Beam Energy and Centrality Dependence of Direct-Photon Emission from Ultrarelativistic Heavy-Ion Collisions.

The PHENIX collaboration presents first measurements of low-momentum (0.4<p_{T}<3  GeV/c) direct-photon yields from Au+Au collisions at sqrt[s_{NN}]=39 and 62.4 GeV. For both beam energies the direct-photon yields are substantially enhanced with respect to expectations from prompt processes, similar to the yields observed in Au+Au collisions at sqrt[s_{NN}]=200. Analyzing the photon yield as a function of the experimental observable dN_{ch}/dη reveals that the low-momentum (>1  GeV/c) direct-photon yield dN_{γ}^{dir}/dη is a smooth function of dN_{ch}/dη and can be well described as proportional to (dN_{ch}/dη)^{α} with α≈1.25. This scaling behavior holds for a wide range of beam energies at the Relativistic Heavy Ion Collider and the Large Hadron Collider, for centrality selected samples, as well as for different A+A collision systems. At a given beam energy, the scaling also holds for high p_{T} (>5  GeV/c), but when results from different collision energies are compared, an additional sqrt[s_{NN}]-dependent multiplicative factor is needed to describe the integrated-direct-photon yield.

The PHENIX collaboration presents first measurements of low-momentum (0.4 < pT < 3 GeV/c) direct-photon yields from Au+Au collisions at √ s N N =39 and 62.4 GeV. For both beam energies the direct-photon yields are substantially enhanced with respect to expectations from prompt processes, similar to the yields observed in Au+Au collisions at √ s N N =200. Analyzing the photon yield as a function of the experimental observable dN ch /dη reveals that the low-momentum (>1 GeV/c) directphoton yield dN dir γ /dη is a smooth function of dN ch /dη and can be well described as proportional to (dN ch /dη) α with α≈1. 25. This scaling behavior holds for a wide range of beam energies at the Relativistic Heavy Ion Collider and the Large Hadron Collider, for centrality selected samples, as well as for different, A+A collision systems. At a given beam energy the scaling also holds for high pT (> 5 GeV/c) but when results from different collision energies are compared, an additional √ s N N -dependent multiplicative factor is needed to describe the integrated-direct-photon yield.
Measurements of direct photons provide information about the strongly coupled quark-gluon plasma (QGP) produced in heavy ion collisions and its "fireball" evolution to hadron resonance matter. Due to their long mean free path photons do not interact with the matter and thus their spectra provide information about all stages of the collision integrated over space and time [1][2][3]. In particular low p T photons in the momentum range up to a few GeV/c are expected to carry information about the hot and dense fireball.
In experiments direct photons are detected simultaneously with a much larger number of photons from hadron decays, mostly from π 0 and η mesons. The main challenge is to subtract these decay contributions from the measurement to obtain the photons directly emitted from the collision. In addition to photons from the hot fireball, direct photons include those emitted from initial hard scattering processes, such as quark-gluon Compton scattering among the incoming partons [4]. Disentangling this prompt component from the photons emitted from the fireball is an additional challenge.
First evidence for direct photon emission from heavy ion collisions came from WA98 [5,6], with conclusive results only for p T > 1.5 GeV/c. PHENIX established that a large number of low p T direct photons are radiated from the fireball created in Au+Au collisions at √ s N N = 200 GeV [7] and that their yield increases with a power of N part while the inverse slopes of the spectra are independent of the centrality of the collisions [8]. Simultaneously, low p T direct photon emission exhibits a significant azimuthal anisotropy with respect to the re-action plane [9,10].
ALICE has published [11,12] similar observations of low p T direct photons from Pb+Pb collisions at √ s N N = 2760 GeV.
STAR also reported a measurement of the direct photon yields in Au+Au at √ s N N = 200 GeV [13], the published yields are significantly lower compared to PHENIX results. The origin of the discrepancy remains unresolved [14].
A large body of theoretical work on low p T direct photon emission in A+A collisions exists in the literature. Many model calculations are qualitatively consistent with the data, but a quantitative description remains difficult, primarily due to the simultaneous observation of large yields and large azimuthal anisotropies .
