Production of large transverse momentum dileptons and photons in pp , dA and AA collisions by photoproduction processes
aa r X i v : . [ nu c l - t h ] N ov Production of large transverse momentum dileptons and photons in pp , dA and AA collisions by photoproduction processes Yong-Ping Fu and Yun-De Li Department of Physics, Yunnan University, Kunming 650091, China1) [email protected]; 2) [email protected] (Dated: November 8, 2018)The production of large P T dileptons and photons originating from photoproduction processesin pp , dA and AA collisions is calculated. We find that the contribution of dileptons and photonsproduced by photoproduction processes is not prominent at RHIC energies. However, the numericalresults indicate that the modification of photoproduction processes becomes evident in the large P T region for pp , dA and AA collisions at LHC energies.PACS numbers:12.39.St, 13.85.Qk, 25.75.-q, 12.38.Mh I. INTRODUCTION
Hadronic processes for producing large transversemomentum( P T ) dileptons and photons are very impor-tant in the research of relativistic pp , dA and AA col-lisions. Since photons and dileptons do not participatein the strong interaction directly, the photon or dilep-ton production can test the predictions of pQCD calcu-lations, and probe the strong interacting matter(quark-gluon plasma, QGP). The hard scattering of partons is awell-known source of large P T dileptons and photons inrelativistic hadronic collisions. The photons(and dilep-tons) are produced from various processes in relativistic AA collisions(relativistic heavy ion collisions): primaryhard photons from initial parton collisions [1–11], ther-mal photons from the QGP [12–21] and hadronic gas[22–26], photons from the jet-photon conversion in thethermal medium [27–30], and photons from hadronic de-cays after freeze-out [31]. In relativistic AA collisions thecontribution of photons produced by the jet-photon con-version in the thermal medium is also important in thelarge P T region [27, 28].In the present work, we investigate the production oflarge P T dileptons and photons induced by photopro-duction processes in pp , dA and AA collisions at Rel-ativistic Heavy Ion Collider(RHIC) and Large HadronCollider(LHC) energies. The photoproduction processesplay a fundamental role in the ep deep inelastic scatteringat Hadron Electron Ring Accelerator(HERA) [32–35]. Inphotoproduction processes of the ep deep inelastic scat-tering, a high energy photon emitted from the incidentelectron directly interacts with the proton by the inter-action of γp → jets . Besides, the uncertainty principleallows the high energy photon for a short time to fluc-tuate into a quark-antiquark pair which then interactswith the partons of the proton. In such interactions theresolved photon can be regarded as an extended objectconsisting of quarks and also gluons. The interactionsare the so-called resolved photoproduction processes.We extend the photoproduction mechanism to the pho-ton and dilepton production in pp , dA and AA collisions.Charged partons of the incident nucleon also can emithigh energy photons(and resolved photons) in relativis- tic hadron-hadron, hadron-nucleus and nucleus-nucleuscollisions. The photon spectrum from the charged par-ton is given by [36, 37] f γ/q ( z ) = e q α π − z ) z ln (cid:18) Q Q (cid:19) , (1)where α is the electromagnetic coupling parameter, z isthe momentum ratio of the photon energy and the en-ergy of the quark, the values Q and Q stand for themaximum and minimum value of the momentum