Nonprompt direct-photon production in $\text{Au}+\text{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV

The measurement of the direct-photon spectrum from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV is presented by the PHENIX Collaboration using the external-photon-conversion technique for 0%–93% central collisions in a transverse-momentum ($p_T$) range of 0.8–10 $\text{GeV}/c$. An excess of direct photons, above prompt-photon production from hard-scattering processes, is observed for $p_T<6\text{GeV}/c$. Nonprompt direct photons are measured by subtracting the prompt component, which is estimated as $N_{\mathrm{coll}}$-scaled direct photons from $p+p$ collisions at 200 GeV, from the direct-photon spectrum. Results are obtained for $0.8<p_T<6.0\text{GeV}/c$ and suggest that the spectrum has an increasing inverse slope from $\approx 0.2$ to 0.4 $\text{GeV}/c$ with increasing $p_T$, which indicates a possible sensitivity of the measurement to photons from earlier stages of the evolution of the collision. In addition, like the direct-photon production, the $p_T$-integrated nonprompt direct-photon yields also follow a power-law scaling behavior as a function of collision-system size. The exponent, $\alpha$, for the nonprompt component is found to be consistent with 1.1 with no apparent $p_T$ dependence.

Figure 1

(a) The beam view of the PHENIX central-arm spectrometer for the year 2014. (b) A magnified view of the silicon-vertex detector. The solid curves correspond to the electron and positron tracks from photon conversion.

Figure 2

Artificial $e^{+}{e}^{-}$ pair mass for external photon conversions. Each curve corresponds to a different radius region, which roughly maps to the locations of beam pipe, layers 1 (B0) through 4 (B3) of the VTX, and the VTX (CF) carbon-fiber enclosure.

Figure 3

Schematic view of the conversion-reconstruction algorithm. The two tracks are reconstructed to the same radius $r$. $\delta \varphi$ is the azimuthal-angular difference between the two tracks for a given reconstruction radius. $\delta \varphi$ is zero at the conversion point.

Figure 4

Mass distribution, $m_{e^{+}{e}^{-}}$, of the $e^{+}{e}^{-}$ pairs after conversion selection cuts are applied. All four panels are for the same $p_T$ range $1.0<p_T<1.2 \text{GeV}/c$ for four different centrality selections (a) 0%–20%, (b) 20%–40%, (c) 40%–60%, and (d) 60%–93%. Shown are the foreground ${\mathrm{FG}}^{\mathrm{ee}}$, background ${\mathrm{BG}}^{\mathrm{ee}}$, and signal ${\mathrm{SG}}^{\mathrm{ee}}$.

Figure 5

Mass distribution, $m_{ee\gamma }$, for $e^{+}{e}^{-}$ pairs with $p_T$ from 1.0 to 1.2 $\text{GeV}/c$, for four centrality selection (a), (e) 0%–20%, (b), (f) 20%–40% (c), (g) 40%–60%, and (d), (h) 60%–93%. Panels (a) through (d) show the foreground ${\mathrm{FG}}^{ee\gamma }$ and the uncorrelated background ${\mathrm{BG}}_{\mathrm{uncorr}}^{ee\gamma }$. Panels (e) through (h) show the difference ${\mathrm{FG}}^{ee\gamma }-{\mathrm{BG}}_{\mathrm{uncorr}}^{ee\gamma }$, together with the correlated background ${\mathrm{BG}}_{\mathrm{corr}}^{ee\gamma }$.

Figure 6

Mass distribution, $m_{ee\gamma }$, for $e^{+}{e}^{-}$ pairs from the 0%–20% centrality selection for four different $e^{+}{e}^{-}$ pair $p_T$ regions, (a), (e) 0.8 to 1.0, (b), (f) 1.4 to 1.6, (c), (g) 2.0 to 2.5, and (d), (h) 3.5 to 4 $\text{GeV}/c$. Panels (a) through (d) show the foreground ${\mathrm{FG}}^{ee\gamma }$ and the uncorrelated background ${\mathrm{BG}}_{\mathrm{uncorr}}^{ee\gamma }$. Panels (e) through (h) show the difference ${\mathrm{FG}}^{ee\gamma }-{\mathrm{BG}}_{\mathrm{uncorr}}^{ee\gamma }$, together with the correlated background ${\mathrm{BG}}_{\mathrm{corr}}^{ee\gamma }$.

