Systematic measurements of identified particle spectra in $\mathit{pp}$, $d+\mathrm{Au}$, and $\mathrm{Au}+\mathrm{Au}$ collisions at the STAR detector

Identified charged-particle spectra of ${\pi }^{\pm }$, $K^{\pm }$, $p$, and $\overline{p}$ at midrapidity ($\left|y\right|<0.1$) measured by the $\mathit{dE}/\mathit{dx}$ method in the STAR (solenoidal tracker at the BNL Relativistic Heavy Ion Collider) time projection chamber are reported for $\mathit{pp}$ and $d+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and for $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4, 130, and 200 GeV. Average transverse momenta, total particle production, particle yield ratios, strangeness, and baryon production rates are investigated as a function of the collision system and centrality. The transverse momentum spectra are found to be flatter for heavy particles than for light particles in all collision systems; the effect is more prominent for more central collisions. The extracted average transverse momentum of each particle species follows a trend determined by the total charged-particle multiplicity density. The Bjorken energy density estimate is at least several GeV/${\mathrm{fm}}^3$ for a formation time less than 1 fm/$c$. A significantly larger net-baryon density and a stronger increase of the net-baryon density with centrality are found in $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4 GeV than at the two higher energies. Antibaryon production relative to total particle multiplicity is found to be constant over centrality, but increases with the collision energy. Strangeness production relative to total particle multiplicity is similar at the three measured RHIC energies. Relative strangeness production increases quickly with centrality in peripheral $\mathrm{Au}+\mathrm{Au}$ collisions, to a value about 50% above the $\mathit{pp}$ value, and remains rather constant in more central collisions. Bulk freeze-out properties are extracted from thermal equilibrium model and hydrodynamics-motivated blast-wave model fits to the data. Resonance decays are found to have little effect on the extracted kinetic freeze-out parameters because of the transverse momentum range of our measurements. The extracted chemical freeze-out temperature is constant, independent of collision system or centrality; its value is close to the predicted phase-transition temperature, suggesting that chemical freeze-out happens in the vicinity of hadronization and the chemical freeze-out temperature is universal despite the vastly different initial conditions in the collision systems. The extracted kinetic freeze-out temperature, while similar to the chemical freeze-out temperature in $\mathit{pp}$, $d+\mathrm{Au}$, and peripheral $\mathrm{Au}+\mathrm{Au}$ collisions, drops significantly with centrality in $\mathrm{Au}+\mathrm{Au}$ collisions, whereas the extracted transverse radial flow velocity increases rapidly with centrality. There appears to be a prolonged period of particle elastic scatterings from chemical to kinetic freeze-out in central $\mathrm{Au}+\mathrm{Au}$ collisions. The bulk properties extracted at chemical and kinetic freeze-out are observed to evolve smoothly over the measured energy range, collision systems, and collision centralities.

Figure 1

Uncorrected charged-particle multiplicity distribution measured in the TPC in $\left|\eta \right|<0.5$ for $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4 and 200 GeV. The shaded regions indicate the centrality bins used in the analysis. The 200 GeV data are scaled by a factor of 5 for clarity.

Figure 2

(a) Uncorrected charged-particle multiplicity distribution measured in the E-FTPC (Au-direction) within $-3.8<\eta <-2.8$ in $d+\mathrm{Au}$ collisions at 200 GeV. The shaded regions indicate the centrality bins used in the analysis. (b) The TPC midrapidity multiplicity distributions ($\left|\eta \right|<0.5$) for the corresponding E-FTPC selected centrality bins.

Figure 3

Uncorrected charged-particle multiplicity distribution measured in the TPC within $\left|\eta \right|<0.5$ in $\mathit{pp}$ collisions at 200 GeV.

Figure 4

(a) Ratio of the transverse overlap area $S_{\perp }$ to $(N_{\mathrm{part}}/2){}^{2/3}$ vs $(N_{\mathrm{part}}/2){}^{2/3}$. (b) Ratio of the charged-pion multiplicity to the transverse overlap area $\frac{{\mathit{dN}}_{\pi }/\mathit{dy}}{S_{\perp }}$ vs $N_{\mathrm{coll}}/N_{\mathrm{part}}$. Errors shown are total errors, dominated by systematic uncertainties. The systematic uncertainties are correlated between $N_{\mathrm{part}}$, $N_{\mathrm{coll}}$, and $S_{\perp }$, and are largely canceled in the plotted ratio quantities.

