Thermal photons as a quark-gluon plasma thermometer reexamined

Chun Shen, Ulrich Heinz, Jean-François Paquet, and Charles Gale

Phys. Rev. C 89, 044910 – Published 28 April 2014

Abstract

Photons are a penetrating probe of the hot medium formed in heavy-ion collisions, but they are emitted from all collision stages. At photon energies below 2–3 GeV, the measured photon spectra are approximately exponential and can be characterized by their inverse logarithmic slope, often called the “effective temperature” $T_{eff}$ . Modeling the evolution of the radiating medium hydrodynamically, we analyze the factors controlling the value of the $T_{eff}$ and how it is related to the evolving true temperature $T$ of the fireball. We find that at the energies available at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider most photons are emitted from fireball regions with $T \sim T_{c}$ near the quark-hadron phase transition, but that their effective temperature is significantly enhanced by strong radial flow. Although a very hot, high-pressure early collision stage is required for generating this radial flow, we demonstrate that the experimentally measured large effective photon temperatures $T_{eff} > T_{c}$ , taken alone, do not prove that any electromagnetic radiation was actually emitted from regions with true temperatures well above $T_{c}$ . We explore tools that can help to provide additional evidence for the relative weight of photon emission from the early quark-gluon and late hadronic phases. We find that the recently measured centrality dependence of the total thermal photon yield requires a larger contribution from late emission than presently encoded in our hydrodynamic model.

Received 11 August 2013
Revised 28 March 2014

DOI:https://doi.org/10.1103/PhysRevC.89.044910

Authors & Affiliations

Chun Shen^* and Ulrich Heinz

Department of Physics, The Ohio State University, Columbus, Ohio 43210-1117, USA

Jean-François Paquet

Department of Physics, McGill University, 3600 University Street, Montreal, Quebec, Canada H3A 2T8

Charles Gale

Department of Physics, McGill University, 3600 University Street, Montreal, Quebec, Canada H3A 2T8 and Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, D-60438 Frankfurt am Main, Germany

^*shen@mps.ohio-state.edu

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Vol. 89, Iss. 4 — April 2014

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Images

Figure 1
Measured and calculated photon spectra in $0 - 20 %$ centrality $Au + Au$ collisions at the RHIC (a) and $0 - 40 %$ centrality $Pb + Pb$ collisions at the LHC (b). Photons from thermal sources and from pQCD are shown separately, as well as their sum. The $Au + Au$ collision data at RHIC (a) are from the PHENIX Collaboration [6], and those for $Pb + Pb$ collisions at the LHC (b) are from the ALICE Collaboration [7]. See text for a detailed discussion. The shaded curves below 1 GeV are to remind of the uncertainties in extrapolating pQCD to low values of the photon transverse momentum [25].
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Figure 2
The inverse photon slope parameter $T_{eff} = - 1 / slope$ as a function of the local fluid cell temperature, from the equilibrium thermal emission rates (solid green lines) and from hydrodynamic simulations (open and solid circles), compared with the experimental values (horizontal lines and error bands) for (a) $Au + Au$ collisions at the RHIC and (b) $Pb + Pb$ collisions at the LHC. The experimental values and error bands in panel (a) are from the PHENIX Collaboration [6] and those in panel (b) are from the ALICE Collaboration [7]. We note that the corresponding plot for $Au + Au$ collisions at $20 - 40 %$ centrality looks very similar to the case of $0 - 20 %$ centrality shown in panel (a), in agreement with what the PHENIX Collaboration [6] found. See text for a detailed discussion.
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Figure 3
The inverse photon slope parameter $T_{eff} = - 1 / slope$ as a function of emission time from hydrodynamic simulations, compared with the experimental (time-integrated) values (horizontal lines and error bands), for (a) $Au + Au$ collisions at the RHIC and (b) $Pb + Pb$ collisions at the LHC. The blue solid lines and surrounding shaded areas show for comparison the time evolution of the average fireball temperature and its standard deviation. See text for further discussion.
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Figure 4
Contour plots of the normalized differential photon yields $\frac{d N^{γ} (T, τ) / (d y d T d τ)}{d N^{γ} / d y}$ [panels (a) and (c)] and $\frac{d N^{γ} (T_{eff}, τ) / (d y d T_{eff} d τ)}{d N^{γ} / d y}$ [panels (b) and (d)] for $Au + Au$ collisions at the RHIC at 0–20% centrality [panels (a) and (b)] and for $Pb + Pb$ collisions at the LHC at 0–40% centrality [panels (c) and (d)]. The color bars translate the colors into absolute values [in $c /$ (GeV fm)] for the quantities plotted. See text for discussion.
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Figure 5
The differential photon yield, as a function of the temperature $T$ , for different windows in the photon transverse momentum for $Au + Au$ collisions at the RHIC (a) and $Pb + Pb$ collisions at the LHC (b).
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Figure 6
The centrality dependence of the photon yield for $Au + Au$ collisions at the RHIC. The centrality may be expressed in terms of (a) $N_{part}$ or (b) $d N^{ch} / d η$ .
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