trans-fer, respectively. In direct photoproduction processes,the high energy photon emitted from the charged partonof the incident nucleon interacts with the parton of an-other incident nucleon by the interaction of qγ → qγ ∗ (or γ ). In resolved photoproduction processes, the hadron-like photon interacts with the parton of the nucleon bythe interactions of q γ ¯ q → gγ ∗ , q γ g → qγ ∗ and g γ q → qγ ∗ ,here q γ ( g γ ) denotes the parton of the resolved photon.The paper is organized as follows. In Sec.II we presentthe production of large P T dileptons and photons inhadronic collisions. The direct and resolved photopro-duction processes are presented. In Sec.III we brieflyreview the production of thermal dileptons and pho-tons in the QGP. In Sec.IV the production rate of jet-dilepton(photon) conversion is discussed. The numericalresults at RHIC and LHC energies are plotted in Sec.V.Finally, the summary is given in Sec.VI. II. LARGE P T DILEPTON AND PHOTONPRODUCTIONA. Large P T dilepton production The large P T dileptons produced by initial parton col-lisions can be divided into two categories: direct dilep-tons produced by the annihilation and Compton scatter-ing of partons, fragmentation dileptons produced by thebremsstrahlung emitted from final state partons [4–6].The direct dileptons ( dir.l + l − ) produced by the subpro-cesses q ¯ q → g ( γ ∗ → l + l − ) and qg → q ( γ ∗ → l + l − ) in thehadronic collisions( AB → l − l + X ) satisfy the following -2 -1 -2 -1 Dileptons at RHIC p+p 200 GeV dir.+fra. dir. pho. res. pho. sum E d / d p ( pb / G e V ) P T (GeV)a b Dileptons at LHC p+p 7 TeV dir.+fra. dir. pho. res. pho. sum P T (GeV) FIG. 1: a: Invariant cross section of dileptons for y=0 in p + p collisions at √ s =200 GeV. (Dash line)The sum of directdileptons(dir.) and fragmentation dileptons(fra.). (Dash dot dot line)Dileptons produced by direct photoproduction pro-cesses(dir.pho.). (Dash dot line)Dileptons produced by resolved photoproduction processes(res.pho.). (Solid line)The sum ofdirect dileptons, fragmentation dileptons and dileptons produced by photoproduction processes. b: Same as panel a but for p + p collisions at √ s =7 TeV. invariant cross section [2, 4–6] dσ dir.l + l − dM dP T dy = 1 π Z dx a G a/A ( x a , Q ) G b/B ( x b , Q ) × x a x b x a − x d ˆ σdM d ˆ t ( x a , x b , P T , M ) , (2)where the functions G a/A ( x a , Q ) and G b/B ( x b , Q ) areparton distributions of nucleons, x a and x b are the par-ton’s momentum fraction. We have x b = ( x a x − τ ) / ( x a − x ). The variables are x = (cid:0) x T + 4 τ (cid:1) / e y / x = (cid:0) x T + 4 τ (cid:1) / e − y / x T = 2 P T / √ s NN and τ = M /s NN . y is the rapidity, M is the invariant mass ofthe lepton pair and √ s NN is the energy of the nucleonin the center-of-mass system.The cross section of the subprocesses ab → l + l − d withthe invariant mass squared M and Mandelstam variableˆ t can be written as [2, 4] d ˆ σdM d ˆ t ( ab → l + l − d ) = α πM r − m l M (cid:18) m l M (cid:19) × d ˆ σd ˆ t ( ab → γ ∗ d ) , (3)where m l is the lepton mass. Here d ˆ σ/d ˆ t ( ab → γ ∗ d )denotes the cross section of q ¯ q → gγ ∗ and qg → qγ ∗ [2].The parton distribution G i/A ( x i , Q ) of the nucleon isgiven by [8] G i/A ( x i , Q )= R i/A ( x i , Q ) (cid:20) ZA p i ( x i , Q )+ NA n i ( x i , Q ) (cid:21) , (4)where R i/A ( x i , Q ) is the nuclear modification factor [11], Z is the proton number, N is the neutron number and A is the nucleon number. p i ( x i , Q ) and n i ( x i , Q ) are the parton distributions of