Figure 5

(a) Truncated $\langle \mathit{dE}/\mathit{dx}\rangle$ of specific ionization energy loss of ${\pi }^{-}$, $e^{-}$, $K^{-}$, and $\overline{p}$ as a function of $p_{\perp }$ for particles in $\left|\eta \right|<0.1$ measured in 200 GeV minimum-bias $\mathit{pp}$ collisions by the STAR-TPC. The Gaussian centroids for ${\pi }^{-}$, $e^{-}$, $K^{-}$ and $\overline{p}$ fit to the kaon $z_K$ distributions are shown with circles. (b) $z_K$ variable for kaon vs $p_{\perp }$ in 200 GeV minimum-bias $\mathit{pp}$ collisions. Particles are restricted in $\left|y_K\right|<0.1$ where the kaon mass is used in the rapidity calculation. In this narrow rapidity (or pseudorapidity) slice, $p_{\perp }$ is approximately equal to $p_{\mathrm{mag}}$.

Figure 6

Distributions of $z_{\pi }$ for ${\pi }^{-}$ (upper panels) and $z_K$ for $K^{-}$ (lower panels) in 200 GeV minimum-bias $\mathit{pp}$ collisions. Four $p_{\perp }$ bins are shown. Errors shown are statistical only. The curves represent the Gaussian fits to the $z_{\pi }$ and $z_K$ distributions, with individual particle peaks plotted separately.

Figure 7

Hit resolution and mean hit residual as a function of the track crossing angle at the hit position, the track dip angle, and the hit $z$ coordinate. The data are an enriched $K^{+}$ sample (via $\mathit{dE}/\mathit{dx}$ cut) within $\left|y\right|<1$ and $0.4<p_{\perp }<0.5\hspace{0.5em}\mathrm{GeV}/c$ in 62.4 GeV $\mathrm{Au}+\mathrm{Au}$ collisions. Errors shown are statistical only.

Figure 8

Comparison of $d_{\mathrm{ca}}$ distributions between $K^{+}$ candidates from real data and $K^{+}$ from MC embedding. Two $p_{\perp }$ bins are shown for 200 GeV $\mathit{pp}$ collisions and for 62.4 GeV 5% central $\mathrm{Au}+\mathrm{Au}$ collisions, respectively. Kaon candidates are selected from data by a $\mathit{dE}/\mathit{dx}$ cut of $\pm 0.5\sigma$ from the Bethe-Bloch expected values. Errors shown are statistical only. The distributions have been normalized to unit area to only compare the shapes.

Figure 9

Comparison of distributions of the number of fit points between ${\pi }^{-}$ candidates from real data and ${\pi }^{-}$ from MC embedding. Two $p_{\perp }$ bins are shown for 200 GeV $\mathit{pp}$ collisions and for 62.4 GeV 5% central $\mathrm{Au}+\mathrm{Au}$ collisions. Pion candidates are selected by a $\mathit{dE}/\mathit{dx}$ cut of $\left|z_{\pi }\right|<0.3$. Errors shown are statistical only. The distributions have been normalized to unit area to only compare the shapes.

Figure 10

Energy loss effect for (a) ${\pi }^{\pm }$, (b) $K^{\pm }$, and (c) $p$ and $\overline{p}$ at midrapidity ($\left|y\right|<0.1$) as a function of particle momentum magnitude in 200 GeV $\mathit{pp}$ and 62.4 GeV central 0–5% $\mathrm{Au}+\mathrm{Au}$ collisions. Only negative particles are shown; energy loss for particles and antiparticles are the same. Errors shown are statistical only. The pion energy loss is already corrected by the track reconstruction algorithm.

Figure 11

Vertex-finding efficiency ${\epsilon }_{\mathrm{vtx}}$ and fake vertex rate ${\delta }_{\mathrm{fake}}$ as a function of the number of (a) good global tracks and (b) good primary tracks. Errors shown or smaller than the point size are statistical only.

