aa r X i v : . [ nu c l - e x ] M a y Overview of charm production at RHIC
Yifei Zhang
Dept. of Modern Physics, University of Science and Technology of China, Hefei,Anhui, China, 230026E-mail: [email protected]
Abstract.
We present an overview of the recent abundant measurements for charm productionat RHIC. The significant information of charm cross sections in different collisionsystem at 200 GeV and charmed hadron freeze-out and flow properties extracted fromthese measurements are presented. The heavy flavor energy loss in the medium andheavy flavor related azimuthal correlations in heavy ion collisions are also discussed.PACS numbers: 25.75.Dw, 13.20.Fc, 13.25.Ft, 24.85.+p
1. Introduction
Charm quarks are a unique tool to probe the hot-dense matter created in relativisticheavy-ion collisions at RHIC. Charm quarks are believed to be produced only in theearly stages and their production rate is reliably calculable by perturbative QCD [1, 2].Studies of the binary collision ( N bin ) scaling of the total charm cross section can beused to test theoretical calculations and determine if charm is indeed a good probe withwell-defined initial states. Measurements of charm production at low p T , in particularradial and elliptic flow, probe the QCD medium and are thus sensitive to bulk mediumproperties like density and the drag constant or viscosity. And charm flow propertiesmay help understand the light flavor thermalization [3]. Due to their large mass ( ≃ c ), charm quarks are predicted to lose less energy than light quarks by gluonradiation in the medium [4]. Measure heavy quark energy loss via its semileptonic decayelectrons may provide us information on the interactions of heavy quarks with the hotdense matter produced in nuclear collisions at RHIC. The strong energy loss of lighthadrons modified the di-hadron azimuthal correlation functions [5]. Measurement of theheavy flavor electron-hadron correlation may help look insight the mechanism of heavyquark interactions with the hot dense medium. Bottom quark is much heavier thancharm quark, their energy loss and flow behavior may be very different. The separationof the bottom and charm contribution in the non-photonic electron measurement is vitalto clearly understand the charm and bottom quark production and their interactionswith the medium.In this paper, instead of going through the details for all the measurements oranalyses, we prefer the discussion on those hot physics about charm cross section, verview of charm production at RHIC
2. D-mesons and leptons from heavy flavor decays
STAR experiment has measured open charm via hadronic channel ( D → Kπ ,B.R.=3.83%) at low p T ( < ∼ c ) in d +Au [6], minbias Cu+Cu [7] and minbiasAu+Au [8] collisions at 200 GeV. Good signals ( > ∼ σ ) are observed in the Kπ invariantmass distributions after the combinatorial background subtraction using event-mixingmethod. Another hadronic channel ( D → Kππ , B.R.=14.1%) to reconstruct opencharm was measured by PHENIX experiment in p + p collisions at 200 GeV [9]. In thismeasurement, the π was identified by EMCal trigger via π → γγ decay, and ∼ σ signal was seen in the p T range of 5-15 GeV/ c .Due to the difficulty to reconstruct D-meson hadronic decay vertex using currentdetectors, both STAR and PHENIX have measured open charm indirectly via itssemileptonic decays to electrons or muons. STAR measured non-photonic electronsusing TPC+TOF [6, 8] and TPC+EMC [10], these two results are consistent witheach other but are systematically higher than PHENIX results, which were measuredusing RICH and EMC in a lower material environment [11, 12, 13]. But the nuclearmodification factors ( R AA ) of electrons from heavy quark decays are consistent betweenSTAR and PHENIX. STAR TOF has the capability to measure single muon at verylow p T range (0.17-0.21 GeV/ c ) at mid-rapidity, which constrain 90% of the charmproduction cross section [14, 8]. PHENIX measured muons at high p T ( > c )using forward muon detector at rapidity h y i = 1 .
65 [15]. In addition, the di-electronfrom heavy flavor decays in p + p collisions at 200 GeV has been measured by PHENIXexperiment using a cocktail method. At mid-rapidity, the charm and bottom crosssection are derived from the comparison between the e + e − invariant mass distributionsfrom data and those from PYTHIA simulations [16].
3. Charm production cross section
Both STAR and PHENIX have measured charm production cross section in severalcollision systems. Left panel of Fig. 1 shows dσ NNc ¯ c /dy as a function of number of binarycollisions N bin . The STAR previous result, the charm production cross section at mid-rapidity in d +Au collisions [6] is shown as the red circle. The charm cross sectionin Au+Au minbias collisions, derived by combining three independent measurements of D → Kπ ( p T < c ), muon (0 . < p T < .
