Production of $\varphi$ mesons at midrapidity in $\sqrt{s_{\mathit{NN}}}=200\mathrm{GeV}\mathrm{Au}+\mathrm{Au}$ collisions at relativistic energies

We present the results of $\varphi$ meson production in the $K^{+}{K}^{-}$ decay channel from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200\mathrm{GeV}$ as measured at midrapidity by the PHENIX detector at Brookhaven National Laboratory's Relativistic Heavy Ion Collider. Precision resonance centroid and width values are extracted as a function of collision centrality. No significant variation from the Particle Data Group accepted values is observed, contrary to some model predictions. The $\varphi$ transverse mass spectra are fitted with a linear exponential function for which the derived inverse slope parameter is seen to be constant as a function of centrality. However, when these data are fitted by a hydrodynamic model the result is that the centrality-dependent freeze-out temperature and the expansion velocity values are consistent with the values previously derived from fitting identified charged hadron data. As a function of transverse momentum the collisions scaled peripheral-to-central yield ratio $R_{\mathrm{CP}}$ for the $\varphi$ is comparable to that of pions rather than that of protons. This result lends support to theoretical models that distinguish between baryons and mesons instead of particle mass for explaining the anomalous (anti) proton yield.

Figure 1

(Color online) Beam's-eye view of the PHENIX central arm detector subsystems.

Figure 2

(Color online) Mass-squared distribution of all accepted tracks passing through the TOF for six selected momentum bins. The identified kaons within $2\sigma$ mass-squared boundaries at the different momentum bins are shown by the shaded region on each plot.

Figure 3

(Color online) Mass-squared distribution of all selected tracks passing through the PbSc for four momentum bins. The identified kaons within $2\sigma$ mass-squared boundaries at the different momentum bins are shown by the shaded region on each plot.

Figure 4

(Color online) $K^{+}{K}^{+}$ [(a) and (a${}^{\text{'}}$)] and $K^{-}{K}^{-}$ [(b) and (b${}^{\text{'}}$)] invariant mass spectra and ratio of real to mixed event spectra, respectively, for the TOF-PbSc combination.

Figure 5

(Color online) $K^{+}{K}^{-}$ invariant mass spectra for the measured and mixed events (top) in the TOF-PbSc combination, and the subtracted mass spectrum showing the $\varphi$ meson peak clearly above the background (bottom).

Figure 6

Detector acceptance efficiency vs transverse mass of the simulated $K^{+}{K}^{-}$ pairs for the TOF-TOF, TOF-PbSc, and PbSc-PbSc combinations. The statistical errors are smaller than the size of the data symbols.

Figure 7

Multiplicity-(occupancy-)dependent efficiency correction for detecting the $\varphi$ meson in the PHENIX detector as a function of the collision centrality. The most central collisions are to the right; the most peripheral collisions are to the left. The statistical errors are less than the size of the data points.

Figure 8

(Color online) Minimum-bias $\varphi \to K^{+}{K}^{-}$ invariant mass spectrum using the kaons identified in the PHENIX detector. The top panel shows the same event (circles) and combinatorial background $K^{+}{K}^{-}$ mass distributions. The bottom panel shows the subtracted mass spectrum fitted with a relativistic Breit-Wigner function convolved with a Gaussian resolution function.

Figure 9

(Color online) Centrality dependence of the $\varphi$ mass centroid (left panel) and $\varphi$ intrinsic width (right panel), where the $N_{\mathrm{part}}$ to Centrality correspondence is given in Table 1. For the mass centroid plot, the 1σ systematic error limits on the data points are shown by the two continuous bands. The dotted line shows the PDG centroid value (1.019456 GeV/$c^2$). The solid line indicates the centroid value obtained from a one-parameter-fit assumption. For the width plot the systematic errors on the RBW widths are indicated as bands on each data point. Similarly, the dotted line shows the PDG width value (4.26 MeV/$c^2$), and the solid line shows a one-parameter-fit result for the measured data points.

Figure 10

Minimum-bias $m_T$ spectra of the measured $\varphi$ mesons for three different PHENIX subsystem combinations, with scale factors as indicated. The combined spectrum is fitted with an exponential function in $m_T$, Eq. (3). The lines drawn through the individual spectra (TOF-TOF, TOF-PbSc, and PbSc-PbSc) represent the same fit parameters as in the minimum-bias case. Statistical error bars are shown.

