Drell Yan Dileptons at RHIC

Transcription

1 Dre Yan Dieptons at RHIC Athanasios Petridis Iowa State University Abstract The study if the production of diepton pairs is an important component of the research to be accompished at the Reativistic Heavy Ion Coider (RHIC) due to each reevance to QuarkGuon Pasma search and the investigation of hard QCD processes. We present an event generator program that produces DreYan diepton pairs for symmetric heavy ion coisions. It computes NLO cross sections incuding possibe nucear (shadowing, EMCtype) effects. The code been used to estimate the acceptance and the event rate in the PHENIX experiment centra arm for DreYan dieptons. The event rate at the design RHIC uminosity at m = 4 GeV is of the order of a hundred per year. 1 Introduction PHENIX is one of the major experiments that is under contruction at the Reativistic Heavy Ion Coider that wi start operating in Brookhaven Nationa Laboratory in the year Its major goa is to search for the QuarkGuon Pasma (QGP) and investigate other interesting phenomena that pertain to matter at extremey high temperatures. The production of diepton pairs is of particuar importance since a their sources must be studied in order to estabish a therma component as expected the in the case of QCP formation. In the course of preparing ourseves for rea data from PHENIX we woud ike to foow a compete chain of cacuations reated to events of specific interest to the experiment. We shoud simuate such events starting from theoretica cacuations and continuing by buiding an event generator that produces spectra to be processed by the Monte Caro PHENIX detector response code (caed PISA). The resuts can then anaysed ike rea events. 1

2 In the case of DreYan dieptons we woud ike to study the acceptance and event rate and examine if possibe nucear effects can be detected. In particuar, such effects may be present in the initia state [1]. For DreYan dieptons, the hard cross sections are known and there is no ambiguity due to meson wave functions or fina state interactions. So such measurements compement those of heavy uarkonia. There is the additiona issue of studying higher twist effects in QCD [2] by means of DreYan dieptons. Such effects may present themseves as modifications (owering) of the cross section at ow transverse momentum, p T, or in nonstandard poar ange distributions of the dieptons [3]. An event generator has been deveoped that incudes NexttoLeading Order (NLO) terms and nucear effects based on a custer formation mode. The program is given vaues of the Lab momentum per nuceon, P Lab,the suare of the virtua photon invariant mass, m 2, the photon ongitudina momentum fraction (Feynmanx), x F, and the nucear atomic and mass numbers and outputs N events (dieptons of choice) with the computed p T distribution. 2 Theory 2.1 Partoneve cross sections The hard (parton eve) cross sections that are incuded are described by the foowing Feynman diagrams: DreYan (LeadingOrder, LO), annihiation, and g Compton scattering (NLO). The LO term contributes ony at p T = if the transverse momenta of partons and hadrons are ignored. It can be turned off in the code. NNLO terms have not been incuded yet but are necessary to resum arge ogarithms that appear when p T < 1GeV.Insteadaconstant Kfactor eua to 2.5 has been used. Contributions of the Zboson have not been incuded. They become significant ony at very arge m 2 and/or p T. 3 active (anti)uark favours are used with Λ QCD = 2 MeV (this is adjustabe in the code). The convention Q 2 = p 2 T has been used for the cacuation of the strong couping constant. 2

3 (i) x P 1 Lab (j) x 2 P Lab γ + 2 m, P (a) γ + g g γ + (b) γ + γ + (c) g g Figure 1: Feynman diagrams contributing to the DreYan epton pair production. (a) LO QED process. (b) annihiation. (c) g Compton scattering. The kinematics is defined in (a). One parton carries momentum fraction x (i) 1 of the positivey moving hadron momentum, and the other one carries x (j) 2 of the negativey moving hadron. 2.2 Nuceareve cross section and nucear effects The partoneve cross sections must be convouted with the appropriate structure functions which are sums of products of parton densities to yied the nuceon eve cross section. Taking into account the composition of the nuceus we can cacuate the cross section at the eve of coiding nucei. The nucear effect (shadowingantishadowing pattern) is introduced by means of a mode that invokes uantum mechanica overap of bound nuceons to form mutiuark coor singets (custers) with higher mass and softer parton distributions [4]. The nucear state is expanded as A = α 3 + β 6 + γ This expansion gives good resuts in DIS, J/Ψproduction in ha and AB coisions and direct photon, DreYan production in ha coisions (in Dre Yan the nucear effect is visibe in differentia cross sections versus x F or p T ). It is sufficient to truncate this expansion to the 6 term. 3

