Centrality dependence of the direct photon yield and elliptic flow in heavy-ion collisions at sqrt(s)=200 GeV

TL;DR

This study models the centrality dependence of direct photon production and elliptic flow in heavy-ion collisions at 200 GeV, revealing insights into thermal photon spectra, source contributions, and flow characteristics across collision centralities.

Contribution

It provides a detailed transport model analysis of direct photon yields, spectra, and flow, incorporating multiple sources and their centrality dependence, which advances understanding of photon production mechanisms.

Findings

Thermal photon spectra deviate from simple exponential distributions.

Effective temperatures are above the deconfinement transition, indicating radial flow.

Photon elliptic flow is larger in peripheral collisions due to late-stage hadronic contributions.

Abstract

We calculate the centrality dependence of direct photons produced in Au+Au collisions at sqrt{s}=200GeV and their transverse momentum spectra within the Parton-Hadron-String Dynamics (PHSD) transport approach. As sources for 'direct' photons, we incorporate the interactions of quarks and gluons as well as hadronic interactions (pi+pi->rho+gamma, rho+pi->pi+gamma, meson-meson bremsstrahlung m+m->m+m+gamma, meson-baryon bremsstrahlung m+B->m+B+gamma), the decays of phi and a_1 mesons and the photons produced in the initial hard collisions ('pQCD'). We find that the pT spectra of the 'thermal' photons (i.e. the direct photons after the pQCD contribution is subtracted) deviate from exponential distributions and, consequently, observe a strong dependence of the inverse slope parameter T_eff on the fitting range in pT. On the other hand, all the obtained 'effective temperatures' are well above the critical temperature for the deconfinement phase transition even for peripheral collisions, reflecting primarily a 'blue shift' due to radial collective motion of hadrons. Our calculations suggest that the channel decomposition of the observed spectrum changes with centrality with an increasing (dominant) contribution of hadronic sources for more peripheral reactions. Furthermore, the thermal photon yield is found to scale roughly with the number of participant nucleons as N_part^alpha with alpha=1.5, whereas the partonic contribution scales with an exponent alpha_p=1.75. Additionally, we provide predictions for the centrality dependence of the direct photon elliptic flow v_2(pT). The direct photon $v_2$ is seen to be larger in peripheral collisions compared to the most central ones since the photons from the hot deconfined matter in the early stages of the collision carry a much smaller elliptic flow than the final hadrons.

Tables

Table 1. Table 1: The slope parameter T e ​ f ​ f subscript 𝑇 𝑒 𝑓 𝑓 T_{eff} of the spectrum of thermal photons (Fig.  4 ) produced in Au+Au collisions at s N ​ N = 200 subscript 𝑠 𝑁 𝑁 200 \sqrt{s_{NN}}=200  GeV at various centralities. The value T e ​ f ​ f subscript 𝑇 𝑒 𝑓 𝑓 T_{eff} was obtained by approximating the spectrum by an exponential function in the transverse momentum range 0.6 < p T < 2 0.6 subscript 𝑝 𝑇 2 0.6<p_{T}<2  GeV.

I The slope parameter $T_{eff}$ (in MeV) I
I Centrality I	I $N_{part}$ I	I $T_{eff}$
0-20%	280	I $265\pm 20$
20-40%	137	I $260\pm 20$
40-60%	60	I $250\pm 20$
60-92%	15	I $260\pm 20$

Equations

$$q_0\frac{d^3{\sigma }^{\gamma }}{d^{3}q}$$

$$\bar{\sigma }(s)$$

Full text

I Introduction

The ’direct photons’ from relativistic heavy-ion collisions are a valuable probe of the collision dynamics at early times and provide information on the characteristics of the initially created matter once the final state hadronic decay photons are subtracted from the experimental spectra Shuryak (1978a, b); Feinberg (1970, 1976); Bjorken and Weisberg (1976); Peitzmann and Thoma (2002); Aurenche (2002). In the last years, the PHENIX Collaboration Adare et al. (2012, 2010a, 2010b); Tserruya (2013) has measured the spectra of the photons produced in minimal bias Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and found a strong elliptic flow $v_{2}(p_{T})$ of ’direct photons’, which is comparable to that of the produced pions. Since direct photons were expected to be essentially produced in the initial hot medium before the collective flow has developed, this observation was in contrast to the theoretical expectations and predictions Chatterjee et al. (2006); Liu et al. (2009a); Dion et al. (2011a, b); van Hees et al. (2011). Also more recent studies employing event-by-event hydrodynamical calculations Chatterjee et al. (2013); Shen et al. (2013a, b) severely have underestimated the elliptic flow of direct photons and alternative sources of direct photons from the conformal anomaly have been suggested Basar et al. (2012). Furthermore, in order to distinguish direct photons from the strong magnetic field of spectator protons (due to the conformal anomaly) it has been suggested to explore the centrality dependence of the direct photon $v_{2}$ in correlation with the elliptic flow from pions Bzdak and Skokov (2013).