Figure 12

$p_{\perp }$ dependent correction to particle spectra due to fake vertex events, ${\epsilon }_{\mathrm{fake}}(p_{\perp })$, in 200 GeV minimum-bias $\mathit{pp}$ and $d+\mathrm{Au}$ collisions. Errors shown are statistical only.

Figure 13

Efficiency (product of tracking efficiency and detector acceptance) of ${\pi }^{-}$, $K^{-}$, and $\overline{p}$ in (a) $\mathit{pp}$ and (b) $d+\mathrm{Au}$ collisions at 200 GeV as a function of input MC $p_{\perp }$. Errors shown are binomial errors. The curves are parametrizations to the efficiency data and are used for corrections in the analysis.

Figure 14

Efficiency (product of tracking efficiency and detector acceptance) of ${\pi }^{-}$, $K^{-}$, and $\overline{p}$ in (a) 70–80% peripheral $\mathrm{Au}+\mathrm{Au}$ and (b) 0–5% central $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4 GeV as a function of input MC $p_{\perp }$. Errors shown are binomial errors. The curves are parametrizations to the efficiency data and are used for corrections in the analysis.

Figure 15

$d_{\mathrm{ca}}$ distributions of protons and antiprotons for $0.40<p_{\perp }<0.45\hspace{0.5em}\mathrm{GeV}/c$ and $0.70<p_{\perp }<0.75\hspace{0.5em}\mathrm{GeV}/c$ in 200 GeV minimum-bias $d+\mathrm{Au}$ (upper panels) and 62.4 GeV 0–5% central $\mathrm{Au}+\mathrm{Au}$ collisions (lower panels). Errors shown are statistical only. The dashed curve is the fit proton background; the dotted histogram is the $\overline{p}$ distribution scaled up by the fit $p/\overline{p}$ ratio; and the solid histogram is the fit $p$ distribution by Eq. (6). The range $3.2<d_{\mathrm{ca}}<5$ cm is excluded from the fit for the $d+\mathrm{Au}$ data. Note the logarithm scale of the right panels.

Figure 16

Pion background fraction from weak decays ($\Lambda ,K_S^0$) and ${\mu }^{\pm }$ contamination as a function of $p_{\perp }$ in minimum-bias $d+\mathrm{Au}$ collisions at 200 GeV. Errors shown are statistical only.

Figure 17

Midrapidity identified antiproton spectra in (a) 200 GeV minimum-bias $d+\mathrm{Au}$ and (b) 62.4 GeV central $\mathrm{Au}+\mathrm{Au}$ collisions measured by $\mathit{dE}/\mathit{dx}$ together with those by TOF [46, 47]. The $\mathit{dE}/\mathit{dx}$ data are from $\left|y\right|<0.1$ and the TOF data are from $\left|y\right|<0.5$. The curves are various fits to the $\mathit{dE}/\mathit{dx}$ data for extrapolation. The quadratic sum of statistical errors and point-to-point systematic errors are plotted, but are smaller than the point size.

Figure 18

Midrapidity ($\left|y\right|<0.1$) identified particle spectra in $d+\mathrm{Au}$ collisions at 200 GeV. The $p$ and $\overline{p}$ spectra are inclusive, including weak decay products. Spectra are plotted for three centrality bins and for minimum-bias events. Spectra from top to bottom are for 0–20% scaled by 4, 20–40% scaled by 2, minimum bias not scaled, and 40–100% scaled by 1/2. Errors plotted are statistical and point-to-point systematic errors added in quadrature, but are smaller than the point size. The curves are the blast-wave model fits to the minimum-bias data; the normalizations of the curves are fixed by the corresponding negative particle spectra.

Figure 19

Midrapidity ($\left|y\right|<0.1$) identified particle spectra in $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4 GeV. The $p$ and $\overline{p}$ spectra are inclusive, including weak decay products. Spectra are plotted for nine centrality bins, from top to bottom, 0–5%, 5–10%, 10–20%, 20–30%, 30–40%, 40–50%, 50–60%, 60–70%, and 70–80%. Errors plotted are statistical and point-to-point systematic errors added in quadrature, but are smaller than the point size. The curves are the blast-wave model fits to the spectra; the normalizations of the curves in (a) and (b) are fixed by the corresponding negative particle spectra.