protons and neutrons, respec-tively. We choose the momentum scale as Q = 4 P T .The fragmentation dileptons ( f ra.l + l − ) are producedby the hard scattering ab → ( c → xl + l − ) d [2, 4–6]. Theinvariant cross section of fragmentation dileptons is dσ fra.l + l − dM dP T dy = 1 π Z dx a Z dx b G a/A ( x a , Q ) G b/B ( x b , Q ) × D l + l − q c ( z c , Q ) x a x b z c ( x a x b − τ ) × d ˆ σ par. d ˆ t ( x a , x b , z c , P T , M ) , (5)where z c = ( x a x + x b x ) / ( x a x b − τ ) is the momentumfraction of the final state dilepton. The dilepton frag-mentation function is given by D l + l − q c ( z c , M , Q ) = α πM r − m l M (cid:18) m l M (cid:19) × D γ ∗ q c ( z c , Q ) , (6)where D γ ∗ q c ( z c , Q ) is the virtual photon fragmentationfunction [4]. d ˆ σ par. /d ˆ t denotes the cross section of thesubprocesses. These subprocesses are qq ′ → qq ′ , q ¯ q ′ → q ¯ q ′ , qq → qq , q ¯ q → q ′ ¯ q ′ , q ¯ q → q ¯ q , gg → q ¯ q , qg → qg , q ¯ q → gg and gg → gg [1]. B. Photoproduction processes in large P T dileptonproduction In direct photoproduction processes, the parton a ofthe incident nucleon A can emit a large P T photon, thenthe high energy photon interacts with the parton b ofanother incident nucleon B by the interaction of q b γ → -13 -12 -11 -10 -9 -8 -7 -12 -11 -10 -9 Dileptons at RHIC d+Au 200A GeV dir.+fra. dir. pho. res. pho. sum d N / d P T dy ( / G e V ) P T (GeV)a b Dileptons at LHC d+Pb 6.2A TeV dir.+fra. dir. pho. res. pho. sum P T (GeV) FIG. 2: Dilepton yield for y=0 in central d +Au collisions at √ s NN =200 GeV(panel a) and d +Pb collisions at √ s NN =6.2TeV(panel b). q ( γ ∗ → l + l − ). The invariant cross section of large P T dileptons produced by direct photoproduction processes(dir. pho.) is given by dσ dir.pho. dM dP T dy = 2 π Z dx a Z dx b G a/A ( x a , Q ) G b/B ( x b , Q ) × f γ/q a ( z a ) x a x b z a x a x b − x a x × d ˆ σdM d ˆ t ( x a , x b , z a , P T , M ) , (7)where f γ/q a ( z a ) is the photon spectrum from the quark.According to [37] we choose Q to be the maximumvalue of the momentum transfer given by ˆ s/ − m l andthe choice of the momentum transfer Q =1 GeV ismade such that the photon is sufficiently off shell forthe parton model to be applicable. ˆ s = x a x b z a s NN is the square of the center-of-mass energy for the sub-processes. The function d ˆ σ/dM d ˆ t denotes the crosssection of subprocess qγ → q ( γ ∗ → l + l − ) [2]. Here z a = ( x b x − τ ) / ( x a x b − x a x ) is the momentum fractionof the photon emitted from the quark of the nucleon.In resolved photoproduction processes, the parton a ofthe incident nucleon A emits a high energy resolved pho-ton, then the parton a ′ of the resolved photon interactswith the parton b of another incident nucleon B by the in-teractions of q a ′ ¯ q b → gγ ∗ , q a ′ g b → qγ ∗ and q b g a ′ → qγ ∗ .The invariant cross section of large P T dileptons pro-duced by resolved photoproduction processes (res. pho.)can be written as dσ res.pho. dM dP T dy = 2 π Z dx a Z dx b Z dz a ′ G a/A ( x a , Q ) × G b/B ( x b , Q ) f γ/q a ( z a ) G q a ′ /γ ( z a ′ , Q ) × x a x b z a z a ′ x a x b z a ′ − x a z a ′ x × d ˆ σdM d ˆ t ( x a , x b , z a , z a ′ , P T , M ) , (8) where G q a ′ /γ ( z a ′ , Q ) is the parton distribution of theresolved photon [10]. The cross section d ˆ σ/dM d ˆ t of q ¯ q → g ( γ ∗ → l + l − ) and qg → q ( γ ∗ → l + l − ) is discussedin Eq.(3). The variable z a ′ denotes the momentum frac-tion of the parton of the resolved photon emitted from thequark. Here we have z a = ( x b x − τ ) / ( x a x b z a ′ − x a z a ′ x )and ˆ s = x a x b z a z a ′ s NN . C. Real photon production
