Photons from the early stages of relativistic heavy-ion collisions

We present results about photon-production in relativistic heavy-ion collisions. The main novelty of our study is the calculation of the contribution of the early-stage photons to the photon spectrum. The initial stage is modeled by an ensemble of classical gluon fields which decay to a quark-gluon plasma via the Schwinger mechanism, and the evolution of the system is studied by coupling classical field equations to relativistic kinetic theory; photon production is then computed by including the pertinent collision processes into the collision integral. We find that the contribution of the early-stage photons to the direct photon spectrum is substantial for $p_T\approx 2$ GeV and higher, the exact value depending on the collision energy; therefore, we identify this part of the photon spectrum as the sign of the early stage. Moreover, the amount of photons produced during the early stage is not negligible with respect to those produced by a thermalized quark-gluon plasma: We support the idea that there is no dark age in relativistic heavy-ion collisions.

Figure 1

Microscopic processes implemented in the collision integral: (a) Compton scattering; (b) pair annihilation.

Figure 2

Function $\mathrm{\Phi }\left(T\right)$ appearing in Eqs. (17) and (18) versus the effective temperature $T=E/3N$.

Figure 3

Photon production rate for several values of the temperature. Dashed lines correspond to the AMY rate at a given temperature, while squares represent the rate implemented in our collision integral.

Figure 4

Quark, gluon, and total particle numbers for the AFTm initialization, compared with the values used in the Glauber initialization. (a) A collision at the RHIC energy; (b) a collision at the LHC energy. Squares, diamonds, and circles correspond to gluons, quarks, and total particle number of the AFTm, respectively. Both panels refer to collisions belonging to the $20\%–40\%$ centrality class.

Figure 5

Final spectra for gluons and quarks at RHIC [panels (a) and (b), respectively] and at LHC [panels (c) and (d), respectively]. In the panels, squares correspond to AFTm and circles to Glauber calculations.

Figure 6

Photon spectra at midrapidity. Panel (a) corresponds to collisions at RHIC and panel (b) is the analogous for the LHC case. In both panels, solid maroon lines correspond to the spectrum obtained within the AFTm, while blue dashed lines stand for the spectrum obtained in simulations with the Glauber initialization. Green dot-dashed lines denote the photon spectrum in the AFTm at $t_0=0.6$ fm/$c$ for RHIC and $t_0=0.3$ fm/$c$ for LHC: In both cases we call this the early-stage spectrum. Finally, the orange dotted lines correspond to the difference between the maroon and the green lines, that we call the late-stage spectrum. See the text for more details.

Figure 7

Ratio of photon spectrum of the AFTm over the one corresponding to the Glauber calculation. The green solid line corresponds to RHIC collision and the blue dashed line to LHC collision.

Figure 8

Photon spectrum produced by the quark-gluon plasma for a RHIC collision, within three different calculations based on relativistic transport: blue circles correspond to PHSD [11], thin red solid line denotes the BAMPS result [18] with a fixed strong coupling, while the dashed green line corresponds to the BAMPS result with a running coupling; finally the maroon squares correspond to our result.

Figure 9

In the top panel we plot the direct photon spectrum for a RHIC collision. The maroon solid line corresponds to our result for the quark-gluon plasma, to which we have added the prompt photons of Ref. [5] and the hadron gas contribution of Ref. [11]. For comparison, we have shown the IP-glasma + hydro result of Ref. [5], represented by the green dashed line. The red dot-dashed line denotes the PHSD result [11]. Green squares correspond to the experimental data from the PHENIX Collaboration [71]. In the bottom panel we plot the direct photon spectrum for an LHC collision. Line styles and colors are the same as in the top panel. Experimental data are from the ALICE Collaboration [72].