4 The nucear effect is generated by the higher mass of the 6 custers (2m p ) which give an effectivey arger s and the softer parton distributions in 6 objects. In the scaing imit the momentum distributions behave as: U N (x) = B u N x(1 x) b u N,D N (x) = B d N x(1 x) b d N,S N (x) = A N (1 x) a N, and G N (x) =C N (1 x) c N where, (b u 3,a 3,c 3 )=(3, 9, 6), (b u 6,a 6,c 6 )=(9, 11, 1), and b d N = b u N + 1. Here, x is the parton momentum fraction in the custer, normaized to 1. There are pp, pn and nntype of 6 custers formed with isospin invariance reations connecting the parton distribution in them. The ocean incudes u, d, and s uarks and antiuarks. The nucear effect is controed by the effective probabiity for 6 custer formation, f n A( A 1/3 ). The code provides options for the choice of parton distributions (PDFs). 2.3 Virtua photon decay to dieptons The virtua photon is produced with uniform φdistribution. After production the virtua photon decays into e + e or μ + μ according to the user s choice. The initia kinematics is done in the diepton CM frame with zaxis parae to the momentum vector of the photon in the aboratory frame. This choice is not identica to the GottfriedJackson or tha CoinsSopper frames. In the diepton CM frame (as defined here) the poar ange, θ of one epton foows a 1+cos 2 θ distribution since the intermediate photon has ongitudina heicity with J z = ±1 but not. There is an additiona term to account for the epton nonzero mass. The θ distribution is not entirey correct since it negects the mass of strange uarks in the ocean and the backwardforward A bf, asymmetry introduced by the omitted Zboson contribution. The atter is A bf a weak a em /a 2 em = G F m 2 /(4πα) =1 4 m 2 which between the J/Ψ and the Υ is at most 1%. It is more than 2% at m =5GeV.TheCompton scattering process introduces a sin 2 θ component to the distribution at arge p T since, in this case, the virtua photon is not entirey transverse [3]. Higher twist effects affect both the poar and azimutha distributions [2]. The CM φdistribution of the dieptons is uniform. The epton momenta are 3Drotated (so that the zaxis meets that of Lab frame) and 3Dboosted back to the Laboratory frame. A gaussian vertex distribution is aso incuded. The user contros its variance, σ z. This distribution is produced using the centra imit theorem. 4

5 3 Resuts 3.1 Differentia cross section for virtua photon production In Fig. 2 the cross section cacuated using the code that has been described here is presented as a function of p T at x F =.1 in centra AuAu coisions at RHIC energy. The soid curve corresponds to maxima nucear effect and the dotted one to resuts without any nucear effect. At ow p T shadowing can be observed. At high p T antishadowing occurs. PHENIX wi mosty probe the shadowing region Max. nucear effect.1.1 No nucear effect Figure 2: Cross section w/o nucear effects. 5

6 3.2 Cross section ratio versus data The cross section cacuated with the mode that has been described here can be used to evauate the cross section ratio of heavy to ight nucei in pa coisions where ther are data to compare to. In Fig. 3 we present such a ratio cacuated with the simpest possibe version of the mode in which ony vaence partons are invoved and with ony the eading order cross section. The mode describes the trend of the data. The two curves deineate the theoretica error band Figure 3: Heavy to ight nuceus cross section ratio versus x 2 (target). Ony LO term incuded with no P ab dependence. The probe is pion. Data are from Ref. [6], with P Lab = 286 GeV (circes) and P Lab = 14 GeV (suares) integrated over m 2 away from resonances. 3.3 Spectra from the compete cacuation In this subsection we present spectra produced by the event generator. Nucear effects are incuded. Fig. 4 shows the diepton spectra (for fixed invariant mass) in the aboratory frame, i.e., after rotation and boosting. 6