Because a virtual photon can directly decay into adilepton, the invariant cross sections of large P T pho-tons can be derived from the cross sections of the dilep-ton production if the invariant mass of the lepton pair iszero( M = 0). The maximum momentum transfer Q inEq.(1) is ˆ s/ dir.γ )and the fragmentation process ( f ra.γ ). The invariantcross section for direct photons is given by [1–3] E dσ dir.γ d P = 1 π Z dx a G a/A ( x a , Q ) G b/B ( x b , Q ) x a x b x a − x × d ˆ σd ˆ t ( x a , x b , P T ) , (9)where x b = x a x / ( x a − x ). In the real photon case wehave x = x T e y / x = x T e − y /
2. The function d ˆ σ/d ˆ t of Eq.(9) denotes the cross section of subprocesses q ¯ q → gγ and qg → qγ [1]. The invariant cross section forfragmentation photons is given by [1–3] E dσ fra.γ d P = 1 π Z dx a Z dx b G a/A ( x a , Q ) G b/B ( x b , Q ) × D γq c ( z c , Q ) z c d ˆ σ par. d ˆ t ( x a , x b , z c , P T ) , (10)where D γq c ( z c , Q ) is the real photon fragmentation func-tion and z c = x /x a + x /x b [1, 3]. The cross section d ˆ σ par. /d ˆ t of Eq.(10) is discussed in Eq.(5). -10 -9 -8 -7 -6 -5 -10 -9 -8 -7 -6 -5 dir. + fra. dir. pho. res. pho. th. jet-QGP P T (GeV) d N / d2 P T dy ( / G e V ) Dileptons at RHIC
Au+Au 200A GeV a b dir. pho. res. pho. P T (GeV) Dileptons at RHIC
Au+Au 200A GeV
FIG. 3: a: Dilepton yield for y=0 in central Au+Au collisions at √ s NN =200 GeV. (Solid line)The sum of direct dileptons(dir.)and fragmentation dileptons(fra.). (Dash dot dot line)Dileptons produced by direct photoproduction processes(dir.pho.). (Dashdot line)Dileptons produced by resolved photoproduction processes(res.pho.). (Dash line)Thermal dileptons(th.) produced bythe QGP. (Dot line)The jet-dilepton conversion(jet-QGP) in the plasma. b: The contribution of photoproduction processes atRHIC energies. (Dash line)The sum of direct dileptons, fragmentation dileptons, thermal dileptons produced by the QGP anddileptons from the jet-dilepton conversion. (Solid line)The sum of dash line, dash dot line and dash dot dot line. The invariant cross section of real photons producedby direct photoproduction processes is
E dσ dir.pho. d P = 2 π Z dx a Z dx b G a/A ( x a , Q ) G b/B ( x b , Q ) × f γ/q a ( z a ) x a x b z a x a x b − x a x × d ˆ σd ˆ t ( x a , x b , z a , P T ) , (11)where z a = x b x / ( x a x b − x a x ). The real photon pro-duction of resolved photoproduction processes is E dσ res.pho. d P = 2 π Z dx a Z dx b Z dz a ′ G a/A ( x a , Q ) × G b/B ( x b , Q ) f γ/q a ( z a ) G q a ′ /γ ( z a ′ , Q ) × x a x b z a z a ′ x a x b z a ′ − x a z a ′ x × d ˆ σd ˆ t ( x a , x b , z a , z a ′ , P T ) , (12)where the elementary cross sections d ˆ σ/d ˆ t of Eq.(11) andEq.(12) are similar to the cases of the dilepton productionin Eq.(7) and (8)(but with M =0), respectively. Here wehave z a = x b x / ( x a x b z a ′ − x a z a ′ x ) for Eq.(12). III. PRODUCTION OF THERMAL DILEPTONSAND PHOTONS
The yield of thermal dileptons ( th.l + l − ) with the lowdilepton mass and large transverse momentum can be written as [12, 15, 22] dN th.l + l − dM dP T dy = πR A σ q ¯ q ( M )4(2 π ) M r − m q M τ T P T × (cid:20) G (cid:18) P T T (cid:19) − G (cid:18) P T T c (cid:19)(cid:21) , (13)where R A is the nuclear radius, m q is the quark mass. τ and T are the initial time and the initial temperatureof the system, respectively. We use τ = 0 .
26 fm/ c forRHIC, τ = 0 .
09 fm/ c for LHC( √ s NN = 2 .