On the other hand, in Ref. Linnyk et al. (2013) we have proposed that apart from the partonic production channels the direct photon yield and primarily the strong $v_{2}$ might be due to hadronic sources (such as meson-meson Bremsstrahlung or hadronic interactions as $\pi+\pi\to\rho+\gamma$, $\rho+\pi\to\pi+\gamma$ etc.). Indeed, the interacting hadrons carry a large $v_{2}$ and contribute by more than 50% to the measured ’direct photons’ according to the PHSD calculations in Ref. Linnyk et al. (2013) (cf. also the hydrodynamics calculations in Ref. Dusling and Zahed (2010)). For a quantitative understanding of the direct photon production it is important to verify the decomposition of the total photon yield according to the production sources: the late hadron decays (the cocktail), hadronic interactions beyond the cocktail (during the collision phase) and the partonic interactions in the quark-gluon plasma (QGP). Since previous transport studies have indicated that the duration of the partonic phase substantially decreases with increasing impact parameter (cf. Fig. 4 in Ref. Konchakovski et al. (2012a)) we will study here explicitly the centrality dependence of the direct photon yield together with the essential production channels and their impact on the photon $v_{2}$.

As in Ref. Linnyk et al. (2013) we will employ the Parton-Hadron-String Dynamics (PHSD) transport approach to investigate the photon production in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV at various centralities thus extending our previous investigations for the case of minimum bias collisions. We recall that the PHSD approach has provided a consistent description of the bulk properties of heavy-ion collisions – rapidity spectra, transverse mass distributions, azimuthal asymmetries of various particle species – from low Super-Proton-Synchrotron (SPS) to top Relativistic-Heavy-Ion-Collider (RHIC) energies Bratkovskaya et al. (2011a) and was successfully used also for the analysis of dilepton production from hadronic and partonic sources at SPS, RHIC and Large-Hadron-Collider (LHC) energies  Linnyk et al. (2011). It is therefore of interest to calculate also the photon production in relativistic heavy-ion collisions from hadronic and partonic interactions within the PHSD transport approach, since its microscopic and non-equilibrium evolution of the nucleus-nucleus collision is independently controlled by a multitude of other hadronic and electromagnetic observables in a wide energy range Bratkovskaya et al. (2011b); Konchakovski et al. (2012a, b); Linnyk et al. (2011).

II Photons within PHSD

For the details on the PHSD approach we refer the reader to Refs. Bratkovskaya et al. (2011b); Cassing and Bratkovskaya (2009) and the implementation of the photon production to Refs. Bratkovskaya et al. (2008); Linnyk et al. (2013) (and references therein). Let us recall that the dynamical calculations within the PHSD have reproduced the measured differential spectra of dileptons produced in heavy-ion collisions at SPS and RHIC energies (see Refs. Linnyk et al. (2011)). Furthermore, the dilepton production rate from the QGP constituents - as incorporated in the PHSD - agrees with the dilepton rate from the thermalized QCD medium as calculated by lattice QCD (lQCD). We note, additionally, that the electric conductivity of the QGP from the PHSD, which controls the photon emission rate in equilibrium, is rather well in line with available lQCD results Cassing et al. (2013).

As sources of photon production - on top of the general dynamical evolution - we consider hadronic Turbide et al. (2004); Bratkovskaya et al. (2008); Kapusta et al. (1991); Gale and Kapusta (1987) as well as partonic Feinberg (1976); Shuryak (1978b); Linnyk et al. (2005); Linnyk (2011); Wong and Wang (1998) interactions. In the present study we extend the calculations in Ref. Linnyk et al. (2013) by adding an additional source of photons, i.e. the bremsstrahlung in elastic meson+baryon collisions ($m+B\to m+B+\gamma$). In our previous study (Ref. Linnyk et al. (2013)), we have considered the meson-meson bremsstrahlung, because it had been proposed to be important already in Refs. Gale and Kapusta (1987); Bratkovskaya et al. (2008). At the time we had not realized the potential importance of the photon production in meson-baryon collisions. However, we will see below that this process contributes considerably.