To provide further insights, PHENIX is investigating the system size dependence of direct photon emission from heavy ion collisions by varying beam energy, centrality, and collision species. In this publication we present low-p T direct photon data from Au+Au collisions at √ s N N = 39 GeV and 62.4 GeV taken with the PHENIX experiment in 2010. We compare the centrality selected spectra and integrated yields from Au+Au to those from p+p collisions at √ s N N = 200 GeV [7,8], Cu+Cu collisions at √ s N N = 200 GeV [39], and Pb+Pb collisions at √ s N N = 2760 GeV [11]. This study covers a factor of 70 in √ s N N and nearly two orders of magnitude in system size. The 39 and 62.4 GeV direct photon spectra are obtained from two data samples of minimum-bias (MB) Au+Au collisions that have a total of 7.79×10 7 and 2.12×10 8 events, respectively. The MB trigger and cen-trality selection is derived from data taken with the PHENIX beam-beam counters [40]. The data analysis uses the same techniques deployed for the analysis of the √ s N N = 200 GeV Au+Au data [8], which were taken in the same year under nearly identical conditions. Here we give a brief overview of the setup and data analysis, and refer to our previous publication for more details [8].
Photons are reconstructed through their conversion to e + e − pairs in the detector material, specifically the readout boards of the hadron blind detector (HBD) [41] that are located at a radius of 60 cm from the beam axes. The trajectories and momenta of the e + and e − are determined by the central arm tracking detectors [42]. Each of the two central arms covers 90 • in azimuth and a rapidity range of |η| < 0.35. A transverse momentum cut, p T > 200 MeV/c, is applied to each trajectory. To identify trajectories as e + or e − candidates, we require a minimum of three associated signals in the ring-imaginǧ Cerenkov detector [43] and that the energy measured in the electromagnetic calorimeter (EMCal) [44] matches the measured momentum (E/p > 0.5).
All e + and e − reconstructed in the same arm are matched to pairs. In the 2010 setup there is no tracking near the collision point, so the origin of an individual track is unknown. Thus, for each e + e − pair the mass is calculated twice: first assuming the pair originated at the event vertex (m vtx ), then assuming the e + e − is a conversion pair from the HBD readout boards (m HBD ). In the latter case, m HBD will be consistent with zero, within a mass resolution of a few MeV/c 2 , while m vtx will be about 12 MeV/c 2 . With a cut on both masses a sample of photon conversion is selected with a purity of about 99%. The combinatorial background is negligible, because the conversion material, in radiation length X/X 0 ≈3%, is about 10 times thicker than materials closer to the vertex; and it is at a relatively large distance from the event vertex. The 1% contamination is mostly from π 0 Dalitz decays, π 0 → γe + e − , and from conversions in front of the HBD readout boards.
The direct photon content in the photon sample is determined by the ratio R γ , which is the ratio of all emitted photons (γ incl ) to those from hadron decays (γ hadron ). The ratio R γ is determined from a double ratio: All quantities in this double ratio are functions of the conversion photon p ee T . The measured quantities are the number of detected conversion photons N incl γ and the subset of those that are tagged as π 0 decay photon N π 0 ,tag γ . The tagged photons N π 0 ,tag γ are determined statistically in bins of the p ee T . Each conversion photon is paired with all showers with E > 400 MeV measured in the EMCal of the same arm. The invariant e + e − γ mass is calculated and the counts above the combinatorial background in the π 0 mass peak give N π 0 ,tag γ . To convert the ratio N incl γ /N π 0 ,tag γ to γ incl /γ π 0 only N π 0 ,tag γ needs to be corrected for the momentum averaged conditional acceptance-efficiency ε γ f that the second decay photon can be reconstructed in the EMCal. All other corrections to the numerator and denominator cancel [8]. Because rather loose cuts are applied to the EMCal showers, ε γ f is mostly determined by the π 0 decay kinematics, the detector geometry, and the energy cut. Thus, ε γ f can be calculated to a few percent accuracy using a Monte-Carlo simulation of π 0 decays. Photons from pions are determined from the measured π 0 spectra [45] and two body decay kinematics. The spectrum of decay photons (γ hadron ) is derived from γ π 0 and the η/π 0 ratio [46], which is independent of collision system and energy, with additional contribution from heavier mesons of about 4%.
Once R γ is established, the direct photon spectrum can be calculated as: The uncertainty on γ hadron , approximately 10% [8], cancels in R γ (with that of γ π 0 in Eq. (1)) but has to be applied to γ direct . The systematic uncertainties on the 39 and 62.4 GeV data are similar in magnitude to those for 200 GeV presented in [8]. For integrated yield we treat every systematic uncertainty as p T -correlated in the interest of consistency throughout the different data sets. Figure 1 shows the invariant yield of direct photons normalized to (dN ch /dη) 1.25 , this normalization is dis- To compare data from different beam energies, collisions species, and collision centralities we use the measured charged particle multiplicity dN ch /dη as measure of the system size at hadronization. For a fixed beam energy dN ch /dη is roughly proportional N part . However, unlike N part , dN ch /dη does not saturate but increases monotonically with beam energy for collisions of the same nuclei at the same impact parameter.