76 TeV) and τ = 0 .
088 fm/ c for LHC( √ s NN = 5 . T = 370 MeV forAu+Au collisions at √ s NN =200 GeV, T = 710 MeVfor Pb+Pb collisions at √ s NN =2.76 TeV, and T = 845MeV for Pb+Pb collisions at √ s NN =5.5 TeV. T c (=160MeV) is the critical temperature of the phase transition[3]. Here σ q ¯ q = 4 πα N c N s e q / M is the cross sectionof the process q ¯ q → γ ∗ → l + l − , N c (= 3) is the colornumber, N s (= 2) is the spin number. The function G ( z )is given by G ( z ) = z (8 + z ) K ( z ).The yield of thermal photons ( th.γ ) is given by thefollowing [13, 15] E dN th.γ d P = πR A αα s e q π Z τ c τ τ dτ f th ( p γ ) T × (cid:20) (cid:18) E γ πα s T (cid:19) + C Com. + C ann. (cid:21) , (14)where τ c = τ ( T /T c ) is the critical time of the phasetransition. The parameters are C Com. = − .
416 and C ann. = − . f th is the thermal distribution of ther-mal partons. In the Bjorken expansion, the temperatureevolves as T = T ( τ /τ ) / [14]. -10 -9 -8 -7 -6 -5 -10 -9 -8 -7 -6 dir.+ fra. dir. pho. res. pho. th. jet-QGP Dileptons at LHC
Pb+Pb 2.76A TeV d N / d P T dy ( / G e V ) P T (GeV) a b dir. pho. res. pho. Dileptons at LHC
Pb+Pb 2.76A TeV P T (GeV) FIG. 4: Same as Fig.3 but for central Pb+Pb collisions at √ s NN =2.76 TeV. -10 -9 -8 -7 -6 -5 -4 -10 -9 -8 -7 dir. + fra. dir. pho. res. pho. th. jet -QGP Dileptons at LHC
Pb+Pb 5.5A TeV d N / d P T dy ( / G e V ) P T (GeV) a b dir. pho. res. pho. Dileptons at LHC
Pb+Pb 5.5A TeV P T (GeV) FIG. 5: Same as Fig.3 but for central Pb+Pb collisions at √ s NN =5.5 TeV. IV. JET-DILEPTON(PHOTON) CONVERSION
The jet-dilepton conversion is induced by the annihi-lation of jets passing through the QGP [38, 39]. We rig-orously derive the dilepton production rate of the jet-dilepton conversion. Using the relativistic kinetic the-ory the production rate can be written as R jet − l + l − ∝ / (2 π ) R d p R d p f ( p ) f ( p ) v σ , where the relativevelocity is v = ( p + p ) / p p . After some algebrathe rate can be written as dR jet − l + l − dM dP T = σ q ¯ q M π ) Z dP ′ T f jet ( P ′ T )4 P ′ T e − P T P ′ T T , (15)where f jet is the phase-space distribution of jets with thelarge transverse momentum( P ′ T ). If the jet distributionis replaced by the thermal distribution exp( − E/T ) =exp( − P ′ T cosh y/T ), one can obtain the rate for produc-ing thermal dileptons. The phase-space distribution of jets is given by [27, 28] f jet ( P ′ T ) = (2 π ) gπR ⊥ τ P ′ T cosh y dN jet d P ′ T dy δ ( η − y ) × Θ( τ − τ i )Θ( τ max − τ )Θ( R ⊥ − r ) , (16)where g (= 6) is the spin and color degeneracy of quarks, R ⊥ is the transverse radius of the system, η is the space-time rapidity of the system, τ i is the formation time forthe jet. We take τ max as the smaller of the lifetime ofthe QGP and the time taken by the jet produced at po-sition r to reach the surface of the QGP. The yield of jetsproduced by AA collisions can be written as dN jet d P ′ T dy = T AA E ′ dσ jet d P ′ ( y = 0) , (17)where the nuclear thickness T AA for zero impact param-eter is 9 A / πR ⊥ . The invariant cross section of the jetproduction is given by E ′ dσ jet d P ′ = 1 π Z dx a G a/A ( x a , Q ) G b/B ( x b , Q ) x a x b x a − x × d ˆ σ par. d ˆ t ( x a , x b , P ′ T ) . (18) Photons at RHIC p+p 200 GeV dir.+fra. dir. pho. res. pho. sum E d / d p ( pb / G e V ) P T (GeV)a b Photons at LHC p+p 7 TeV dir.+fra. dir. pho. res. pho. sum P T (GeV) FIG. 6: Same as Fig.1 but for the real photon production in p + p collisions at RHIC(panel a) and LHC(panel b) energies. -9 -8 -7 -6 -5 -4 -8 -7 -6 -5 -4 -3 Photons at RHIC d+Au 200A GeV dir.+fra. dir. pho. res. pho. sum d N / d P T dy ( / G e V ) P T (GeV)a b Photons at LHC d+Pb 6.2A TeV dir.