21 GeV/ c ) from charm decay and non-photonic electron (0 . < p T < c ) from heavy flavor decays, is shown as the redsquare. The result in Au+Au central collisions (red star) is from combing the muon andelectron measurements [8]. The new result from Cu+Cu minbias collisions is obtainedfrom the D ( p T < . c ) measurement with statistics only (red triangle) [7].The results from non-photonic electron measurements in 200 GeV p + p (0 . ≤ p T ≤ . verview of charm production at RHIC c ) [12] and Au+Au (0 . ≤ p T ≤ . c ) [13] collisions at PHENIX, are shown asthe blue circle and the blue square, respectively. The charm production cross section atmid-rapidity scales with number of binary interactions both in STAR and PHENIXexperiments. This indicates that charm quarks are produced in the early stage ofrelativistic heavy-ion collisions. The FONLL calculation [17] shown as the band. Boththe STAR and PHENIX results are higher than the central value (thick line) of theFONLL calculation, but the upper theory value reproduces the experimental results.The central values of the cross sections reported by PHENIX [12, 13] are a factor ofabout two smaller than STAR at all measured p T [10]. The difference is approximately1.5 times the combined uncertainties, also shown in the right panel of Fig. 1 at mid-rapidity. Right panel of Fig. 1 shows the charm cross section as a function of rapiditycompared to theoretical calculations [18], the clear difference is seen between STARand PHENIX results at mid-rapidity with systematical errors dominated. PHENIXalso obtained the charm cross section from muon measurement at forward rapidity( h y i = 1 .
65, 1 . ≤ p T ≤ . c ) in 200 GeV p + p collisions, shown as the triangles.The new result has smaller systematical error and consistent with theory curves [15]. bin number of binary collisions N b ) m ( y = / d y | cc NN s d FONLL in p+pd+Auminbias Cu+Cuminbias Au+AuminbiasAu+Aucentral 12% = 200 GeV NN S Sys. error cc /N D Nsys. err.PHENIX p+p PHENIX Au+Au
Rapidity y b ) m / d y ( NN cc s d +e (Au+Au) m + STAR D +e (d+Au) STAR D (Cu+Cu) STAR DPHENIX e (Au+Au)PHENIX e (p+p) (p+p) m PHENIX sys. error
Color dipole HSD PYTHIA
Figure 1.
Panel (a):Mid-rapidity charm cross section per nucleon-nucleon collision asa function of N bin in d +Au, minbias and 0 −
12% central Au+Au collisions. The solidline indicates the average. FONLL prediction is shown as a band around the centralvalue (thick line) [17].
4. Flow and energy loss
In the hot dense medium created at Au+Au collisions, heavy quark is consider as anintruder, put into the hot medium with relatively very high density of light quarks.Due to their large mass, such a heavy quark may acquire flow from the sufficientinteractions with the constituents of a dense medium in analog to Brownian motion.Theoretical calculations have shown that interactions between the surrounding partonsin the medium and heavy quarks could change the measurable kinematics [3, 19], andcould boost the radial and elliptic flow resulting in a different heavy quark p T spectrumshape. Panel (a) of Fig. 2 shows the m T spectra for light hadrons ( π , K ,p), Λ, Ξand multi-strange hadrons ( φ , Ω) in 200 GeV central Au+Au collisions [21, 22], andcharmed hadron ( D ) in 200 GeV minbias Au+Au collisions in symbols [8]. Due to verview of charm production at RHIC ) - mass (GeV/c T m - ) d y ) ( G e V / c T d m T m p N ) / ( ( d -6 -4 -2 - p - Kp LXfW (m.b.) D Blast Wave FitCentral Au+Au 200 GeV f o e xp ec t e d T b (a) (GeV/c) T p A u A u / ( d A u f i t) R – m – e > t b , < fo TBW1: 220, 0.23BW2: 129, 0.48BW3: 100, 0.6 sys. error bin N STAR Preliminary (b) c+b reso.+frag.c+b coll.
Figure 2.
Panel (a): Hadron species dependent freeze-out and flow parameters fromblast wave fits to the hadron m T spectra. Panel (b): Nuclear modification factor( R AuAu/dAu ) for 0 −
12% Au+Au collisions.
