Enhanced Direct Photon Production in Au+Au Collisions at 200 GeV in PHENIX
aa r X i v : . [ nu c l - e x ] J un Proc. 25th Winter Workshop onNuclear Dynamics (2009) 000–000 ¯ on Nuclear Dynamics ¯¯ Big Sky, Montana, USAF¯ebruary 1–8, 2009
Enhanced Direct Photon Production in Au+Au Collisionsat √ s NN = 200 GeV in PHENIX S. Bathe for the PHENIX collaboration RIKEN-BNL Research CenterBrookhaven National LaboratoryUpton NY 11973, USA
Abstract.
The production of electron pairs with p T between 1 and 5 GeV/cand m <
300 MeV has been measured at mid-rapidity in √ s NN = 200 GeV p + p and Au+Au collisions by the PHENIX experiment at RHIC. A significantexcess above the hadronic background was observed in both p + p and Au+Aucollisions. Treating the excess as internal conversion of direct photons, thedirect photon yield in Au+Au was found to be enhanced compared to thebinary-scaled p + p yield. The enhancement is consistent with an exponentialinverse slope of 221 ± ±
18 MeV and predictions from hydrodynamical modelswith initial temperature between 300 and 600 MeV at formation times of 0.6–0.15 fm/c.
Keywords: direct photons, nucleus-nucleus collisions, p + p collisions, heavy ion,elactron pair production, PHENIX, RHIC PACS:
1. Introduction
A multitude of results from the Relativistic Heavy Ion Collider (RHIC) at BrookhavenNational Laboratory (BNL) indicates the creation of a high-density, thermalizedmedium in ultra-relativistic collisions of heavy ions [ 1]. Such a medium is expectedto radiate thermal photons [ 2], which, once produced, leave the medium unscathed.Thermal photons from the partonic phase of the collision are predicted to dominatethe direct photon spectrum in the transverse momentum ( p T ) range of 1–3 GeV/cas illustrated in Fig. 1 [ 2]. However, here direct photons are submerged in a back-ground of hadronic decay photons, mainly from the π and η . This backgroundconstitutes a major experimental challenge in the conventional, calorimeter-basedmeasurement. It can be overcome, though, by measuring low-mass electron pairs ina mass range where electron pairs from the π Dalitz decay do not contribute [ 3]. S. Bathe et al. q t [GeV] q d N g / d q [ G e V ] Hadron GasQGP (T i =370MeV)initial pQCD (pp)sum Central Au+Au (s =200AGeV) |y|<0.35
Direct photon sources at RHIC[ 2]. [GeV] ee m ] - [ G e V ee / d m ee d N γ / N -6 -5 -4 -3 -2 -1 γ direct πη Fig. 2.
Illustration of the pair yieldmass dependence for direct photons aswell as for π and η Dalitz pairs.The electron-pair yield above the hadronic background can be treated as internalconversion of direct photons [ 4].
2. Internal Conversion Method
Any source of high-energy photons also emits virtual photons with very low mass[ 4]. Those virtual photons then convert to low-mass e + – e − pairs, which can bemeasured ( Internal Conversion Method ). The pair yield per direct photon falls withthe pair mass as: d n ee dm = 2 α π m r − m e m (cid:16) m e m (cid:17) Sdn γ . (1)Here α is the fine structure constant, m e and m are the masses of the electron andthe e + – e − pair, respectively, and S is a process dependent factor that goes to 1 as m → m ≪ p T . Equation 1 also describes the relation between photons fromhadron decays (e.g. π , η → γγ , and ω → γπ ) and e + – e − pairs from Dalitz decays( π , η → e + – e − γ and ω → e + – e − π ). For π and η , the factor S is given by S = | F ( m ) | (1 − m M h ) [ 5], where M h is the meson mass and F ( m ) is the form factor.Figure 2 illustrates the pair yield mass dependence for direct photons as well as for π and η Dalitz pairs. The cut-off of the π pairs at the π mass can be exploitedto increase the signal-to-background ratio from 10%, where it is comparable to thesystematic uncertainty and therefore not significant, to 50%, making a significantmeasurement possible. Since the measurement at low p T is systematics limited, thesimultaneous reduction in statistical significance is an acceptable trade-off . There are about 0.001 virtual photons with m ee > M π for every real photon. irect Photons in PHENIX 3
3. Data Set And Backgrounds
The analysis is based on two data sets: Au+Au at √ s NN = 200 GeV acquiredin 2004 consisting of 0.8 billion minimum bias events (4.9 pb − p + p equivalent); p + p at the same cms energy acquired in 2005 with 2.25 pb − . Charged trackswere measured with the Drift Chamber and Pad Chamber of the PHENIX [ 6]Central Arms covering | η | < .