Figure 11

$m_T$ spectra of $\varphi$ mesons for 0–10%, 10–40%, 40–92%, and minimum-bias (0–92%) centrality classes, with scale factors as indicated. Each spectrum is fitted with an exponential function in $m_T$, Eq. (3), with the fit parameters listed in Table 5. Statistical error bars are shown.

Figure 12

(Color online) Centrality dependence of $\varphi$ yield at midrapidity. The value of $\mathit{dN}/\mathrm{dy}$ increases steadily with the number of participants $N_{\mathrm{part}}$ (left) whereas the $\mathit{dN}/\mathrm{dy}$ per participant pairs increases slightly from peripheral to midcentral events and saturates after that (right). The error bars indicate the statistical errors. The shaded boxes on each data point are the systematic errors.

Figure 13

(Color online) Centrality dependence of the inverse slope T.

Figure 14

(Color online) Centrality dependence of particle ratios for (a) $K^{+}/{\pi }^{+}$, (b) $K^{-}/{\pi }^{-}$, (c) $\varphi /[0.5({\pi }^{+}+{\pi }^{-})]$ (scaled by a factor of 5), and (d) $\varphi /[0.5(K^{+}+K^{-})]$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=$ 200 GeV. The data points have been placed in the center of each centrality bin. An increase in $\varphi$ production, similar to kaons, would shift the lowest bin slightly to the right by about 20% to an N${}_{\mathrm{part}}$ of about 40, in (c).

Figure 15

(Color online) Centrality dependence of $\varphi$ yields at different collision energies. STAR data are from [43], NA49 data are from [39], and E917 are from [38].

Figure 16

(Color online) $\varphi /\pi$ (top) and $\varphi /K^{-}$ (bottom) ratios as a function of collision energy. The data symbols have the same meanings in both the top and the bottom parts of the figure.

Figure 17

Mass and centrality dependence of inverse slope parameters T in $m_T$ spectra for positive (left) and negative (right) particles in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=$ 200 GeV. The fit ranges are 0.2–1.0 GeV/$c^2$ for pions and 0.1–1.0 GeV/$c^2$ for kaons, protons, and antiprotons in $m_T-m_0$. Figure taken from Ref. [50].

Figure 18

(Color online) Contour plots for the hydrodynamical fit to the 200-GeV single-particle transverse momentum spectra for the ${\pi }^{\pm },K^{\pm },p,\mathrm{\hspace{1em}\hspace{1em}}\text{and}\mathrm{\hspace{1em}\hspace{1em}}\overline{p}$ in the 0–10% centrality bin. The contour lines are in 1σ steps. The upper plot is from a simultaneous fit with the best value shown as the dot. The lower plot is from independent fits for the six-particle spectra.

Figure 19

(Color online) Transverse momentum data and best-fit hydrodynamical results for the 0–10% centrality bin for the 200-GeV ${\pi }^{\pm },K^{\pm },p,\mathrm{\hspace{1em}\hspace{1em}}\text{and}\mathrm{\hspace{1em}\hspace{1em}}\overline{p}$, along with the prediction for the $\varphi$ transverse momentum spectrum. The transverse momentum ranges for the fit are indicated by the solid lines; the dashed lines indicate the extrapolated predictions for each particle species.

Figure 20

(Color online) Transverse momentum data and best-fit hydrodynamical results for the 10–40% centrality bin for the 200-GeV ${\pi }^{\pm },K^{\pm }$, and $p,\overline{p}$, along with the prediction for the $\varphi$ transverse momentum spectrum.

Figure 21

(Color online) Transverse momentum data and best-fit hydrodynamical results for the 40–92% centrality bin for the 200-GeV ${\pi }^{\pm },K^{\pm }$, and $p,\overline{p}$, along with the prediction for the $\varphi$ transverse momentum spectrum.

Figure 22

(Color online) $p_T$ spectra of protons and $\varphi$ mesons at different centralities scaled down by their respective number of $N_{\mathrm{coll}}.$

Figure 23

(Color online) $N_{\mathrm{coll}}$ scaled central to peripheral ratio $R_{\mathrm{CP}}$ for $(p+\overline{p})$/2, ${\pi }^0$, and ϕ. The proton and pion results are published [30]. The vertical dotted bar on the right represents the error on $N_{\mathrm{coll}}^{0-10\%}/N_{\mathrm{coll}}^{40-92\%}$. The shaded solid bar around $R_{\mathrm{CP}}\hspace{1em}=\hspace{1em}1$ represents 12% systematic error, which can move the proton and/or $\varphi$ points with respect to one another. The dotted horizontal line at $R_{\mathrm{CP}}=$ 0.62 is a straight-line fit to the $\varphi$ data.