Virtual Photons Shed Light on the Early Temperature of Dense QCD Matter

Dileptons produced during heavy-ion collisions represent a unique probe of the QCD phase diagram, and convey information about the state of the strongly interacting system at the moment their preceding off-shell photon is created. In this study, we compute thermal dilepton yields from $\mathrm{Au}+\mathrm{Au}$ collisions performed at different beam energies, employing a ($3+1$)-dimensional dynamic framework combined with emission rates accurate at next-to-leading order in perturbation theory and which include baryon chemical potential dependencies. By comparing the effective temperature extracted from the thermal dilepton invariant mass spectrum with the average temperature of the fluid, we offer a robust quantitative validation of dileptons as an effective probe of the early quark-gluon plasma stage.

Figure 1

The perturbative diagrams included in our evaluation. For the LPM class of ladder diagrams, indicates that rungs are screened with HTL gluon self-energies while it should be understood that the valence quarks are evaluated at their asymptotic thermal mass.

Figure 2

Dielectron excess mass spectra within rapidity $|y|<1$, normalized by midrapidity charged hadron multiplicity $\mathrm{d}{N}_{\mathrm{ch}}/\mathrm{d}y$, for 0%–80% $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=19.6$, 27, 39, 62.4, 200 GeV. The markers with error bars and open boxes indicate the STAR experimental measurements with statistical and systematic uncertainties, while the dot-dashed lines represent model calculations.

Figure 3

Initial temperatures (red dots) and final temperatures (blue squares) of the hydrodynamic evolution, along with effective temperatures derived from dilepton spectra (green triangles) for 40%–50% $\mathrm{Au}+\mathrm{Au}$ collisions, presented as a function of beam energy. The error bars associated with the hydrodynamic temperatures indicate standard deviations, while the error bars of the effective temperatures represent uncertainties resulting from the fitting procedure in the temperature extraction method.

Figure 4

Correlation between initial average hydrodynamic temperatures $⟨T_{\mathrm{in}}⟩$ and the derived effective temperature $T_{\mathrm{eff}}$ from dilepton spectra for $\mathrm{Au}+\mathrm{Au}$ collisions at eight beam energies, spanning from 7.7 to 200 GeV, within centrality bins from 0%–10% to 70%–80% (see the Supplemental Material [59] for a table containing all data points). The black dashed line denotes a global fit to all data points, and the gray band illustrates the uncertainties associated with the fitting procedure.