the statistical model [40] to those of the constrained Tsallis fits for various particles. Results for fits to PHENIX data are shown in the upper panel and STAR data in the lower panel. The band reflects the uncertainty of the Tsallis fit results and includes the trigger uncertainty of 9.7% for PHENIX. The lower panel has smaller uncertainties because the model prediction was based on published STAR data given in Table 9. There are no points outside the plot boundaries. The vertical dashed line separates mesons and baryons.