Direct photon elliptic flow at energies available at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider

We use an event-by-event hydrodynamical description of the heavy-ion collision process with Glauber initial conditions to calculate the thermal emission of photons. The photon rates in the hadronic phase follow from a spectral function approach and a density expansion, while in the partonic phase they follow from the Arnold-Moore-Yaffe (AMY) perturbative rates. The calculated photon elliptic flows are lower than those reported recently by both the ALICE and PHENIX collaborations.

Figure 1

Photon emission rates from $W_{1\pi }$ and $W_{2\pi }$ with ${\mu }_{\pi }=0$ for $T=100$, 150, and 200 MeV.

Figure 2

Ratio of the thermal photon rates used in [26] (Rapp) to our corrected rates (SBU) for $T=100$ MeV. Note that the prompt photon contribution is not included in the thermal photon rate.

Figure 3

Photon emission rates from $W_{1\pi }$ and $W_{2\pi }$ with ${\mu }_{\pi }=0$ for $T=$ 200 MeV are compared to the AMY rates (Arnold et al. [27] with $N_f=3$) for $T=200$ MeV. Also shown are the nonperturbative soft gluon corrections from [4, 29].

Figure 4

Running strong coupling constant ${\alpha }_s$ up to two-loop order used in the AMY rates [31].

Figure 5

Prompt-photon spectra fitted to PHENIX $p+p$ data [37, 38].

Figure 6

Spectra of direct photons for RHIC. Experimental data for PHENIX $\mathrm{Au}+\mathrm{Au}$ are taken from [38, 39]. See text.

Figure 7

Spectra of direct photon for ALICE. Experimental data for ALICE $\mathrm{Pb}+\mathrm{Pb}$ are taken from [41]. Note that LHC1-2 (LHC3-4) was averaged over two centrality ranges, 0–10% and 10–20% (20–30% and 30–40%), weighted by the number of photons at each centrality bin [44]. See text.

Figure 8

Elliptic flow $v_2$ of charged particles (${\pi }^{\pm },p,\overline{p}$) for PHENIX [7]. Simulation parameters are summarized in Table 1. Best-fit results in a given centrality region are displayed.

Figure 9

Direct-photon elliptic flow $v_2^{\gamma }$ for PHENIX [8, 9]. For the hadronic part before the phase transition, first-order (CRF1 in red; up to one-pion contribution) and second-order (CRF2 in blue; up to two-pion contribution) hadronic resonance gas (HRG) models are used. In this calculation, $T_{\mathrm{crit}}$ is 190 MeV and $T_{\mathrm{FO}}$ is 137.44 MeV. The solid lines are full simulation results from $T_{\mathrm{init}}$ to $T_{\mathrm{FO}}$ with the phase transition from QGP to HRG. The dashed and dotted lines are the results with partial contributions from the HRG (below $T_{\mathrm{crit}}$) and the QGP (above $T_{\mathrm{crit}}$), respectively. The vertical error bars on each data point indicate the statistical uncertainties and the grey shaded regions indicate the systematic uncertainties of the experiment. RXN correspond to the data from a dedicated reaction-plane detector (RXN) of PHENIX [8]. BBC correspond to the data from beam-beam counters (BBC) of PHENIX [8].

Figure 10

Elliptic flow $v_2$ of charged particles (${\pi }^{\pm },p,\overline{p}$) for ALICE and CMS [10, 12]. Simulation parameters are summarized in Table 2. Best-fit results in a given centrality region are shown.

Figure 11

Direct-photon elliptic flow $v_2^{\gamma }$ for ALICE [11]. Before the phase transition, first-order HRG (CRF1 in re; up to one-pion contribution) and second-order HRG (CRF2 in blu; up to two-pion contribution) are used. $T_{\mathrm{crit}}$ is 190 MeV and $T_{\mathrm{FO}}$ is 131 MeV. $T_{\mathrm{init}}$ are summarized in Table 2. The solid lines are full simulation results from $T_{\mathrm{init}}$ to $T_{\mathrm{FO}}$. The dashed and dotted lines are the results with partial contributions from the HRG (below $T_{\mathrm{crit}}$) and the QGP (above $T_{\mathrm{crit}}$), respectively. Note that the centrality range of the experimental data are 0–40%. LHC1-4 is an average of our four predictions over four centrality ranges weighted by the number of photons at each centrality range [44]. The vertical error bars on each data point indicate the statistical uncertainties and the grey shaded regions indicate the systematic uncertainties of the experiment.