Transverse energy production and charged-particle multiplicity at midrapidity in various systems from $\sqrt{s_{NN}}=7.7$ to 200 GeV

Measurements of midrapidity charged-particle multiplicity distributions, $d{N}_{\mathrm{ch}}/d\eta$, and midrapidity transverse-energy distributions, $d{E}_T/d\eta$, are presented for a variety of collision systems and energies. Included are distributions for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$, 130, 62.4, 39, 27, 19.6, 14.5, and 7.7 GeV, $\mathrm{Cu}+\mathrm{Cu}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ and 62.4 GeV, $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV, $\mathrm{U}+\mathrm{U}$ collisions at $\sqrt{s_{{}_{NN}}}=193$ GeV, $d+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV, ${}^3\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV, and $p+p$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV. Centrality-dependent distributions at midrapidity are presented in terms of the number of nucleon participants, $N_{\mathrm{part}}$, and the number of constituent quark participants, $N_{\mathrm{qp}}$. For all $A+A$ collisions down to $\sqrt{s_{{}_{NN}}}=7.7$ GeV, it is observed that the midrapidity data are better described by scaling with $N_{\mathrm{qp}}$ than scaling with $N_{\mathrm{part}}$. Also presented are estimates of the Bjorken energy density, ${\varepsilon }_{\mathrm{BJ}}$, and the ratio of $d{E}_T/d\eta$ to $d{N}_{\mathrm{ch}}/d\eta$, the latter of which is seen to be constant as a function of centrality for all systems.

Figure 1

Raw $E_{T\mathrm{EMC}}$ (a) and $N_{\mathrm{ch}}$ (b) distributions for $\sqrt{s_{NN}}=14.5$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions. Shown are the minimum-bias distribution along with the distributions in 5% wide centrality bins. All the plots are normalized so that the integral of the minimum-bias distribution is unity.

Figure 2

$(d{E}_T/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (a) and $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (b) at midrapidity as a function of $N_{\mathrm{part}}$ for $\mathrm{Au}+\mathrm{Au}$ collisions 200, 130, 62.4, 39, 27, 19.6, 14.5, and 7.7 GeV. The lines bounding the points represent the trigger efficiency uncertainty within which the points can be tilted. The error bars represent the remaining total statistical and systematic uncertainty.

Figure 3

The ratio of $\sqrt{s_{{}_{NN}}}=200$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions to $\sqrt{s_{{}_{NN}}}=7.7$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions for $(d{E}_T/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (a) and for $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (b). The lines bounding the points represent the trigger efficiency uncertainty within which the points can be tilted. The error bars represent the total statistical and systematic uncertainties.

Figure 4

The excitation function of $(d{E}_T/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (a) and $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (b) for central collisions at midrapidity as a function of $\sqrt{s_{{}_{NN}}}$. The error bars represent the total statistical and systematic uncertainties. For $(d{E}_T/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (a), data are shown from FOPI [28], E802 [29], NA49 [30, 31], STAR [18], and CMS [31]. For $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (b), data are shown from FOPI [28], E802 [29, 32, 33], NA49 [30], STAR [18, 34], PHOBOS [17], ALICE [35], and ATLAS [36].

Figure 5

The $E_T/N_{\mathrm{ch}}$ ratio as a function of $N_{\mathrm{part}}$ for $\mathrm{Au}+\mathrm{Au}$ collisions at varying values of $\sqrt{s_{{}_{NN}}}$. The lines bounding the points represent the trigger efficiency uncertainty within which the points can be tilted. The error bars represent the total statistical and systematic uncertainties.

Figure 6

The $E_T/N_{\mathrm{ch}}$ ratio as a function of $\sqrt{s_{{}_{NN}}}$ for central $\mathrm{Au}+\mathrm{Au}$ collisions and $\mathrm{Pb}+\mathrm{Pb}$ collisions at midrapidity. The error bars represent the total statistical and systematic uncertainties. The Large Hadron Collider, LHC, data point has been obtained by taking the ratio of the CMS $d{E}_T/d\eta$ data [31] with the average of the ALICE [35] and the ATLAS [36] data. For $(d{E}_T/d\eta )/\left(0.5N_{\mathrm{part}}\right)$, data are taken from FOPI [28], E802 [29], NA49 [30, 31], STAR [18], and CMS [31]. For $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{part}}\right)$, data are taken from FOPI [28], E802 [29, 32, 33], NA49 [30], STAR [18, 34], PHOBOS [17], ALICE [35], and ATLAS [36].

Figure 7

The Bjorken energy density, ${\varepsilon }_{\mathrm{BJ}}$, multiplied by $\tau$ as a function of $N_{\mathrm{part}}$ for $\mathrm{Au}+\mathrm{Au}$ collisions at varying values of $\sqrt{s_{{}_{NN}}}$. The error bars represent the total statistical and systematic uncertainties.

Figure 8

The Bjorken energy density, ${\varepsilon }_{\mathrm{BJ}}$, multiplied by $\tau$ as a function of $\sqrt{s_{{}_{NN}}}$ for central $\mathrm{Au}+\mathrm{Au}$ (PHENIX) and $\mathrm{Pb}+\mathrm{Pb}$ (CMS) [31] collisions at midrapidity. The error bars represent the total statistical and systematic uncertainties.

