Dilepton radiation measured in PHENIX probing the strongly interacting matter created at RHIC
aa r X i v : . [ nu c l - e x ] S e p Dilepton radiation measured in PHENIX probing the stronglyinteracting matter created at RHIC
Yasuyuki Akiba a for the PHENIX collaboration a RIKEN Nishina Center for Accelerator-Based Science, Hirosawa, Wako, Saitama 351-0198, Japan
Abstract
PHENIX has measured e + e − pairs from p + p and Au + Au collisions as function of mass and p T .The data can be used to probe the properties of dense matter formed in Au + Au collision. Therelation between electron pairs and virtual photons is discussed.
1. Introduction
It is now well established that high density partonic matter is formed in collisions of heavynuclei at RHIC[1]. Photons and lepton pairs are the cleanest probes of the dense matter. Sincethese electromagnetic probes have little interaction with the matter, they carry direct informationdeep inside of the medium. From the emission rate of photons and dileptons, we can directlyprobe the temperature of the medium, the properties of hadrons inside of the medium, and thematter’s properties.
2. Relation between dilepton and virtual photon
The thermal emission rate of electron pairs per space-time volume can be described in termsof the electromagnetic (EM) spectral function as [2] dR ee d q = − α π L ( M ) M Im Π µ em ,µ ( M , q ; T ) f B ( q , T ) , (1) L ( M ) = r − m e M (1 + m e M ) . (2)Here Π µ em ,ν is the in-medium EM spectral function and f B ( q , T ) = / ( e q / T −
1) is the Boltz-mann factor. The equation shows that from the emission rate we can probe the medium propertyencoded in the EM spectral function as well as its temperature in the Boltzmann factor. The EMspectral function in vacuum for the low mass region is well described as a sum of contributions ofthe low mass vector mesons ( ρ , ω , and φ ). Modification of the properties of these mesons showsup as modification of the EM spectral function.Using the same notation, the emission rate of virtual photons is described as [2, 3] q dR γ ∗ d q = − α π Im Π µ em ,µ ( M , q ; T ) f B ( q , T ) . (3) Preprint submitted to Nuclear Physics A August 14, 2018 he virtual photon and the electron pair emission rate are related as q dR ee dM d q = dR ee d q = α π L ( M ) M q dR γ ∗ d q . (4)The same relation holds for the yield of photons and electron pairs after space-time integration.This relation between the virtual photon and electron pair emission is exact to the order of α inQED and is exact to all orders of strong couplings. For M →
0, the virtual photon yield becomesthe real photon yield ( N γ ∗ → N γ ). Thus this relation can be used to determine the yield of realphotons. Recently, PHENIX measured the yield of direct photon in Au + Au from the yield oflow mass e + e − pairs using this relation.[4].The equation (4) can be rewritten as q dN γ ∗ d q ≃ π α Mq dN ee d qdM . (5)This equation can be used to convert the yield of e + e − pair to virtual photon yield. Such con-version is useful since the virtual photon emission rate is just the product of the EM spectralfunction and the Boltzmann factor. mass (GeV)0 0.2 0.4 0.6 0.8 1 1.2 1.4 d M d y t dp T pd N -8 -7 -6 -5 -4 -3 -2 Vaccuum spectral functionHadronic Many Body Theory annihilation (LO)qq+ =1.025 GeV/c T p (a) mass (GeV)0 0.2 0.4 0.6 0.8 1 1.2 1.4 d M d y t dp T pd N M -8 -7 -6 -5 -4 -3 -2 Vaccuum spectral functionHadronic Many Body Theory annihilation (LO)qq+ =1.025 GeV/c T p (b) Figure 1: Electron pair emission rate (left panel) and virtual photon emission rate (right panel) calculation by R. Rapp[5].The solid and dashed curve uses the EM spectral function in the medium and in vacuum, respectively. The dotted curveshows q ¯ q annihilation contribution. Figure 1 illustrates the relation between electron pair mass spectrum and virtual photon yield.The left panel of the figure shows the di ff erential electron pair spectrum, (1 / p T ) dN ee / dMd p T dy at p T = .
