Transverse-energy distributions at midrapidity in $p+p$, $d+\mathrm{Au}$, and $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{\text{NN}}}}=62.4$–200 GeV and implications for particle-production models

Measurements of the midrapidity transverse-energy distribution, $d{E}_T/d\eta$, are presented for $p+p$, $d+\mathrm{Au}$, and $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV and additionally for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=62.4$ and 130 GeV. The $d{E}_T/d\eta$ distributions are first compared with the number of nucleon participants $N_{\mathrm{part}}$, number of binary collisions $N_{\mathrm{coll}}$, and number of constituent-quark participants $N_{qp}$ calculated from a Glauber model based on the nuclear geometry. For $\mathrm{Au}+\mathrm{Au}$, $\langle d{E}_T/d\eta \rangle /N_{\mathrm{part}}$ increases with $N_{\mathrm{part}}$, while $\langle d{E}_T/d\eta \rangle /N_{qp}$ is approximately constant for all three energies. This indicates that the two-component ansatz, $d{E}_T/d\eta \propto (1-x)N_{\mathrm{part}}/2+x{N}_{\mathrm{coll}}$, which was used to represent $E_T$ distributions, is simply a proxy for $N_{qp}$, and that the $N_{\mathrm{coll}}$ term does not represent a hard-scattering component in $E_T$ distributions. The $d{E}_T/d\eta$ distributions of $\mathrm{Au}+\mathrm{Au}$ and $d+\mathrm{Au}$ are then calculated from the measured $p+p$ $E_T$ distribution using two models that both reproduce the $\mathrm{Au}+\mathrm{Au}$ data. However, while the number-of-constituent-quark-participant model agrees well with the $d+\mathrm{Au}$ data, the additive-quark model does not.

Figure 1

Schematic diagram showing the locations of the PHENIX electromagnetic calorimeter sectors in the central arm spectrometer. The sectors labeled W1, W2, W3, E2, and E3 were used in this analysis

Figure 2

$E_T{}_{\mathrm{EMC}}$ distributions for $\sqrt{s_{\mathit{NN}}}=62.4$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions. Shown are the MB distribution along with the distributions in 5% wide centrality bins selected using the BBCs. All the plots are normalized so that the integral of the MB distribution is unity.

Figure 3

Corrected $E_T=d{E}_T{/d\eta |}_{\eta =0}$ distributions at $\sqrt{s_{\mathit{NN}}}=200$ GeV for five sectors of PbSc (a) $\mathrm{Au}+\mathrm{Au}$; (b) $p+p$, $d+\mathrm{Au}$. The correction factors for each data set are listed in Table 2. All the plots are normalized so that the integral of each distribution is unity.

Figure 4

(a) The number of quark participants as a function of the number of nucleon participants. The error bars represent the systematic uncertainty estimate on the MC-Glauber calculation. The dashed line is a linear fit to the 200 GeV $\mathrm{Au}+\mathrm{Au}$ points with $N_{\mathrm{part}}>100$ to illustrate the nonlinearity of the correlation at low values of $N_{\mathrm{part}}$. (b) The ratio of the number of quark participants to the number of nucleon participants as a function of the number of nucleon participants. The error bands represent the systematic uncertainty estimate on the MC-Glauber calculation.

Figure 5

$d{E}_T/d\eta$ normalized by the number of participant pairs as a function of the number of participants for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}$ = 200, 130, and 62.4 GeV. The Type A uncertainties are represented by error bars about each point. The Type B uncertainties are represented by the lines bounding each point. The Type C uncertainties are represented by the error bands to the right of the most central data point.

Figure 6

$d{E}_T/d\eta$ normalized by the number of participant quark pairs as a function of the number of participants for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}$ = 200, 130, and 62.4 GeV. The Type A uncertainties are represented by error bars about each point. The Type B uncertainties are represented by the lines bounding each point. The Type C uncertainties are represented by the error bands to the right of the most central data point.

Figure 7

$d{E}_T/d\eta$ as a function of the number of quark participants for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}$ = 200, 130, and 62.4 GeV. The Type A uncertainties are represented by error bars about each point. The Type B uncertainties are represented by error bands about each point shown. The Type A and Type B uncertainties are typically less than the size of the data point. The Type C uncertainties are represented by the error bands to the right of the most central data point. The lines are straight line fits to the data.

Figure 8

Fits of the $p+p$ data to a single $\Gamma$ distribution for the ranges $E_T<13.3$ and $E_T<26.6$ GeV.

Figure 9

Distribution of the number of quark participants in $\mathrm{Au}+\mathrm{Au}$ at $\sqrt{s_{\mathit{NN}}}=200$ GeV.

