Beam-energy and centrality dependence of direct-photon emission from ultra-relativistic heavy-ion collisions

The PHENIX collaboration presents first measurements of low-momentum ($0.4<p_T<3$ GeV/$c$) direct-photon yields from Au$+$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 Au$+$Au collisions at $\sqrt{s_{{}_{NN}}}$=200. Analyzing the photon yield as a function of the experimental observable $d{N}_{\mathrm{c}\mathrm{h}}\mathrm{/}d\eta$ reveals that the low-momentum ($>$1,GeV/$c$) direct-photon yield $d{N}_{\gamma }^{\mathrm{d}\mathrm{i}\mathrm{r}}\mathrm{/}d\eta$ is a smooth function of $d{N}_{\mathrm{c}\mathrm{h}}\mathrm{/}d\eta$ and can be well described as proportional to $(d{N}_{\mathrm{c}\mathrm{h}}\mathrm{/}d\eta {)}^{\alpha }$ 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 $p_T$ ($>5$,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.