35 and ∆ φ = 2 × π/ cross pairs withone electron/positron from either virtual photon in a double-Dalitz decay; jet pairs from two different Dalitz decays within the same jet or from back-to-back jets.These contributions can be well understood in a Monte Carlo calculation and havebeen subtracted.
4. Signal Extraction
After subtraction of the combinatorial background and the cross and jet pairs, thepair mass spectrum is compared to a “cocktail” of known hadronic sources [ 7, 8]. ) (GeV/c - e + e m0 0.05 0.1 0.15 0.2 0.25 0.3 / G e V ) i n P H E N I X acce p t a n ce ( c - e + e d N / d m -9 -8 -7 -6 -5 -4 -3 (a) p+p <2 GeV/c T T T T ) (GeV/c - e + e m0 0.05 0.1 0.15 0.2 0.25 0.3 / G e V ) i n P H E N I X acce p t a n ce ( c - e + e d N / d m -7 -6 -5 -4 -3 -2 -1 (b) Au+Au (Min Bias) Fig. 3.
Pair mass spectra for data (points) and hadronic cocktail (lines) in thePHENIX acceptance for different p T intervals for p + p (left) and Au+Au (right) [3]. S. Bathe et al.Figure 3 shows this comparison for different p T intervals for both p + p and Au+Au.The cocktail is normalized to the data for m <
30 MeV, where the π Dalitz decaydominates the yield. The “knee” at 100 MeV comes from the π cut-off leading tothe 80% background reduction mentioned above.In p + p , the pair yield is consistent with the hadronic background for thelowest p T interval. At higher p T a small excess is visible for m > m π . In Au+Au amuch larger excess appears at all p T , indicating an enhanced production of virtualphotons .To quantify the direct photon fraction, the mass spectrum is fit with a two-component function f ( m ee ) = (1 − r ) f c ( m ee ) + rf dir ( m ee ) as illustrated in Fig. 4.Here f c ( m ee ) is the shape of the cocktail mass distribution (shown in Fig. 3), f dir ( m ee ) is the expected shape of the direct photon internal conversion, and r is the fit parameter. Both f c ( m ee ) and f dir ( m ee ) are separately normalized to thedata for m ee <
30 MeV/ c , where their shapes are nearly identical. This preservesthe meaning of r as the real direct photon fraction. From the agreement between (GeV/c) - e + e m0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 / G e V ) i n P H E N I X acce p t a n ce ( c - e + e d N / d m -5 -4 -3 -2 -1 <1.5 GeV/c T Au+Au (MB) 1.0
Illustration of two-component fit to the mass distribution [ 3].data and fit it can be concluded that the data matches the expected shape for directphotons.The so extracted direct photon fraction, r , is plotted as a function of p T inFig. 5. While in case of p + p the direct photon fraction is consistent with pQCD,for Au+Au r is enhanced above pQCD.As this measurement is based on shape differences to extract the direct photonfraction, the η/π ratio is the largest source of systematic uncertainty. This results This excess is in a different kinematic region (higher p T , lower mass) than the low-massenhancement reported in [ 7], which is expected to be dominated by the hadronic gas phase. irect Photons in PHENIX 5 (GeV/c) T p1 1.5 2 2.5 3 3.5 4 4.5 γ /i n c l u s i ve γ r = d i r ec t (a) p+p (GeV/c) T p1 1.5 2 2.5 3 3.5 4 4.500.050.10.150.2 (b) Au+Au Min. Bias Fig. 5.
Direct photon fraction, r , as a function of p T for p + p and Au+Au eventscompared to a pQCD calculation for three different scales. In the case of Au+Authe pQCD result is scaled by the nuclear overlap function, T AA [ 3].in a 7% uncertainty in p + p and 17% in Au+Au. Other sources contribute only afew percent as the cocktail is normalized to the data and no absolute normalizationis required.In the next step, r is converted into the direct photon yield as dN dir ( p T ) = r × dN incl ( p T ). The inclusive photon yield for each p T bin is determined by dN inclγ = N dataee × ( dN cγ /N cee ), where N dataee and N cee are the measured and the absolutelynormalized cocktail e + – e − pair yields, respectively, both for m ee <
30 MeV/ c ;and dN cγ is the yield of photons from the cocktail. Here we use the fact that theratio of the photon yield to the e + – e − pair yield for m ee <
30 MeV/ c calculatedfrom Eq. 1 is the same within a few percent for any photon source. The systematicuncertainty of γ incl is 14% from the e + – e − pair acceptance.