+fra. dir. pho. res. pho. sum P T (GeV) FIG. 7: Same as Fig.2 but for the real photon production in central d +Au collisions at RHIC(panel a) and d +Pb collisions atLHC(panel b). Jets passing through the QGP will lose energy. In-duced gluon bremsstrahlung, rather than elastic scatter-ing of partons, is the dominant mechanism of the jet en-ergy loss [3, 27, 28, 40, 41]. Based on the AMY for-mulism, the energy loss of the final state partons can bedescribed as a dependence of the final state parton spec-trum dN jet /dE on time [3, 42]. Besides, the energy lossof jets can be scaled as the square of the distance trav-eled through the medium [43]. Jets travel only a shortdistance through the plasma before the jet-photon(or vir-tual photon) conversion, and do not lose a significantamount of energy. The energy loss effect of jets beforethey convert into photons(or virtual photons) is found tobe small, about 20% [3, 27, 28].The rate of the photon production by Compton scat-tering and annihilation of jets in the hot medium can bewritten as [27, 28] E dR jet − γ d P = αα s e q π f jet ( p γ ) T (cid:20) (cid:18) E γ πα s T (cid:19) + C (cid:21) , (19)where the constant is C = C Com. + C ann. . The detailedprocesses of the thermal contribution and jet- γ ( γ ∗ ) con- version are discussed in Ref.[29, 30]. We briefly reviewthe contribution of thermal photons and dileptons. TheLandau-Pomeranchuk-Migdal (LPM) effect for the ther-mal production and jet- γ ( γ ∗ ) conversion [29, 30] is notconsidered in our paper. In the calculation we use theBjorken 1+1 D evolution, the authors of Ref.[29, 30] con-sider the transverse expansion of the hot and dense mat-ter (3+1 D) in the thermal photon and dilepton produc-tion. V. NUMERICAL RESULTS
The yield of large P T dileptons in a mass range between M min and M max can be defined as [4, 5] dN AB → l + l − X d P T dy = Z M max M min Mπ dN AB → l + l − X dM dP T dy dM, (20)in this paper we choose the range 100 MeV M AA collisions in theminimum bias case are plotted. In Fig.1 and 2 we plot -8 -7 -6 -5 -4 -3 -2 -8 -7 -6 -5 -4 dir. + fra. dir. pho. res. pho. th. jet-QGP d N / d P T dy ( / G e V ) P T (GeV) Photons at RHIC
Au+Au 200A GeV a b dir. pho. res. pho. P T (GeV) Photons at RHIC
Au+Au 200A GeV
FIG. 8: Same as Fig.3 but for the real photon production in central Au+Au collisions at RHIC energies. -8 -7 -6 -5 -4 -3 -2 -1 -8 -7 -6 -5 -4 dir. + fra. dir. pho res. pho. th. jet-QGP Photons at LHC
Pb+Pb 2.76A TeV d N / d P T dy ( / G e V ) P T (GeV) a dir. pho. res. pho. b Photons at LHC Pb+Pb 2.76A TeV P T (GeV) FIG. 9: Same as Fig.4 but for the real photon production in central Pb+Pb collisions at √ s NN =2.76 TeV. the contribution of dileptons produced by direct and re-solved photoproduction processes for pp and dA collisionsat RHIC and LHC energies. In the panel a of Fig.1 and2 the dilepton spectra of direct and resolved photopro-duction processes(dash dot line and dash dot dot line)are compared with the spectrum of direct and fragmen-tation dileptons(dash line) for p + p collisions and d +Aucollisions at RHIC, respectively. We find that the contri-bution of photoproduction processes is not prominent for p + p and d +Au collisions at RHIC energies. However,photoproduction processes start playing an interestingrole for p + p collisions and d +Pb collisions at LHC. Thecontribution of photoproduction processes is evident inthe region of P T > p + p collisions(the panelb of Fig.1), and P T > d +Pb collisions at LHCenergies(the panel b of Fig.2).In the panel a of Fig.3 we plot the results for directdileptons(dir.), fragmentation dileptons(fra.), the jet-dilepton conversion(jet-QGP) in the thermal plasma, andthermal dileptons(th.) produced by the QGP in Au+Aucollisions at RHIC. The dilepton spectra of direct(dir.pho.) and resolved photoproduction processes(res. pho.)are