Figure 7

(a) An example for ${\mathrm{FG}}^{ee\gamma }$ and the various background components after normalization in the indicated regions. (b) The ratio $({\mathrm{FG}}^{ee\gamma }-{\mathrm{BG}}^{ee\gamma })/{\mathrm{BG}}_{\mathrm{uncorr}}^{ee\gamma }$ and the polynomial fit to determine the residual-background correction $f_{ee\gamma }$.

Figure 8

Conditional probability $\langle {\epsilon }_{\gamma }f\rangle$ as a function of $p_T$ in 0%–20%, 20%–40%, 40%–60%, and 60%–93% centrality classes.

Figure 9

Cocktail ratio as a function of $p_T$ in the most central (0%–20%) and the most peripheral (60%–93%) centrality classes.

Figure 10

Systematic uncertainties of $R_{\gamma }$ as a function of conversion photon $p_T$ in 0%–20%, 20%–40%, 40%–60%, and 60%–93% centrality bins. The black curve corresponds to total uncertainty, and colored curves correspond to individual sources. The lines representing uncertainties from the energy scale and the conversion loss overlap at 3%, as do the lines representing uncertainties from the $\gamma$ reconstruction efficiency, acceptance, and input $p_T$ spectra.

Figure 11

Systematic uncertainties of ${\gamma }^{\mathrm{hadr}}$ as a function of photon $p_T$.

Figure 12

The ratio $R_{\gamma }={\gamma }^{\mathrm{incl}}/{\gamma }^{\mathrm{hadr}}$ as a function of conversion photon $p_T$ in 0%–20%, 20%–40%, 40%–60% and 60%–93% centrality bins. The 2014 $\text{Au}+\text{Au}$ data at $\sqrt{s_{NN}}=200$ GeV are compared to results from previous PHENIX publications (see Refs. [3, 6, 39]).

Figure 13

$R_{\gamma }$ of direct photons as a function of conversion photon $p_T$ in 0%–10% to 80%–93% centrality bins. The 2014 $\text{Au}+\text{Au}$ data at $\sqrt{s_{NN}}=200$ GeV are compared to results from previous PHENIX publications (see Refs. [3, 39]).

Figure 14

Invariant yield of direct photons as a function of conversion photon $p_T$ in 0%–10% to 80%–93% centrality bins.

Figure 15

Invariant yield of direct photons as a function of conversion photon $p_T$ in (a) 0%–20%, (b) 20%–40%, (c) 40%–60%, and (d) 60%–93% centrality bins. The 2014 $\text{Au}+\text{Au}$ data at $\sqrt{s_{NN}}=200$ GeV are compared to results from previous PHENIX publications (see Refs. [3, 6, 39]).

Figure 16

Nonprompt direct-photon yield as a function of conversion photon $p_T$ in (a) 0%–20%, (b) 20%–40%, (c) 40%–60%, and (d) 60%–93% centrality bins are compared to results from previous PHENIX publications (see Ref. [6]).

Figure 17

Ratio of the yield of nonprompt direct photons over the exponential fit result ($T_{\mathrm{eff}}$ fixed to 0.26 $\text{GeV}/c$) as a function of photon $p_T$.

Figure 18

$T_{\mathrm{eff}}$ as a function of charged-particle multiplicity at midrapidity.

