Beam Energy and Centrality Dependence of Direct-Photon Emission from Ultrarelativistic Heavy-Ion Collisions

The PHENIX collaboration presents first measurements of low-momentum ($0.4<p_T<3\mathrm{GeV}/c$) direct-photon yields from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=39$ and 62.4 GeV. For both beam energies the direct-photon yields are substantially enhanced with respect to expectations from prompt processes, similar to the yields observed in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$. Analyzing the photon yield as a function of the experimental observable $d{N}_{\mathrm{ch}}/d\eta$ reveals that the low-momentum ($>1\mathrm{GeV}/c$) direct-photon yield $d{N}_{\gamma }^{\mathrm{dir}}/d\eta$ is a smooth function of $d{N}_{\mathrm{ch}}/d\eta$ and can be well described as proportional to $(d{N}_{\mathrm{ch}}/d\eta {)}^{\alpha }$ with $\alpha \approx 1.25$. This scaling behavior holds for a wide range of beam energies at the Relativistic Heavy Ion Collider and the Large Hadron Collider, for centrality selected samples, as well as for different $A+A$ collision systems. At a given beam energy, the scaling also holds for high $p_T$ ($>5\mathrm{GeV}/c$), but when results from different collision energies are compared, an additional $\sqrt{s_{NN}}$-dependent multiplicative factor is needed to describe the integrated-direct-photon yield.

Figure 1

Direct photon spectra normalized by $(d{N}_{\mathrm{ch}}/d\eta {)}^{1.25}$ for $\mathrm{Au}+\mathrm{Au}$ at 39 and 64.2 GeV (a) and (b) at 200 GeV [8]; panel (c) compares for different $A+A$ systems at different $\sqrt{s_{NN}}$ [11, 40]. Panels (a) and (b) also show $p+p$ data [8, 48, 49, 50]. All panels show pQCD calculations for the corresponding $\sqrt{s}$ [21, 51]. The errors shown are the quadratic sum of systematic and statistical uncertainties. Uncertainties on the $d{N}_{\mathrm{ch}}/d\eta$ are not included.

Figure 2

Number of binary collisions, $N_{\mathrm{coll}}$ vs $d{N}_{\mathrm{ch}}/d\eta$, for four beam energies. The errors shown reflect the uncertainty of $N_{\mathrm{coll}}$ from the Glauber calculation. Fitting Eq. (3) simultaneously to all data with a common $\alpha$ results in $\alpha =1.25$ and a $\sqrt{s_{NN}}$ dependence SY as shown in the text below Eq. (3).

Figure 3

Integrated direct photon yield ($p_T>1.0\mathrm{GeV}/c$) vs $d{N}_{\mathrm{ch}}/d\eta$, for data sets shown in Fig. 1. The dashed line is a power law fit with a fixed slope of $\alpha =1.25$. The two upper limits correspond to the data in 20%–40% and 40%–80% $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2760\mathrm{GeV}$. The integrated yields of the fit to $p+p$ data and of the pQCD calculations are shown as well, both scaled by $N_{\mathrm{coll}}$ [21, 51].

Figure 4

Integrated direct photon yield ($p_T>5.0\mathrm{GeV}/c$) vs $d{N}_{\mathrm{ch}}/d\eta$, for different data sets. The dashed lines show power law fits to the data with fixed slope of $\alpha =1.25$. Integrated yields from pQCD calculations scaled by $N_{\mathrm{coll}}$ are also shown.