also plotted. The results for Pb+Pb collisions at √ s NN =2.76 TeV and 5.5 TeV are shown in the panel aof Fig.4 and the panel a of Fig.5, respectively. In thepanel b of Fig.3 we see that the contribution of photo-production processes is still weak for Au+Au collisionsat RHIC. However, the contribution of photoproductionprocesses becomes evident in the large P T region at LHCenergies. In the panel b of Fig.4 and 5 the spectra ofdileptons produced by direct and resolved photoproduc-tion processes(dash dot line and dash dot dot line) arecompared with the spectrum of direct dileptons, fragmen-tation dileptons, thermal dileptons and the jet-dileptonconversion(dash line), we find that the contribution ofdileptons produced by photoproduction processes is evi-dent in the region of P T > √ s NN =2.76 TeV, and P T > √ s NN =5.5 TeV.The contribution of real photons produced by directand resolved photoproduction processes is also negligi-ble for pp , dA and AA collisions at RHIC energies(thepanel a of Fig.6 and 7; Fig.8). However, the contributionof photoproduction processes is evident in the region of P T > p + p collisions at √ s =7 TeV(the panel bof Fig.6), P T > d +Pb collisions at √ s NN =6.2 -7 -6 -5 -4 -3 -2 -1 -7 -6 -5 dir. + fra. dir. pho res. pho. th. jet-QGP Photons at LHC
Pb+Pb 5.5A TeV d N / d P T dy ( / G e V ) P T (GeV) a dir. pho. res. pho. b Photons at LHC Pb+Pb 5.5A TeV P T (GeV) FIG. 10: Same as Fig.5 but for the real photon production in central Pb+Pb collisions at √ s NN =5.5 TeV. TeV(the panel b of Fig.7), P T > √ s NN =2.76 TeV(the panel b of Fig.9), and P T > √ s NN =5.5 TeV(thepanel b of Fig.10).The photon spectrum f γ/q from the charged partondepends on the collision energy √ s NN . We express thephoton spectrum as f γ/q ∝ ln (cid:0) (ˆ s/ − m l ) / GeV (cid:1) =ln( s NN / GeV ) + ln( x a x b z a .../ − m l /s NN ), where ˆ s = x a x b z a s NN for direct photoproduction processes and ˆ s = x a x b z a z a ′ s NN for resolved photoproduction processes.Since the collision energy at LHC is larger than the colli-sion energy at RHIC( s LHCNN ≫ s RHICNN ), the photon spec-trum becomes important at LHC energies. Therefore thecontribution of photoproduction processes is evident atLHC.We also plot the spectra of thermal dileptons and pho-tons, because the contribution of the thermal informa-tion is dominant in the small P T region. We show theresults of the jet-dilepton(photon) conversion taking intoaccount an effective 20% energy loss of jets before con-version into dileptons(photons) [3, 28]. The spectra ofthe jet-dilepton conversion fall off with the transversemomentum of dileptons faster than the spectrum of pri-mary hard dileptons due to the attenuation functionexp( − P T / P ′ jetT T ) in Eq.(15)(see the panel a of Fig.3,4 and 5). Since the rate of the jet-photon conversion is R jet − γ ∝ f jet , the spectra of the jet-photon conversion do not drop quickly with the transverse momentum(seethe panel a of Fig.8, 9 and 10). VI. SUMMARY
We investigate the production of large P T dileptonsand photons in relativistic pp , dA and AA collisions bydirect and resolved photoproduction processes. In theinitial parton scattering the charged parton of the inci-dent nucleon can emit large P T photons, then the highenergy photons interact with the partons of another inci-dent nucleon by the QED Compton scattering. Further-more, the hadron-like photons also can interact with thepartons of the nucleon by the annihilation and Comp-ton scattering. The numerical results indicate that thecontribution of photoproduction processes is negligiblefor pp , dA and AA collisions at RHIC energies, but thecontribution becomes evident at LHC energies. VII. ACKNOWLEDGEMENTS
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