5. Results
Figure 8 shows the invariant yield of direct photons as a function of p T for p + p andthree different centrality classes in Au+Au. The p + p data is again compared tothe pQCD calculation. The calculation is consistent with the data for p T > A pp (1 + p T /b ) − n , fits the data over the entire p T range. S. Bathe et al. The modified power law appears to yield an at least as good description of the dataat low p T as the pQCD calculation. What is the significance of this observation?It is obvious that the power-law behavior of hard scattering has to break down for p T →
0. For hadrons, soft production sets in with an exponential slope. This isillustrated in Fig. 6, which shows a parameterization of π production in p + p [ [GeV/c] T p ] c - [ m b G e V dp σ E d -3 -2 -1
110 exp(-5.6*pT)pow(pT,-8.1) data para π hard =data-expturnon=hard/pow Fig. 6.
Parameterization of π produc-tion in p + p [ 9] and its various contri-butions (for details see text). (GeV/c) T p ) c - ( m b G e V dp σ E d -6 -5 -4 -3 -2
10 =4.02n A=5.39e-03, b=3.62, n /b) (1+pA B=9.78e-03, n=5.32 nT pB ICA EMC chi2/ndf=16.2/7 chi2/ndf=59.1/8 direct photon Fig. 7.
Fit of direct photon cross sec-tion with both a power law and a mod-ified power law.9]. The parameterization is the sum of a power law and an exponential with aWoods-Saxon transition between the two. The two functions are shown separately.The exponential dies out at high p T while the power law diverges at low p T . Thehard-scattering contribution can be understood as the difference between the dataparameterization and the exponential contribution. One can see that it flattens outtowards low p T , deviating from the power law. This flattening corresponds to anonset of hard scattering as illustrated by the ratio of the hard scattering contributionto the power law.This onset is not directly observable for hadrons as the production at low p T is dominated by soft physics. Direct photons, however, are only produced in hardscatterings. This makes the onset of hard scattering at low p T directly measurable.The onset has also been measured in Drell-Yan production [ 10].To evaluate the statistical significance of the onset, the PHENIX data werefitted with both a power law and a modified power law. As shown in Fig. 7, themodified power law yields a smaller reduced χ than the pure power law. For 1 < p T < T AA -scaled modified power law that was fit to the p + p data (Fig. 8). It can bewell described, however, if an exponential is added. The resulting fit yields negativeinverse exponential slopes of about 220 MeV . If the medium were static, T could If the p + p data are fit with a pure power law, T increases by 24 MeV in central events. irect Photons in PHENIX 7 (GeV/c) T p1 2 3 4 5 6 7 ) c - ( m b G e V / dp σ ) o r E d c - ( G e V N / dp E d -7 -6 -5 -4 -3 -2 -1 AuAu MB x10 AuAu 0-20% x10AuAu 20-40% x10p+p
Fig. 8.
Invariant yield of direct photons as a function of p T for p + p and threedifferent centrality classes in Au+Au (solid symbols). The result of an earlier EMCalmeasurement is also shown (open symbols) [ 11, 12]. The p + p data is comparedto a pQCD calculation shown as three lines for different scales. The dashed line isa fit of a modified power law to the p + p data. The Au+Au data are compared tothe T AA -scaled p + p fit (dashed line). The solid line shows the result of a fit wherean exponential is added to the T AA -scaled p + p fit [ 3].be interpreted as its temperature. For a more realistic temperature estimate, thedata is compared to hydrodynamical models. Models that fit the data assume initialtemperatures, T i , between 300 and 600 MeV at formation times, τ , between 0.6and 0.15 fm/c, where the temperature and the formation time are anti-correlated.The 221 ± ±
6. Conclusion
An excess of low-mass e + – e − pairs above the hadronic background was observed atintermediate p T (1 GeV < p T < p + p and Au+Au collisions. The S. Bathe et al.excess can be understood as the internal conversion of direct photons and shows theexpected 1 /m dependence. In p + p , the direct photon yield is consistent with theresult of a pQCD calculation. In Au+Au, the yield is much larger. It is enhancedabove the binary-scaled p + p yield, represented by a modified power law fit tothe p + p data and scaled by T AA . The Au+Au yield can be well described if anexponential is added to the binary-scaled p + p fit. The negative inverse slope ofthe exponential is 221 ±
23 (stat.) ±
18 (sys.) MeV in central Au+Au. For astatic medium, this could be interpreted as the temperature. For an expandingmedium, it serves as a lower limit of the temperature. It is well above the criticaltemperature of about 170 MeV. Hydrodynamical models that fit the data assumeinitial temperatures, T i , between 300 and 600 MeV at formation times, τ , between0.15 and 0.6 fm/c. Together with the earlier WA98 measurement [ 13], this result canbe interpreted as the first experimental evidence that strongly interacting mattercan exceed the Hagedorn temperature of 170 MeV [ 14]. Acknowledgments
I thank the RIKEN-BNL Research Center for supporting my work and the DOEfor operating RHIC and PHENIX.
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