The bremsstrahlung production of photons is calculated using the soft photon approximation as in Refs. Gale and Kapusta (1987); Eggers et al. (1996a); Bratkovskaya et al. (2008); Linnyk et al. (2013). The soft-photon approximation (SPA) relies on the assumption that the radiation from internal lines is negligible and the strong interaction vertex is on-shell. In this case the strong interaction part and the electromagnetic part can be separated, so the soft-photon cross section for the reaction $h_{1}+h_{2}\to h_{1}+h_{2}+\gamma$ can be written as

[TABLE]

where $M_{1}$ is the mass of the charged accelerated particle, $M_{2}$ is the mass of the second particle; $q_{0},q$ are the energy and momentum of the photon. In (1) $\sigma(s)$ is the on-shell cross section for the reaction $h_{1}+h_{2}\to h_{1}+h_{2}$, i.e. the elastic scattering of the two hadrons.

Let us point out that the resulting yield of the bremsstrahlung photons depends on the model assumptions such as the cross sections for the meson-meson and meson-baryon elastic scatterings, incoherence of the individual scatterings and the soft photon approximation. The theoretical uncertainty of up to a factor of 2 due to the unmeasured elastic scattering cross sections has to be kept in mind. The adequacy of the SPA assumption has been checked in Ref. Eggers et al. (1996a). We recall here that the soft photon approximation is no longer valid for high energies of the produced photons or at high $\sqrt{s}$ of the meson+meson or meson+baryon collisions Eggers et al. (1996b). Thus we have restricted our kinematics by considering only meson+meson and baryon+meson collisions with available energies $\sqrt{s}$ below 3 GeV. Our conclusions on the centrality dependence of the direct photons are not sensitive to the actual value of the cut-off within reasonable variations.

The assumption of incoherent photon production in individual hadron-hadron collisions is not applicable at very low transverse momenta of the photons. The Landau-Pomeranchuk-Migdal (LPM) effect is the suppression of bremsstrahlung photon emission due to the multiple scattering of the production source (in this case meson or baryon) during the time needed for the formation of the radiated photon. In this case the bremsstrahlung amplitudes interfere destructively. For the hadronic bremsstrahlung, the LPM effect in the thermal medium has been calculated in Ref. Cleymans et al. (1993). The suppression depends on the length of the formation zone of the photon $z(\gamma)$, which is defined by the uncertainty principle and depends on the energy of the photon. The suppression becomes significant for photon energies below a certain value, for which $z(\gamma)$ becomes larger than the mean free path of the hadron $\lambda$ Anthony et al. (1997); Wang et al. (1995). For the photon at mid-rapidity, $z(\gamma)=2\omega/p_{T}^{2}=2/p_{T}$. On the other hand, the mean free path of the hadrons $\lambda=1/(\sigma n)$ is governed by the hadronic scattering cross section (typically of the order of $\sigma=20$ mb) and the hadron density, which after the hadronization does not exceed $n_{max}=0.5$ fm*-3*. Accordingly, the suppression due to the LMP effect is expected to be important for these processes at $p_{T}<0.4$ GeV, where, however, no data are available yet. At present, we do not include the LMP effect on the bremsstrahlung photon production in our calculations due to the lack of data at sufficiently low $p_{T}$.