7 DreYan diepton data. Momenta and energies in GeV, anges in degrees. ID 1 ID 5 Entries 2 8 Entries Mean Mean RMS.762 RMS MOM ID Entries Mean RMS THETA ID Entries Mean RMS PHI 1 1 Z Figure 4: Dieectron spectra in the aboratory frame, for m 2 =4GeV 2, x F =.1. Momentum (upper eft pane), θ (upper right), φ (ower eft), and emission vertex (ower right). 4 PHENIX Centra Arm Acceptance The acceptance, α of the PHENIX centra arm (Δφ = 18 o, η <.35) to dieectrons at x F = has been computed using the Cherenkov detector with the owest possibe trigger threshod. (1 pe/tie) for centra AuAu coisions at P Lab = 1 GeV. PISA with the entire detector and the magnetic fied turned ON) and PISORP have been used for the simuations, A vertex smearing of σ z = 3 cm is incuded. The acceptance is defined as Number of events that passed the trigger α =, Number of produced events where the number of produced events is just the number of dieptons input into PISA. 7

8 The θ distribution is very sharpy peaked around 9 o. Because of this the acceptance as cacuated here is very cose to that cacuated using geometry cuts in the poar ange to take into account the centra arm pseudorapidity coverage. The acceptance to dieptons, integrated from p T =.1 to 12.1 GeV is.22 ±.8 at m = 3 GeV and.47 ±.7 at m =4GeV.These numbers incude the not very reiabe ow p T region. Further simuations to estimate the acceptance integrated over p T = 1.1 GeV to 1.1 GeV have given.23 ±.6 for m = 3 GeV,.23 ±.1 for m = 4 GeV,.32 ±.3 for m = 5 GeV,.38 ±.3 for m = 6 GeV,.43 ±.25 for m = 7 GeV, and.57 ±.26 for m = 8 GeV. The acceptance drops very rapidy as x F increases. 4.1 PHENIX centra arm acceptance versus p T It is interesting to examine the acceptance as a function of p T.Fig.5shows the singe eectron and dieectron acceptance for m = 3and4GeV.The bottomright pane presents the nonmonotonic dieectron acceptance versus p T which is characteristic of the PHENIX centra arms. At arge p T the opening ange between the two eptons is sma and they can be both detected by the same arm (east or west). As p T decreases the opening ange increases and in some cases one member of the diepton is not detected, faing out of the two arms. Thus the acceptance decreases. As p T decreases further the opening ange becomes arge enought for each epton in the pair to be detected by a different arm and the acceptance increases. It may aso be of interest to observe that if vertex smearing is not incuded, i.e., σ z =, then the ow p T acceptance is arger since in the case of dieptons that emitted at arge z sometimes one or both members hit the centra magnet. Simuations show that in the p T range 2.1 to 3.1 GeV the dieectron acceptance (with σ z =andm = 4 GeV) is.21 ±.6 and in the range 3.1 to 4.1 GeV it is.12 ±.3. 5 Event Rate in the PHENIX Centra Arms The event rates presented here are for centra AuAu coisions at P Lab = 1 GeV. The event rate for m =5GeVaty =(Δy =.5, Δp T =.25 GeV, Δm =1GeV,Δt = s, L = cm 2 s 1 ) has been cacuated and agrees with the predictions of the Ramona Vogt (RV) parametrization [9] 8

