A Reanalysis of Single Photon Data at CERN SPS
Charles Gale, Rupa Chatterjee, Dinesh K. Srivastava, Sangyong Jeon
aa r X i v : . [ nu c l - t h ] S e p A Reanalysis of Single Photon Data at CERN SPS
Charles Gale a , , Rupa Chatterjee b , Dinesh K. Srivastava b , and Sangyong Jeon a a Department of Physics, McGill University, Montreal, Canada H3A 2T8 b Variable Energy Cyclotron Centre, 1 / AF Bidhan Nagar, Kolkata 700 064, India
Abstract
We reanalyze the WA98 single photon data [1] at CERN SPS by incorporating several recentdevelopments in the study of prompt and thermal photon production from relativistic heavy ioncollisions [2]. Isospin and shadowing corrected NLO pQCD, along with an optimized scalefor factorization, fragmentation and renormalization are considered for prompt photon produc-tion. Photons from thermal medium are estimated by considering a boost invariant azimuthallyanisotropic hydrodynamic expansion of the plasma along with a well tested equation of state andinitial conditions. A quantitative explanation of the data is obtained by combining κ × promptwith thermal photons, where κ is an overall scaling factor. We show that, elliptic flow of thermalphotons can play a crucial role to distinguish between the ‘with’ and ‘without’ phase transitionscenarios at SPS energy.
1. Introduction
The first observation of single photons by the WA98 Collaboration at CERN SPS is con-sidered as a well anticipated turning point in the study of relativistic heavy ion collisions usingelectromagnetic probes [1]. Earlier observations like the one by the WA80 [3] Collaboration,provided only a useful upper limit of this study (for recent developments in the field of directphoton production from relativistic heavy ion collisions, see Ref. [4, 5]). The study of electro-magnetic radiations, and in particular photons, as a probe of heavy ion collisions is advantageouscompared to the study of hadrons, for two main reasons. First of all, photons are emitted fromeach and every stage of the expanding system, whereas hadrons are emitted only from the surfaceof freeze-out after su ff ering strong interactions. Secondly, photons do not su ff er final state inter-action (for being electromagnetic in nature, their mean free path is larger than the system size)and carry undistorted information from the production point to the detector. The major problemin the study of single photons from heavy ion collisions arises from the very small signal tobackground ratio. However, recent developments in the background subtraction methods havereduced the size of error bars in the direct to decay ratio for photons considerably. We reanalyzethe single photon WA98 data by incorporating several new improvements in our understandingof prompt photon production from heavy ion collisions and considering the latest developmentsin the field of thermal photon production along with a well defined equation of state and suitableinitial conditions [2]. Speaker, Quark Matter 2009 (QM09), March 30-April 4, 2009, Knoxville, TN, USA.
Preprint submitted to Nuclear Physics A November 1, 2018 .0 3.0 4.0 5.0 p T (GeV/c) -1 E d σ / d p ( pb / G e V c - ) NLO pQCD (Sum)C+AnnFragmentationNA3; Conversion TriggerNA3; Calorimeter Trigger E704E629
Single Photons; pp@s =19.4 GeV Q= µ R = µ F =p T /2 p T (GeV/c) R AA A+A, 17.3 AGeV
Prompt γ, NLO pQCD pn/ppnn/ppPbPb/ppPbPb/pp (EKS98)
Figure 1: [Left panel] Prompt photons from p + p collisions at √ s = + pcollisions and those estimated from p + C collisions by E629 [7] and NA3 [8] experiments are given for a comparison.[Right panel] E ff ect of isospin and parton shadowing on the production of prompt photons at √ s NN =
2. Reanalysis of single photon data at CERN SPS
The study of prompt photon production in p + p collisions has reached a higher level ofsophistication and all the available data have now been successfully analyzed with NLO pQCDtreatment [9] without the inclusion of intrinsic k T for protons. In particular, the suppression ofsingle photons at large p T for Au + Au collisions with respect to the single photons resulting from p + p collisions at the same nucleon-nucleon center of mass energy may be largely due to thedi ff erence in valence quark structure of protons and neutrons [10].We calculate the prompt photon production from p + p collisions using NLO pQCD treatmentalong with an optimized scale for factorization, fragmentation and renormalization (all equal to p T /
2) at √ s = . k T ) and compare our results withvarious experimental data available at that energy (with proper mass number normalization for p + C collisions). This comparison is done as no experimental data are available for p + p or n + n collisions at the WA98 center of mass energy ( √ s NN = . √ s = . + annihilation processes. Our result using NLO pQCD matches well with the NA3 [8]data, while it underestimates the E704 [6] and E629 [7] data, same as reported by earlier studies.For prompt photon production from 158A GeV Pb + Pb collisions, isospin and shadowing [11]corrected NLO pQCD treatment is used with the same scaling factor of p T / ff ect of isospin and shadowing on photon productionfrom heavy ion collisions are investigated by calculating nuclear modification factor ( R AA ) asfunction of p T and x T ( = p T / √ s ) for di ff erent beam energies. Results for p + p normalized R AA as a function of p T for p + n, n + n, and Pb + Pb collisions are shown in right panel of Fig. 1. We seethat the photon production from Pb + Pb collisions is suppressed significantly in the intermediateand high p T range, compared to the production from p + p collisions. For thermal photons, centrality dependent azimuthally anisotropic boost invariant ideal hy-drodynamics is used along with di ff erent sets of initial parameters. A well tested equation of state2 .0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 p T (GeV/c)10 -9 -7 -5 -3 -1 E d N / d p ( c / G e V ) WA98Prompt (NLO )QMHMThermal (QM+HM)Thermal+2.7XPrompt