Since a new production mechanism has been added to the hadronic production channels (the meson-baryon bremsstrahlung), we first check whether this addition does not lead to an overestimation of the data from the PHENIX Collaboration Adare et al. (2010a, b) in minimal bias $Au+Au$ collisions in Fig. 1. Since the decays of mesons as ’late’ hadronic sources are less sensitive to the creation of the hot and dense medium and to its properties, they are usually subtracted experimentally from the total photon yield to access the ‘direct’ photon spectrum. In our calculations of the direct photon spectrum in Fig. 1 the following sources are taken into account: the decays of $\omega$, $\eta$’, $\phi$ and $a_{1}$ mesons; the reactions $\pi+\rho\to\pi+\gamma$, $\pi+\pi\to\rho+\gamma$; the photon bremsstrahlung in meson-meson and meson-baryon collisions $m+m\to m+m+\gamma$, $m+B\to m+B+\gamma$; photon production in the QGP in the processes $q+{\bar{q}}\to g+\gamma$, and $q({\bar{q}})+g\to q({\bar{q}})+\gamma$ as well as the photon production in the initial hard collisions (”pQCD”), which is given by the hard photon yield in p+p collisions scaled with the number of binary collisions $N_{coll}$. We find that our PHSD calculations are in a reasonable agreement with the PHENIX data Adare et al. (2010a, b) and show a clear dominance of the hadronic production channels over the partonic channels for transverse momenta below about 0.7 GeV/c. In particular, the bremsstrahlung contributions are responsible for the ’banana shape’ spectrum and the strong increase for low $p_{T}$. On the other hand, this increase should be softened to some degree by the LPM effect. Accordingly, especially experimental data well below 1 GeV/c in $p_{T}$ will be helpful in disentangling the various sources.

In Fig. 2, we show explicitly the elliptic flow $v_{2}$ of direct photons in minimum bias collisions in comparison to the data and the previous centrality integrated results also for (the green dashed line) from the Ref. Linnyk et al. (2013). Note that the photons from the decays of $\omega$ and $\eta$’ mesons have been subtracted from the $v_{2}$ data by experimental methods. We calculated the direct photon $v_{2}$ as a sum of $v_{2}(i)$ of each individual contributed channel, weighted with the channel’s contribution to the $p_{T}$ spectrum. The considered channels are: $\pi+\rho\to\pi+\gamma$, $\pi+\pi\to\rho+\gamma$; the photon bremsstrahlung in meson-meson collisions $m+m\to m+m+\gamma$; photon production in the QGP in the processes $q+{\bar{q}}\to g+\gamma$, and $q({\bar{q}})+g\to q({\bar{q}})+\gamma$ as well as the photon production in the initial hard collisions (”pQCD”). The new calculations include additionally the meson bremsstrahlung processes $m+B\to m+B+\gamma$ and are shown by the blue solid line. The agreement with experiment has slightly improved compared to Ref. Linnyk et al. (2013).

III Results for different centralities

The calculated results for the direct photon spectrum in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV are presented in Fig. 3 for various centralities as functions of the transverse momentum $p_{T}$ at mid-rapidity $|y|<0.35$. The direct photons are obtained experimentally from the total photon spectrum by subtracting meson decay photons base on measured meson yields. Therefore, in this case we disregard all hadron decays except the $\phi,a_{1}$ photonic decays, which are subleading. The following contributions are addressed as ’direct photons’: the decays of $\phi$ and $a_{1}$ mesons; the reactions $\pi+\rho\to\pi+\gamma$, $\pi+\pi\to\rho+\gamma$; the photon bremsstrahlung in meson-meson and meson-baryon collisions $m+m\to m+m+\gamma$, $m+B\to m+B+\gamma$; photon production in the QGP in the processes $q+{\bar{q}}\to g+\gamma$, and $q({\bar{q}})+g\to q({\bar{q}})+\gamma$ as well as the photon production in the initial hard collisions (”pQCD”). The direct pQCD contributions dominates above $p_{T}\approx$ 2 GeV/c.

The spectra of “thermal” photons are obtained from the direct photon spectra (channels listed above) by additionally subtracting the photons produced in the initial hard pQCD processes. The pQCD photons are not expected to have thermal spectrum and practically give no contribution to the direct photon elliptic flow. The thermal photons in 0-20 % central, 20-40 % central, 40-60 % central and 60-92 % central Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV within the PHSD approach are displayed in Fig. 4. We only specify the dominant channels in Fig. 4, i.e. the contributions from m+m and m+B bremsstrahlung as well as the QGP contribution which is seen to become low in more peripheral collisions.