Figure 20

Midrapidity ($\left|y\right|<$ 0.1) identified pion spectra in $\mathrm{Au}+\mathrm{Au}$ collisions at 130 GeV. Spectra are plotted for eight centrality bins, from top to bottom, 0–6%, 6–11%, 11–18%, 18–26%, 26–34%, 34–45%, 45–58%, and 58–85%. Errors plotted are statistical and point-to-point systematic errors added in quadrature, but they are smaller than the data point size. The curves are the Bose-Einstein fits to the spectra; the normalizations of the curves are fixed by the corresponding negative particle spectra.

Figure 21

Comparisons of ${\pi }^{-}$, $K^{-}$, and $\overline{p}$ transverse momentum spectra for (a) minimum-bias $\mathit{pp}$ collisions at 200 GeV, (b) minimum-bias $d+\mathrm{Au}$ collisions at 200 GeV, and (c) $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4 GeV. Two centralities are shown: 0–5% central collisions (filled symbols) and 70–80% peripheral collisions (open symbols). Errors are statistical and point-to-point systematic errors added in quadrature.

Figure 22

Average transverse momenta as a function of (a) ${\mathit{dN}}_{\mathrm{ch}}/\mathit{dy}$ and (b) $\sqrt{\frac{{\mathit{dN}}_{\pi }/\mathit{dy}}{S_{\perp }}}$ for $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4, 130, and 200 GeV. The minimum-bias $\mathit{pp}$ data are also shown. The $d+\mathrm{Au}$ data are shown in panel (a). Errors shown are systematic errors and statistical errors added in quadrature.

Figure 23

Pseudorapidity multiplicity density per participant nucleon pair $\frac{{\mathit{dN}}_{\mathrm{ch}}/d\eta }{N_{\mathrm{part}}/2}$ vs the number of participants $N_{\mathrm{part}}$, with $N_{\mathrm{part}}$ calculated from (a) the optical Glauber model and (b) the MC Glauber model. Data are presented for $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4 GeV (black dots) and 200 GeV (red squares). The vertical errors are total uncertainties including uncertainties on $N_{\mathrm{part}}$. The uncertainties on $N_{\mathrm{part}}$ (horizontal error bars) are smaller than the data point size. The solid curves are the K-N fit by Eq. (10) where $x_{\mathrm{hard}}$ is a fit parameter and $n_{\mathit{pp}}$ is fixed from Eq. (11). The dashed curves are the EKRT fit by Eq. (9) where $C$ is a fit parameter.

Figure 24

Estimate of the product of the Bjorken energy density and the formation time (${\epsilon }_{\mathit{Bj}}\times \tau$) as a function of centrality $N_{\mathrm{part}}$. Errors shown are the quadratic sum of statistical and systematic uncertainties.

Figure 25

Antiparticle-to-particle ratios as a function of ${\mathit{dN}}_{\mathrm{ch}}/\mathit{dy}$ for $\mathit{pp}$ and $d+\mathrm{Au}$ collisions at 200 GeV and $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4, 130, and 200 GeV. Errors shown are the quadratic sum of statistical and systematic uncertainties.

Figure 26

Ratio of charged kaons vs that of antiprotons to protons at various energies. Errors shown are the quadratic sum of statistical and systematic uncertainties. The line is a power-law fit to the data except for the AGS data point (the inverse solid triangle) and the two lowest energy SPS data points (solid squares), which have significant baryon absorption effect. The insert is a linear plot.

Figure 27

$p/{\pi }^{+}$ and $\overline{p}/{\pi }^{-}$ ratios as a function of the charged-particle multiplicity in $\mathit{pp}$, $d+\mathrm{Au}$, and $\mathrm{Au}+\mathrm{Au}$ collisions. Errors shown are the quadratic sum of statistical and systematic uncertainties.