Direct photon production at high p T results from hard scattering, which at a fixed √ s N N scales with the number of binary collisions N coll . We find that N coll exhibits a remarkably simple relation with the dN ch /dη that takes the form: This is shown in Fig. 2 where N coll is plotted versus dN ch /dη for different √ s N N . PHENIX data are taken from [51] and ALICE data at √ s N N = 2760 GeV are from [52]. The exponent α is determined through a simultaneous fit to all data shown in Fig. 2   shown together with data from p+p at the same beam energy. The normalized spectra from Au+Au are very similar for all three centrality selections. Above 3-4 GeV/c the normalized yield is the same as for p+p collisions and can be reproduced by perturbative quantum chromodynamics (pQCD) calculations with a renormalization and factorization scale of µ = 0.5p T [50,53]. Here the pQCD calculation was normalized to the experimental dN ch /dη for √ s = 200 GeV from [54]. Also shown on (b) is an empirical fit to the p+p data [55] of the form [39]. Below 2-3 GeV/c the normalized yield in Au+Au collisions is significantly enhanced compared to that in p+p collisions, but follows the same scaling behavior with (dN ch /dη) 1.25 independent of centrality. Fig. 1 show that for p T below 2-3 GeV/c the same scaling with (dN ch /dη) 1.25 occurs for different √ s N N and collisions systems. Below 2

Panels (a) and (c) of
GeV/c the spectra have very similar shape. We note that the apparent difference of the inverse slopes reported by PHENIX [8] and ALICE [11] is largely due to the different fit ranges used [56].
At higher p T the expected difference with √ s N N is observed. Like for √ s N N = 200 GeV, at high p T the 2760 GeV data are well reproduced by the pQCD calculation, though only above 5-6 GeV/c rather than 3-4 GeV/c. Note that the extrapolated pQCD calculations for p+p at different √ s seem to converge to the same normalized yield at low p T , but at a tenth of the A+A yield.
We quantify direct photon emission by integrating the invariant yield above p T =1.0 GeV/c and p T =5.0 GeV/c. The integrals with the lower threshold will be dominated by excess low p T photons unique to A+A collisions, while the integrals with the higher threshold are more sensitive to photons from initial hard scattering processes. The re- For the p T threshold of 5 GeV/c the integrated yields from Au+Au and p+p at 200 GeV follow the same (dN ch /dη) 1.25 trend, and are described by the pQCD calculation. The 2760 GeV data are also consistent with (dN ch /dη) 1.25 but show a significantly higher yield than at 200 GeV data at the same dN ch /dη. The N coll scaled pQCD calculation is about 30% below the data, which may not be significant considering the 25% systematic uncertainty on the calculation.
While the functional form A(dN ch /dη) α describes the integrated direct photon yields well, it is not unique. For instance the data can be equally well fitted by A(dN ch /dη) + B(dN ch /dη) 4/3 [57]. For the data in Fig. 3 this fit results in parameters A = (8.68 ± 3.06) · 10 −4 and B = (3.09 ± 0.45) · 10 −4 . The important point is that A+A data from different centralities and a wide range of collision energies can be empirically described in terms of dN ch /dη with just two parameters, suggesting some fundamental commonality in the underlying physics.
There are two main conclusions from the analyses pre-sented in this paper. (i) At a given beam energy the direct photon yield scales with dN ch /dη 1.25 or N coll for all observed p T . There seems to be no qualitative change in the photon sources and/or their relative contributions for different collision centrality or system size. (ii) From √ s N N = 39 to 2760 GeV the same scaling is observed for p T < 2 GeV/c. This suggests that the main sources contributing to this p T range are very similar also across beam energies.
If thermal radiation is the source of low p T direct photons, the similarity at the same dN ch /dη across beam energies and centralities for p T < ∼ 2 GeV/c, suggests that the bulk of the matter that emits the radiation is similar in terms of temperature and space time evolution. This would be natural, if most of the photons are emitted near the transition from QGP to hadrons.
While at high p T the scaled yields in p+p and A+A are identical, at low p T they differ by a factor of 10. This implies that there must be a transition from the small p+p yield to the enhanced A+A-like low p T yields in the dN ch /dη range of ≈2 to 20, which will be accessible with the data taken by PHENIX with small systems p+Au, d+Au, and 3 He+Au.
We thank the staff of the Collider-Accelerator and Physics Departments at Brookhaven National Laboratory and the staff of the other PHENIX participating institutions for their vital contributions. We acknowledge support from the Office of Nuclear Physics in the Office of Science of the Department of Energy, the National Science Foundation, Abilene Christian University Research