Though the spectrum presented in Fig. 4 is obviously not exponential in the full momentum range especially due to the bremsstrahlungs channels, one may fit the spectra by exponentials in a finite transverse momentum region and define in this way an effective slope parameter or ‘effective temperature’ as in the experimental analysis Adare et al. (2010a, b). The slope of the transverse momentum spectrum of produced ’thermal photons’ is expected to give a glance at the initial temperatures reached in the collisions Chatterjee et al. (2006); Liu et al. (2009a); Dion et al. (2011a, b); Feinberg (1976); Shuryak (1978b); Kapusta et al. (1991); Alam et al. (2001); Steffen and Thoma (2001); Srivastava and Sinha (2001); Huovinen et al. (2002); Turbide et al. (2004); d’Enterria and Peressounko (2006); Liu et al. (2009b); Turbide et al. (2008); Shen et al. (2013a), and was even used to deduce an ’average temperature’ of the QGP Adare et al. (2010a, b). We will present here the effective temperatures $T_{eff}$ as extracted from the calculated transverse momentum spectra of thermal photons from Fig. 4, addressing them as ’apparent inverse slope parameters’ $T_{eff}$ or energy scales for the photonic radiation. The extracted ‘effective temperatures’ are shown in Table I at the different centralities for the transverse momentum interval 0.6-2 GeV. The ‘temperature’ defined in this way depends on the fit range in transverse momentum and should only serve as a characteristic energy scale as mentioned above. Surprisingly, we find (within error bars) the same slope parameter $T_{eff}$ which is significantly larger than the critical temperature $T_{c}\approx$ 160 MeV for deconfinement. Since here the dominant contributions should be related to binary bremsstrahlung channels the high slope parameters predominantly reflect the ’blue-shift’ of the photon spectra due to the collective flow of hadrons (cf. Ref. Shen et al. (2013a)) which (for PHSD) was shown in Ref. Konchakovski et al. (2012a) to be well in line with experimental observation.

Integrating the thermal photon spectra from Fig. 4 over the transverse momentum $p_{T}$ in the interval $0.4\leq p_{T}\leq 5$, we obtain the number of thermal photons (full squares) as a function of centrality, which is plotted in Fig. 5 as a function of the number of participants $N_{part}$ calculated in the Monte-Carlo Glauber model described in Ref. Miller et al. (2007). Since only binary collision channels contribute to the production of thermal photons in our approach, their yield rises faster than $N_{part}$ as expected from qualitative considerations in Refs. Kajantie et al. (1986); Srivastava and Geiger (1999). A power-law fit to our results gives approximately a scaling $\sim N_{part}^{\alpha}$ with $\alpha\approx$ 1.5. In addition we display in Fig. 5 the scaling with $N_{part}$ for the partonic (full dots) and hadronic bremsstrahlung channels (full triangles) separately, which give exponents of $\approx$ 1.75 and $\approx$ 1.5, respectively.

As one can see in Figs. 3 and 4 qualitatively the contribution of the photons from the QGP is larger in central collisions while the hadronic sources contribute more dominantly in peripheral collisions. We quantify the relative contributions by plotting in Fig. 6 the ratio of the number of photons produced in the QGP to the number of all direct photons (from the QGP, $m+m/B\to m+m/B+\gamma$, $\pi+\pi/\rho\to\rho/\pi+\gamma$ and the pQCD photons). The contribution of the QGP photons is seen to increase with transverse momentum and reaches slightly more than 30% for the most central event bin. On the other hand, the ratio of QGP photons to the total direct photons falls rapidly with decreasing centrality and is below 10% in the most peripheral centrality bin. Accordingly, minimal bias collisions are dominated by the hadronic channels that come along with a large hadronic elliptic flow $v_{2}$.

In Fig. 7 we provide predictions for the centrality dependence of the direct photon elliptic flow $v_{2}(p_{T})$ within the PHSD approach. The direct photon $v_{2}$ is seen to be larger in the peripheral collisions compared to the most central ones. The predicted centrality dependence of the direct photon flow results from the interplay of two independent factors. Firstly, the channel decomposition of the direct photon yield as presented by the ratios in Fig. 6 changes: the admixture of photons from the hadronic phase increases for more peripheral collisions. As has been described in detail in Ref. Linnyk et al. (2013), the PHSD approach predicts a very small $v_{2}$ of photons produced in the initial hot deconfined phase by partonic channels of the order of 2%. On the other hand, the photons from the hadronic sources show strong elliptic flow (up to 10%), on the level of the $v_{2}$ of final hadrons Linnyk et al. (2013). Accordingly, since the channel decomposition of the direct photons changes with centrality, the elliptic flow of the direct photons increases with decreasing centrality and becomes roughly comparable with the elliptic flow of pions in peripheral collisions.