Figure 19

Integrated direct-photon yield (1–5 $\mathrm{GeV}/c$) versus charged-particle multiplicity at midrapidity. The present data are compared to a previous compilation of data from [8, 46] and the $N_{\mathrm{coll}}$ scaled fit to $p+p$ data. Also given are fits with Eq. (11) to different data; the solid line is a fit to the present data resulting in $\alpha =1.11\pm 0.02\left(\mathrm{stat}\right){}_{-0.08}^{+0.09}\left(\mathrm{sys}\right)$, and the dashed line is from fitting previously published PHENIX data [46] that gave $\alpha =1.23\pm$ 0.06 $\pm$ 0.18. The ALICE data are from Ref. [9].

Figure 20

Integrated nonprompt direct-photon yield versus charged particle multiplicity at midrapidity for different $p_T$ integration ranges.

Figure 21

Scaling factors, $\alpha$, extracted from fitting Eq. (11) to integrated direct and nonprompt-photon yields as a function of $d{N}_{\mathrm{ch}}/d\eta$. Values were obtained for different $p_T$ integration ranges tabulated in Table 5.

Figure 22

Nonprompt direct-photon yields for (a) 0%–20% and (b) 20%–40% compared with model predictions from Refs. [10, 47]. (c), (d) Ratios of the yields from data to the sum of yields from thermal and preequilibrium contributions. The 2014 $\text{Au}+\text{Au}$ data at $\sqrt{s_{NN}}=200$ GeV are compared to results from a previous PHENIX publications (see Ref. [6]).

Figure 23

Invariant mass distributions of $e^{+}{e}^{-}$ pairs reconstructed from the high-multiplicity ${\pi }^0$ pseudodata in the $p_T$ range $0.8<p_T<1.0 \text{GeV}/c$. The least-restrictive conversion selection cuts are applied, which only require that the reconstruction algorithm has identified the $e^{+}{e}^{-}$ pair as a conversion candidate. Panel (a) compares foreground, ${\mathrm{FG}}^{\mathrm{ee}}$, the true background, ${\mathrm{BG}}^{\mathrm{ee}}$, and the background determined from the mixed event technique, ${\mathrm{MBG}}^{\mathrm{ee}}$. Panel (b) gives the extracted conversion photon signal.

Figure 24

Invariant mass distributions of $e^{+}{e}^{-}$ pairs reconstructed from the high-multiplicity ${\pi }^0$ pseudodata. Same as Fig. 23, but with an additional constraint that the $e^{+}$ and $e^{-}$ match in beam direction. Panel (a) compares foreground, ${\mathrm{FG}}^{\mathrm{ee}}$, the true background, ${\mathrm{BG}}^{\mathrm{ee}}$, and the background determined from the mixed event technique, ${\mathrm{MBG}}^{\mathrm{ee}}$. Panel (b) gives the extracted conversion photon signal.

Figure 25

Extracted $N_{\gamma }^{\mathrm{incl}}$ after the background subtraction, as a function of conversion photon $p_T$. The diamonds are obtained by subtracting the background from the mixed event technique; they are compared to the open symbols for which the true background was subtracted. Panel (b) shows the ratio of the event-mixing result over the true information result.

Figure 26

Invariant mass distributions of $e^{+}{e}^{-}\gamma$ pairs.

Figure 27

Invariant mass distributions of $e^{+}{e}^{-}\gamma$ pairs from the same event (FG) and different event-mixing setups.

Figure 28

Extracted $N_{\gamma }^{{\pi }^0,\mathrm{tag}}$ as a function of conversion-photon $p_T$ using the (red) true information and (blue) event-mixing technique. The bottom panel shows the ratio of the event-mixing result over the true information result.

Figure 29

Average conditional probability $\langle {\epsilon }_{\gamma }f\rangle$ as a function of conversion photon $p_T$.

Figure 30

Ratio $R_{\gamma }^{\mathrm{pseudo}}$ as a function of conversion photon $p_T$. The dashed line gives a constant offset of 1.3% fit to the points, and the dashed band represents a $\pm 1.5\%$ range around unity.