025 GeV / c from a model calculation of electron pair production by Rapp. The dashedand solid curve show electron pairs from hadronic gas, while the dotted curve show the contri-bution from the leading order (LO) q + ¯ q corrected with a Hard Thermal Loop (HTL) correction.The dashed curve uses the EM spectral function Π EM that is unchanged from its vacuum value sothe line shapes of vector mesons ( ρ, ω, φ ) are unmodified. In the solid curve the spectral functionis calculated by hadronic many body theory (HMT), and the vector mesons are broadened dueto the interactions. It also includes the contributions like a (1260) → π + e + e − , ρ → π + e + e − ,and N + π → N ∗ → Ne + e − . These contributions filled the low mass regions below the two-pionthreshold. In the low mass region, the mass spectrum steeply increases with decreasing M . Thisbehavior is due to the 1 / M factor in γ ∗ → e + e − .2 igure 2: Mass distributions of e + e − pair in p + p (filled) and Au + Au (open). The left panel show the inclusive massspectra (0 < p T < / c ) and the right panel shows the mass spectrum at the low p T region (0 < p T < .
7) GeV / c . The right panel of Fig. 1 shows the same calculations presented as the yield of virtual pho-ton. The steep 1 / M behavior of the electron pair spectrum is removed, and much more smoothbehavior of the virtual photon spectrum is revealed. The plot shows that the virtual photon yieldis almost constant as a function of M . The value of the solid curve at M = M and it becomes the real photon yield in the limit of M = ∝ M in the rightpanel at low mass region since q ¯ q contribution to Π EM is proportional to M . Thus it is stronglysuppressed and have little contribution in the low mass region. In the high mass region, the M behavior of the quark annihilation is suppressed by the Boltzmann factor.It should be noted that the dotted curve does not include processes like q + g → q + γ ∗ thatare associated with real direct photon production in QGP. This is because HTL calculation ofthermal radiation from QGP is only available in the real photon case. Turbide, Gale, and Rapp[6] calculated real photon production in an hadronic gas using the same model and comparedit with real photon production in QGP phase using the complete leading order HTL analysis.They found that real photon from the QGP outshines that of hadronic gas for p T > . / c in Au + Au collisions at RHIC. This means that contribution from processes associated with realphoton production in QGP can be as large as that of HMT (solid curve) and can be much largerthan that of the LO q ¯ q annihilation (dotted). e + e − mass spectra in p + p and Au + Au PHENIX measured the e + e − pair production in Au + Au and in p + p at √ s NN =
200 GeV[7, 8].In p + p the measured mass spectrum in low mass ( M < / c ) is well described by the sumof light hadron decay contributions. The high-mass region is dominated by the contribution ofthe correlated decays of charm and bottom. From the measured mass spectrum the charm crosssection is determined as σ c ¯ c = ± ± µ b, which is consistent with that obtained fromsingle electron measurement[9]. The bottom cross section is determined as σ b ¯ b = . ± . + − µ b,which is consistent with that obtained from e − h correlation[10].Figure 2 compares the e + e − pair mass distributions in p + p and Au + Au collisions andhadronic cocktail for M < . / c . The p + p and Au + Au data are normalized in Dalitz pair3 igure 3: Left: Mass distributions of e + e − pair in p + p (filled) and Au + Au (open) for 1 . < p T < / c . Right: M × dN ee / dM of the excess e + e − pair yield over the cocktail for 1 . < p T < / c (in arbitrary unit). mass region ( M <
30 MeV / c ). While the p + p data is well described by the cocktail shown insolid curve, the Au + Au data show a large enhancement over the cocktail. The enhancement islarger in the low p T region ( p T < . / c ) shown in the left panel of the figure.The left panel of Fig. 3 shows the e + e − mass distribution for p T > . / c . The enhance-ment in Au + Au is still visible for M > . / c but its magnitude is much reduced. In the leftpanel, M × dN ee / dM of the excess yield of the e + e − pair in the Au + Au for 1 . < p T < . / c is shown. Following Eq.4 this corresponds to the yield of virtual photons. The figure shows thatthe yield of virtual photon is approximately constant for M > . / c , which is consistentwith the constant behavior of the HMT calculation by R. Rapp shown in Fig. 1. This could beinterpreted that the virtual photon emission in the high p T region ( p T > . / c )is dominatedby hadronic scattering process like π + ρ → π + γ ∗ or partonic processes like q + g → q + γ ∗ . Bothof these processes give a constant contribution to the EM spectral function at low mass. Sincethe virtual photon yield is almost constant, it can be reliably extrapolated to M =
0. This shouldgive the real photon emission rate.In contrast, the mass distribution in Au + Au at low p T shown in the right panel of Fig. 2 isquite di ff erent. The shape of the excess seems to be incompatible with a constant virtual photonemission rate. The data might suggest that a large enhancement of the EM spectral function atlow mass and low p T in Au + Au collisions.
Acknowledgments
The author thanks R. Rapp for very useful discussion and for providing the calculation.
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