However, there is another (second) factor contributing to the centrality dependence of the photon elliptic flow. Let us recall the centrality dependence of the elliptic flow for charged particles, e.g. Fig.7 of Ref. Konchakovski et al. (2012a). The $v_{2}$ rises almost linearly with increasing impact parameter $b$ at small $b$, and decreases again in the most peripheral collisions. The latter decrease is a sign that the most peripheral collisions can be understood as rather a superposition of elementary collisions, with little collectivity. The elliptic flow in the most peripheral bin is low in Fig.  7, because the all the particles have little flow at this high $b$. This effect is present in the PHSD model as well as in the observation.

IV Summary

The spectra of direct and thermal photons - as produced in Au-Au collisions at $\sqrt{s_{NN}}=200$ GeV - have been calculated differentially in collision centrality within the PHSD transport approach, which has been previously tested in comparison to the measured spectra and flow of photons in minimal bias collisions at the same energy Linnyk et al. (2013). We have found that the channel decomposition of the photon spectra changes with centrality, with a larger contribution of the hadronic sources in more peripheral collisions.

As a consequence, the direct photon $v_{2}$ is larger in peripheral collisions as compared to the most central reactions. We recall that $v_{2}$ of photons produced in the initial hot deconfined phase by partonic channels is small (of the order of 2%) within our approach Linnyk et al. (2013). On the other hand, the photons from the hadronic sources show strong elliptic flow (up to 10%), on the level of the $v_{2}$ of final hadrons Linnyk et al. (2013). Accordingly, since the channel decomposition of the direct photons changes, their elliptic flow increases with decreasing centrality and becomes roughly comparable with the $v_{2}$ of pions in peripheral collisions. Moreover, the $v_{2}$ of the photons increases with decreasing centrality additionally due to the rising of $v_{2}(b)$ with the impact parameter $b$, which was observed for all hadrons (except for the most peripheral bin). The increase of the direct photon $v_{2}(b)$ for the two most central bins has been also indicated in hydrodynamics calculations in Refs. Shen et al. (2013b); Chaudhuri (2013), although with slightly lower absolute values of $v_{2}$. Future measurements of the photon spectra and elliptic flow as a function of the collision centrality will be mandatory for a clarification of the ’photon $v_{2}$ puzzle’ from the experimental side and to estimate the contribution from unconventional sources Bzdak and Skokov (2013); Basar et al. (2012); Goloviznin et al. (2012); Yin (2013); Müller et al. (2013); Skokov (2013).

Additionally, our calculations have shown that the “thermal” photon $p_{T}$ spectra deviate from an exponential distribution at all centralities primarily due to the hadronic bremsstrahlung channels. The effective slopes of these spectra have been extracted in the interval $p_{T}=(0.4-5)$ GeV and are constant with centrality within error bars. Due to the non-exponential shape of the photon spectra these effective slopes depend on the fitting interval in $p_{T}$, however, provide ’effective temperatures’ significantly above the critical temperature $T_{c}\approx$ 160 MeV for the deconfinement phase transition. Since in PHSD the dominant contributions to the thermal photon yield are related to hadronic bremsstrahlung channels the high slope parameters predominantly reflect the ’blue-shift’ of the photon spectra due to the collective flow of hadrons (cf. Ref. Shen et al. (2013a)). Experimental data at low photon $p_{T}$ will help in clarifying the physical sources.

Furthermore, since only collisional channels contribute to the production of thermal photons in PHSD, their yield rises faster than the number of participating nucleons $N_{part}$ as expected also from qualitative considerations in Refs. Kajantie et al. (1986); Srivastava and Geiger (1999). A power-law fit to our results gives approximately a scaling $\sim N_{part}^{\alpha}$ with $\alpha\approx$1.5, whereas the partonic and hadronic channels separately scale with exponents of $\approx$ 1.75 and $\approx$ 1.5, respectively.

We finally point out that respective photon measurements of the ALICE Collaboration at the LHC Wilde (2013); Lohner (2013) should complete the picture presented in this study. A detailed PHSD analysis of photon production and flow at the LHC collision energies will be reported in near future.

Acknowledgements

The authors are grateful for fruitful discussions with B. Bannier, G. David, C. Gale, B. Jacak, L. McLerran, R. Rapp, V. Skokov, A. Toia, V. Toneev and N. Xu. This work was supported in part by the LOEWE center HIC for FAIR.