Single Photons; Pb+Pb@SPS >=0.38 GeV, τ =0.2 fm/c p T (GeV/c)10 -9 -7 -5 -3 -1 E d N / d p ( c / G e V ) WA98PromptQMHMThermal(QM+HM)Thermal+5.9XPrompt
Single Photons; Pb+Pb@SPS >=0.21 GeV, τ =1.0 fm/c Figure 2: Fit to single photon spectra from Pb(158A GeV) + Pb collisions measured by the WA98 [1] experiment for τ = . / c [left panel] and 1.0 fm / c [right panel] using scaling factor κ = is used considering a first order phase transition from the plasma state to the hadronic phase at atransition temperature T c ( ∼ ff erent values of τ are considered ranging from0.2 fm / c to 1.0 fm / c (in steps of 0.2 fm / c ) keeping the total entropy of the system fixed. The timeevolution of average energy density h ǫ i , average temperature h T i and average radial flow velocity h v T / c i at di ff erent τ are compared. We find that the values of h ǫ i ( ∼ T ) changes significantly atlarge τ with changing values of τ , whereas h T i and h v T / c i are not a ff ected much [see Ref. [2] fordetail]. Also, the e ff ective temperature, T e ff = T √ (1 + v T ) / (1 − v T ), (or the blue shifted tempera-ture) is calculated as function of proper time at di ff erent τ to see the combined e ff ect of coolingand expansion (velocity). Thermal photons at di ff erent τ are calculated considering standardrates (QGP photons from Ref. [12], and HM photons from Ref. [13]) of photon production for0-10% most central collisions with freeze-out energy density of about 0.075 GeV / fm .We find that the prompt photon production is about 17% of the total yield measured by WA98and the thermal photon result is almost similar to prompt photon production at τ = . / c .We also note that the thermal photons from hadronic phase are not a ff ected significantly withchanging τ . A quantitative description of the WA98 experimental data is obtained by usingthe relation ‘Thermal + κ × Prompt ′ where, κ is adjusted to reproduce the photon production at p T = .
55 GeV / c . For all τ , a normalization at the same p T ( = / c ) provides a gooddescription of the data in the entire p T range. We find that the scaling factors κ = τ = / c respectively provide agood quantitative agreement with the WA98 data [shown in Fig. 2]. We argue that the factor κ for prompt photons accounts for the Cronin e ff ect, in the case of nucleus-nucleus collisions, aswell as a pre-equilibrium contribution which must surely be included when τ is large. In a potentially interesting observation we show that, one additional experimental result, i.e,the elliptic flow for thermal photons [14] could actually distinguish between the di ff erent valuesof τ . The elliptic flow results for di ff erent τ along with the hadronic matter contribution for158A GeV Pb + Pb collisions at CERN SPS are shown in right panel of Fig. 3. We note that severalearlier studies have explained the WA98 data considering only the formation a hot hadronic gasin the collision and without the formation of QGP phase [15]. The estimation of photon flow at3
S S S S S S S S S S S S SS S S S S S S S S S S S S S p T (GeV/c) v ( p T ) Thermal Photons; Pb+Pb@SPS
S S v (QM+HM)0.5Xv (HM) p T (GeV/c) v ( p T ) Pb+Pb@SPS; b = 7 fm ρ Figure 3: v for thermal photons for di ff erent τ , along with contributions from hadronic matter. [Right panel] v ( p T ) forprimary ρ mesons from Pb + Pb collisions having b = ff erent τ . SPS can distinguish between the two scenarios of ‘with’ and ‘without’ phase transitions as thenature of v would be completely di ff erent in the two cases. We also compute the particle spectraand v ( p T ) for several hadrons and show explicitly that both the spectra and elliptic flow resultsremain una ff ected with changing values of τ for hadrons. v ( p T ) for ρ mesons at di ff erent τ areshown in right panel of Fig. 3.In conclusion, we present a quantitative explanation of the WA98 single photon data at CERNSPS by incorporating several recent developments in the field of prompt and thermal photon pro-duction from heavy ion collisions. Thermal photons at di ff erent τ along with prompt contribu-tion enhanced by a ‘ κ ’ factor describes the data quite well in the entire p T range. We also showthat thermal photon v can distinguish between the di ff erent τ and phase transition scenarios atSPS energies. Acknowledgments
C. G. and S. J. acknowledge funding by the Natural Sciences and Engineering ResearchCouncil of Canada. D. K. S. would like to acknowledge the warm hospitality at McGill Univer-sity, where part of the work was done under the McGill India Strategic Research Initiative.
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