Figure 28

Ratio of midrapidity net-protons to half the number of participants vs the number of participants in $\mathit{pp}$ collisions at 200 GeV and in $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4, 130, and 200 GeV. Errors shown are the quadratic sum of statistical and systematic uncertainties.

Figure 29

Ratio of midrapidity inclusive net-protons to half the number of participants in central heavy-ion collisions as a function of the rapidity shift. The AGS data are from Refs. [75, 86], SPS data from Refs. [87, 88, 89], and BRAHMS data from Ref. [90]. The published SPS data have already been corrected for weak decays, the size of which is of the order 20–25% [88], so we have added 25% to the published net-proton yields to obtain the inclusive ones. Errors shown are total statistical and systematic uncertainties. The dashed line is an exponential fit to the data.

Figure 30

(a) $K^{+}/{\pi }^{+}$ and $K^{-}/{\pi }^{-}$ ratios as a function of the collision energy in $\mathit{pp}$ [106, 107, 108, 109] and central heavy-ion collisions. (b) $K^{+}/K^{-}$ ratio as a function of the collision energy in central heavy-ion collisions. The heavy-ion data not covered in this work are taken from Refs. [17, 76, 77, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105]. The error bars on the heavy-ion data are the quadratic sum of statistical and systematic uncertainties and are statistical only on the elementary collision data. The curves going through the heavy-ion $K^{-}/{\pi }^{-}$ and $K^{+}/K^{-}$ data are phenomenological fits. The curves going through the heavy-ion $K^{+}/{\pi }^{+}$ data are the product of the fit curves. See text for details.

Figure 31

$K^{-}/{\pi }^{-}$ ratio as a function of the charged-particle rapidity density in $\mathit{pp}$, $d+\mathrm{Au}$, and $\mathrm{Au}+\mathrm{Au}$ collisions at RHIC. Errors shown are the quadratic sum of statistical and systematic uncertainties.

Figure 32

$K^{-}/{\pi }^{-}$ ratio as a function of the number of participants $N_{\mathrm{part}}$ in heavy-ion collisions at the AGS [76, 97], SPS [77, 100, 101, 102, 103, 104, 105], and RHIC. Errors shown are the quadratic sum of statistical and systematic uncertainties for the RHIC data, and only statistical for the AGS and SPS data.

Figure 33

$K^{-}/{\pi }^{-}$ ratio as a function of $\frac{{\mathit{dN}}_{\pi }/\mathit{dy}}{S_{\perp }}$ in heavy-ion collisions at the AGS [76, 97], SPS [77, 100, 101, 102, 103, 104, 105], and RHIC. Errors shown are the quadratic sum of statistical and systematic uncertainties for the RHIC data, and statistical only for the AGS and SPS data.

Figure 34

(a) Baryon (${\mu }_B$) and strangeness (${\mu }_S$) chemical potentials extracted from chemical equilibrium model fits to $\mathit{pp}$ and $d+\mathrm{Au}$ data at 200 GeV, and $\mathrm{Au}+\mathrm{Au}$ data at 62.4, 130, and 200 GeV. (b) Ratio ${\mu }_S/{\mu }_B$ of the extracted chemical potentials. Errors shown are the total statistical and systematic errors. The 200 GeV $\mathit{pp}$ and $\mathrm{Au}+\mathrm{Au}$ fit results are from Ref. [17].

Figure 35

Strangeness suppression factor extracted from chemical equilibrium model fit to $\mathit{pp}$ and $d+\mathrm{Au}$ data at 200 GeV, and $\mathrm{Au}+\mathrm{Au}$ data at 62.4, 130, and 200 GeV. Errors shown are the total statistical and systematic uncertainties. The 200 GeV $\mathit{pp}$ and $\mathrm{Au}+\mathrm{Au}$ fit results are from Ref. [17].

Figure 36

Chemical and kinetic freeze-out temperatures as a function of the charged-hadron multiplicity. Errors shown are the total statistical and systematic uncertainties. The 200 GeV $\mathit{pp}$ and $\mathrm{Au}+\mathrm{Au}$ data are from Ref. [17].