Figure 9

$(d{E}_T/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (a) and $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (b) at midrapidity as a function of $N_{\mathrm{part}}$ for $\mathrm{Cu}+\mathrm{Cu}$ and $\mathrm{Cu}+\mathrm{Au}$ collisions. Also shown are results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV for comparison. The lines bounding the points represent the trigger efficiency uncertainty within which the points can be tilted. The error bars represent the remaining total statistical and systematic uncertainty.

Figure 10

The $E_T/N_{\mathrm{ch}}$ ratio as a function of $N_{\mathrm{part}}$ for $\mathrm{Cu}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV (a), $\mathrm{Cu}+\mathrm{Cu}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV (b), and $\mathrm{Cu}+\mathrm{Cu}$ collisions at $\sqrt{s_{{}_{NN}}}=62.4$ GeV (c). The lines bounding the points represent the trigger efficiency uncertainty within which the points can be tilted. The error bars represent the total statistical and systematic uncertainties.

Figure 11

The Bjorken energy density, ${\varepsilon }_{\mathrm{BJ}}$, multiplied by $\tau$ as a function of $N_{\mathrm{part}}$ for $\mathrm{Cu}+\mathrm{Cu}, \mathrm{Cu}+\mathrm{Au}$, and $\mathrm{Au}+\mathrm{Au}$ collisions. The error bars represent the total statistical and systematic uncertainties.

Figure 12

$(d{E}_T/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (a) and $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (b) at midrapidity as a function of $N_{\mathrm{part}}$ for $\mathrm{U}+\mathrm{U}$ collisions. Also shown are results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV for comparison. The lines bounding the points represent the trigger efficiency uncertainty within which the points can be tilted. The error bars represent the remaining total statistical and systematic uncertainty.

Figure 13

$(d{E}_T/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (a) and $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{part}}\right)$ (b) at midrapidity as a function of $N_{\mathrm{part}}$ for $d+\text{Cu}$ and ${}^3\mathrm{He}+\mathrm{Au}$ collisions. Also shown are results from the most peripheral $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV for comparison. The lines bounding the points represent the trigger efficiency uncertainty within which the points can be tilted. The error bars represent the remaining total statistical and systematic uncertainty.

Figure 14

The $E_T/N_{\mathrm{ch}}$ ratio as a function of $N_{\mathrm{part}}$ for 200-GeV $d+\mathrm{Au}$ (a) and 200-GeV ${}^3\mathrm{He}+\mathrm{Au}$ (b) collisions. The error bars represent the total statistical and systematic uncertainties.

Figure 15

$d{E}_T/d\eta$ (a) and $d{N}_{\mathrm{ch}}/d\eta$ (b) at midrapidity as a function of $N_{\mathrm{qp}}$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$, 130, 62.4, 39, 27, 19.6, 14.5, and 7.7 GeV. The error bars represent the total statistical and systematic uncertainties.

Figure 16

$(d{E}_T/d\eta )/\left(0.5N_{\mathrm{qp}}\right)$ (a) and $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{qp}}\right)$ (b) at midrapidity as a function of $N_{\mathrm{qp}}$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$, 130, 62.4, 39, 27, 19.6, 14.5, and 7.7 GeV. The lines bounding the points represent the trigger efficiency uncertainty within which the points can be tilted. The error bars represent the remaining total statistical and systematic uncertainty.

Figure 17

The slopes of the fit to $d{E}_T/d\eta , a_E$ (a), and $d{N}_{\mathrm{ch}}/d\eta , a_N$ (b), as a function of $N_{\mathrm{qp}}$ plotted as a function of $\sqrt{s_{{}_{NN}}}$ for $\mathrm{Au}+\mathrm{Au}$ collisions. The error bars are the uncertainties from the fit. The red line is a second-order polynomial fit to the data.

Figure 18

$d{E}_T/d\eta$ (a) and $d{N}_{\mathrm{ch}}/d\eta$ (b) at midrapidity as a function of $N_{\mathrm{qp}}$ for $\mathrm{Cu}+\mathrm{Cu}$ and $\mathrm{Cu}+\mathrm{Au}$ collisions. The error bars represent the total statistical and systematic uncertainties.

Figure 19

$(d{E}_T/d\eta )/\left(0.5N_{\mathrm{qp}}\right)$ (a) and $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{qp}}\right)$ (b) at midrapidity as a function of $N_{\mathrm{qp}}$ for $\mathrm{Cu}+\mathrm{Cu}$ and $\mathrm{Cu}+\mathrm{Au}$ collisions. The lines bounding the points represent the trigger efficiency uncertainty within which the points can be tilted. The error bars represent the remaining total statistical and systematic uncertainty.

Figure 20

$(d{E}_T/d\eta )/\left(0.5N_{\mathrm{qp}}\right)$ (a) and $(d{N}_{\mathrm{ch}}/d\eta )/\left(0.5N_{\mathrm{qp}}\right)$ (b) at midrapidity as a function of $N_{\mathrm{qp}}$ for $d+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ collisions. Shown for comparison are data from the most peripheral $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV. The lines bounding the points represent the trigger efficiency uncertainty within which the points can be tilted. The error bars represent the remaining total statistical and systematic uncertainty.