9 Figure 5: PHENIX centra arm acceptance to DreYan eectrons and dieectrons at x F =. A behaviour that is characteristic of the doubearm geometry is observed. within 1% to 3%. The RV predictions assume an exponentia decrease in p T and no nucear effects; they are higher than the resuts presented here. Tabe 1 shows the prediction for m =4GeVaty =(Δy =.5, Δp T =1 GeV, Δm =1GeV,Δt = s, L = cm 2 s 1 )forauau coisions at P Lab = 1 GeV incuding maxima nucear effects (these reduce the cross section). No tracking efficiency is incuded and the events are cean, simpe dieptons. The detector efficiency is incuded. We must emphasize that the choice of y, i.e., x F = 2m T s sinh(y) (m T = m 2 + p 2 T ) corresponds to the virtua photons rather than singe eptons on which the actua geometric cuts are appied. Aso a simpe estimate shows that for p T between 1 and 9

10 Tabe 1: Event rate for m =4GeVaty =(Δy =.5, Δp T =1GeV, Δm =1GeV,Δt = s, L = cm 2 s 1 ) for AuAu coisions at P Lab = 1 GeV incuding maxima nucear effects. dσ p T (GeV) dy dm dp T (mb/gev 2 ) α N tot N acc GeVandatm =4GeVΔy =.5 around y = corresponds to Δx F between.2 and.3. Therefore, in this y interva the acceptance and the cross section are not constant but have been treated as such in Tabe 1. The event rate for p T > 2 GeV is very ow. Approximatey one hundred dieptons can be, in principe, detected by the PHENIX centra arms at m = 4 GeV in a nomina RHIC year with the design uminosity in centra AuAu coisions. This number bears some uncertainty due to the choice of parton distributions, the possibe contributions of NNLO and higher twist terms, the mode used to describe the nucear effects the intrinsic transverse momentum and the fact that in the estimate of Tabe 1 the rapidity distribution is assumed to be fat around y =intheinterva Δy =.5. This uncertainty shoud not exceed a factor of 2. To compete the event rate estimate we present resuts obtained for various vaues of the photon invariant mass at y =, integrated over the p T range between 1.1 and 1.1 GeV. The mass bin is 1 GeV. Δx F =.25 is used and the same RHIC conditions isted earier are assumed. Tabe 2 summarizes these resuts. 6 Discussion At the design uminosity and assuming threemonth operation per year (nomina condition) the DreYan dieectron event rate into the PHENIX centra 1

11 Tabe 2: Event rate for various vaues of m (Δm =1GeV)aty =and Δx F =.25, integrated over p T from 1.1 t 1.1 GeV with nucear effects. dσ m (GeV) dy dm 2 (mb/gev 2 ) α N tot N acc arm is very ow. The possibe nucear effect wi be very hard to observe as a function of p T. PHENIX possesses two endcap muon arms which may be more suitabe for measurements of the DreYan cross section. In particuar, the cross section as a function of x F may be measured. The nucear effects are more pronounced versus x F and resut in a characteristic pattern [1]. In pp coisions due to much ceaner events there may be a possibiity of measuring higher twist effects using the shape of owp T distribution and cos(θ) distribution for various vaues of x F as observabes. This work was supported by the US Department of Energy, contract DE FG292ER4692. References [1] A.Petridis,Phys.Rev.C49, 2735 (1994) and references therein. [2] E. Berger and S. Brodsky, Phys. Rev. Lett. 42, 44 (1979). [3] R. Stroynowski, Phys. Rep. 71, 1 (1981). [4] H. Pirner and J. Vary, Phys. Rev. Lett. 46, 1376 (1981). [5] D. M. Kapan et a., Phys.Rev.Lett.4, 435 (1977). [6] P. Bordao et a., Phys. Lett. B193, 368 (1987). [7] D. M. Ade et a., Phys. Rev. Lett. 66, 133 (1991). [8] A.Petridis,Phys.Rev.C54, 848 (1996). [9] R. Vogt, Atomic Data and Nucear Data Tabes 5, 343 (1992). 11