Figure 37

Average transverse radial flow velocity extracted from blast-wave model fit to $\mathit{pp}$ and $d+\mathrm{Au}$ at 200 GeV, and to $\mathrm{Au}+\mathrm{Au}$ collisions at 62.4, 130, and 200 GeV as a function of the charged-hadron multiplicity. Errors shown are the total statistical and systematic uncertainties. The 200 GeV $\mathit{pp}$ and $\mathrm{Au}+\mathrm{Au}$ data are from Ref. [17].

Figure 38

Baryon chemical potential extracted for central heavy-ion collisions as a function of the collision energy. STAR 62.4 and 130 GeV data are from this work; the 200 GeV data are from Ref. [17]. Other data are from SIS [140, 141], AGS [120, 122, 126, 142], SPS [121, 122, 126, 139, 142], and compilation by Refs. [143, 144]. Errors shown are the total statistical and systematic errors.

Figure 39

Extracted chemical (open symbols) and kinetic (filled symbols) freeze-out temperatures for central heavy-ion collisions as a function of the collision energy. The STAR 62.4 and 130 GeV data are from this work; the STAR 200 GeV data are from Ref. [17]. The other kinetic freeze-out results are from FOPI [145], EOS [146], E866 [147], and NA49 [148] experiments. The other chemical freeze-out data are from SIS [140, 141], AGS [120, 122, 126, 142], and SPS [121, 122, 126, 139, 142] and compilation by Refs. [143, 144]. Errors shown are the total statistical and systematic errors.

Figure 40

Average transverse radial flow velocity extracted from the blast-wave model for central heavy-ion collisions as a function of the collision energy. The STAR 62.4 and 130 GeV data are from this work, and the STAR 200 GeV $\mathit{pp}$ and $\mathrm{Au}+\mathrm{Au}$ data from Ref. [17]. The other data are from FOPI [145], EOS [146], E866 [147], and NA49 [148] experiments. Errors shown are the total statistical and systematic errors.

Figure 41

Phase diagram plot of chemical freeze-out temperature vs baryon chemical potential extracted from chemical equilibrium models. Low energy data are from Refs. [120, 121, 122, 126, 139, 140, 141, 142] and compilations in Refs. [143, 144]. Errors shown are the total statistical and systematic errors.

Figure 42

Differential cross sections obtained from the optical and MC Glauber calculations for $\mathrm{Au}+\mathrm{Au}$ collisions at 200 GeV. Statistical errors are smaller than the point size.

Figure 43

Upper panels: Calculated ${\pi }^{-}$, $K^{-}$, and $\overline{p}$ transverse momentum spectra from the primordial thermal component and major resonance decay contributions for $\mathit{pp}$ collisions at 200 GeV. The kinetic freeze-out parameters fit to data are used for the thermal calculations [17]. Lower panels: Resonance contributions relative to the thermal spectrum. $K^{*-}$ decay (not shown) has the same contribution to $K^{-}$ (and $K^{+}$) spectra as $K^{*0}$ decay. Σ and ${\Sigma }_{1385}$ decays (not shown) contribute to the $\overline{p}$ (and proton) spectra with similar magnitude as Λ decays.

Figure 44

Same as Fig. 43, but for the top 5% central $\mathrm{Au}+\mathrm{Au}$ collisions at 200 GeV [17].

Figure 45

Left-most panel: Fit of the calculated spectra (curves) to the measured ones (data points) in $\mathit{pp}$ collisions at 200 GeV [17]. Four calculated spectra are shown for ${\pi }^{-}$ (upper curves): three include resonances with different ρ contributions and one excludes resonances. Only two calculated curves are shown for $K^{-}$ (middle curves) and $\overline{p}$ (lower curves): one includes resonances with 100% ρ and the other excludes resonances. Other panels: Ratios of data spectrum to calculations. Two calculations are shown for $K^{-}$ and $\overline{p}$, while four calculations are shown for ${\pi }^{-}$. Error bars are the quadratic sum of the statistical and point-to-point systematic errors on the data, and are shown for two sets of the data points for ${\pi }^{-}$ and only one set for $K^{-}$ and $\overline{p}$.

Figure 46

Same as Fig. 45, but for the top 5% central $\mathrm{Au}+\mathrm{Au}$ collisions at 200 GeV [17].