Figure 10

(a) Deconvolution fit to the $p+p$ $E_T$ distribution for $E_T<13.3$ GeV at $\sqrt{s_{\mathit{NN}}}=200$ GeV with the corrected weights $w_i^{\prime \mathrm{AQM}}$ calculated in the additive quark model (AQM) using the symmetric color-string efficiency, ${\epsilon }_{\mathrm{AQM}}=1-p_{0_{\mathrm{AQM}}}=0.538$. Lines represent the properly weighted individual $E_T$ distributions for 1, 2, 3 color strings plus the sum. On the $y$-axis intercept, the top line is the sum and the lower curves in descending order are the $E_T$ distributions of 1,2,3 color strings. (b) Deconvolution fit to the same $p+p$ $E_T$ distribution for $E_T<13.3$ GeV with the corrected weights $w_i^{\prime \mathrm{NQP}}$ with ${\epsilon }_{\mathrm{NQP}}=1-p_{0_{\mathrm{NQP}}}=0.659$ calculated in the NQP model. Lines represent the properly weighted individual $E_T$ distributions for the underlying 2, 3, 4, 5, 6 constituent-quark participants plus the sum.

Figure 11

$E_T$ distributions at $\sqrt{s_{\mathit{NN}}}=200$ GeV calculated in the number of constituent-quark participants or NQP model, with ${\epsilon }_{\mathrm{NQP}}=1-p_{0_{\mathrm{NQP}}}=0.659$ for $\mathrm{Au}+\mathrm{Au}$ together with the AQM calculations with efficiencies indicated.

Figure 12

$d+\mathrm{Au}$ measurements compared to the AQM and NQP model calculations.

Figure 13

$E_T$ distributions at $\sqrt{s_{\mathit{NN}}}=200$ GeV in $d+\mathrm{Au}$ calculated in the quark participant (NQP) model with ${\epsilon }_{\mathrm{NQP}}=1-p_{0_{\mathrm{NQP}}}=0.659$ together with the individual visible convolutions for NQP, i.e., 2,3,...33, out of a maximum of 50 NQP considered.

Figure 14

Systematic checks of $E_T\equiv d{E}_T{/d\eta |}_{y=0}$ calculations using $p+p$ fits with $E_T<26.6$ GeV (a) $d+\mathrm{Au}$ data compared to standard calculation in the NQP model with ${\epsilon }_{\mathrm{NQP}}=1-p_{0_{\mathrm{NQP}}}=0.659$, for $1-p_0=0.647$ in a $p+p$ collision from fit with $E_T<13.3$ GeV compared to ${\epsilon }_{\mathrm{NQP}}=1-p_{0_{\mathrm{NQP}}}=0.670$ for $1-p_0=0.660$ when the fit to the $p+p$ data is extended to $E_T<26.6$ GeV. (b) $\mathrm{Au}+\mathrm{Au}$ calculation for the same conditions as $d+\mathrm{Au}$ in (a).

Figure 15

Measured $E_T$ distribution in $\mathrm{Au}+\mathrm{Au}$ at $\sqrt{s_{\mathit{NN}}}=200$ GeV on the same $E_T$ scale as Fig. 13 compared to the calculation in the quark participant (NQP) model with ${\epsilon }_{\mathrm{NQP}}=1-p_{0_{\mathrm{NQP}}}=0.659$ together with the individual visible convolutions for NQP in this $E_T$ range, i.e., 2,3, ...114, out of 584 convolutions with visible contribution to the full distribution, out of a maximum of 1020 NQP considered.

Figure 16

$E_T\equiv d{E}_T{/d\eta |}_{y=0}$ distributions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. (a) $\mathrm{Au}+\mathrm{Au}$ compared to the NQP calculations using the central $1-p_0=0.647$ and $\pm 1\sigma$ variations of $1-p_0=0.582,0.712$ for the probability of getting zero $E_T$ on a $p+p$ collision with resulting ${\varepsilon }_{\mathrm{NQP}}=0.659,0.603,0.716$, respectively. (b) $d+\mathrm{Au}$ calculation for the same conditions as in (a).

Figure 17

$\mathrm{Au}+\mathrm{Au}$ measurement of $d{E}_T/d\eta$ compared to the $N_{\mathrm{part}}$-WNM (dot-dash) and $N_{\mathrm{coll}}$ (dashes) model calculations.

Figure 18

$\mathrm{Au}+\mathrm{Au}$ measurement of $d{E}_T/d\eta$, with 10%–15% centrality region indicated, compared to the calculation of the distribution given by Eq. (21) for $N_{\mathrm{part}}$ = 254 and $N_{\mathrm{coll}}=672$ corresponding to 10%–15% centrality.

Figure 19

$\mathrm{Au}+\mathrm{Au}$ measurement of $d{E}_T/d\eta$, with 10%–15% centrality region indicated, compared to the calculation of the distribution given by Eq. (21) for $N_{\mathrm{part}}$ = 254 and $N_{\mathrm{coll}}=672$ corresponding to 10%–15% centrality, where the distributions have been scaled in $E_T$ by 0.92 and 0.08, respectively.