Panel (b) shows R AuAu/dAu for 0 −
12% Au+Au collisions. To study whethercharmed hadrons have similar radial flow to light hadrons, we have included curvesfor the expected nuclear modification factor from a blast-wave model, using the freeze-out parameters for light hadrons [21] (BW3 in Fig. 2 Panel (b)) and multi-strangehadrons [22] (BW2). The data and best blast-wave fit (BW1) show large deviations fromboth these curves for p T > c , which suggests that the charmed hadron freeze-outand flow are different from light hadrons. We scanned the parameters to a 2-dimensional T fo , h β t i space, the results show little sensitivity to freeze-out temperature, but disfavorlarge radial flow. These findings, together with the observation of large charm ellipticflow [11], are consistent with the recent prediction from hydrodynamics [23]: elliptic flowis built up at partonic stage, and radial flow dominantly comes from hadronic scatteringat later stage where charm may have already decoupled from the system.Since there is no direct charmed meson measurement at high p T currently, the R AA of non-photonic electrons from heavy flavor decays was used to reveal heavy quark energyloss indirectly. The strong suppression similar to light hadrons of the non-photonicelectrons R AA at high p T > ∼ c has been observed in several experiments [10, 11]. Inthis case, STAR and PHENIX are consistent with each other. Theoretical calculationpredicts that heavy quark lose less energy in the medium than light quarks due tosmall gluon radiation angle [4]. As presented in Fig. 2 Panel (b), model calculations ofcoalescence and fragmentation [24] (double-dotted curves), and collisional dissociation verview of charm production at RHIC [GeV/c] T p0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 H eavy F l av o r E l ec t r on v -0.1-0.0500.050.10.150.2 PHENIX Final Run4PHENIX Preliminary Run7 van Hees et al. minimum-bias
Figure 3.
Non-photonic electron elliptic flow v in minbias Au+Au collisions at 200GeV. Error bars are statistical and the shaded boxes are systematical errors. In the mean time, due to the strong angular correlation between heavy flavor hadronand electron from its semileptonic decay at high p T , the non-photonic electron ellipticflow v can be used to measure heavy flavor hadron v . None zero v of electron fromheavy flavor decays was observed at PHENIX. Fig. shows the non-photonic electron v measured from run4 [11] and run7 [26]. This may indicate that the heavy quarkstrongly interact with the dense medium at early stage of heavy ion collisions and thepartonic level collective motion has been observed at RHIC. The none zero but smallernon-photonic electron v is consistent with the none zero but smaller radial flow velocity h β t i compared to light hadrons. Both the observations may suggest that the light flavorthermalization at partonic stage in the hot dense matter created in heavy ion collisions.
5. Correlations
The large amount of energy loss of high p T partons in the dense medium created incentral A + A collisions was observed at RHIC [27]. And their azimuthal correlationswith low p T hadrons are also modified by interacting with the medium, showing abroad or even double-peak structure on the away-side di-hadron correlation [5]. Sincethe similar level of non-photonic electron energy loss as light hadrons was observed atRHIC [10, 11], the study of the e-h azimuthal correlation distribution could help us tounderstand the mechanism of heavy quark energy loss in the dense medium and thecorresponding correlation pattern.The azimuthal angular correlation of non-photonic electron and charged hadronshas been measured at STAR [28]. Left panel of Fig. 4 shows non-photonic e-hcorrelations at 200 GeV Au+Au collisions. Here the v background has been subtracted.Despite large statistical errors, the azimuthal correlation distribution shows clearstructure. On the near side, there is one single peak representing the heavy quarkfragmentation, and possible interactions with the medium. On the away side, insteadof one peak around π as in p + p collisions, the correlation functions are modified tobe a broad even a double-peak structure, which is similar to the di-hadron correlationin Au+Au [5]. A single peak structure expected from PYTHIA calculations can not verview of charm production at RHIC f D -1 0 1 2 3 4 f D d N / d t r i g / N -1012345 Systematical error from v S T AR p r e li m i n a r y (GeV/c) T p B / ( B + D ) (PYTHIA fit) e-D (MC@NLO fit) e-De-h, Run5 (PYTHIA fit)e-h, Run6 (PYTHIA fit)PHENIX e-h, Run5+6 (PYTHIA fit), prel.FONLL STAR preliminary = 200 GeVsp+p @
Figure 4.
Left Panel: Non-photonic electron-hadron correlation in Au+Au collisionsat 200 GeV after the v background subtraction. The dashed curve fitting to the datais from PYTHIA expectations on the away side. The error bars are statistical, andthe error band around zero shows the systematical uncertainty. Right Panel: Relativebottom contribution to the total non-photonic electron yield derived from e-h and e- D correlations. describe the measured away side correlations. This observation of non-photonic e-hcorrelation probably indicates heavy quark interaction with the dense medium and theheavy quark energy loss may generate conical emission in the hot dense matter createdin heavy ion collisions at RHIC.As discussed above, the mechanism of the heavy quark interactions with thedense medium is still not very clear. Thus it is of great interest to separate non-photonic electron energy loss into the contributions from charm and bottom quarks.Since the near-side e-h azimuthal correlation from B decays is much wider than thatfrom D decays for the same electron p T , STAR’s previous study [29] compared theexperimental correlation results in p+p collisions with PYTHIA simulations, and founda substantial B contribution to non-photonic electrons up to electron pt ∼ c (blue circles in the right panel of Fig. 4). And in Run7 this measurement has beenextended to pt ∼ c (blue triangles). Furthermore, STAR presents anotheranalysis technique to separate charm and bottom quark contributions in the non-photonic electron measurement via triggering on the leading non-photonic electronazimuthal correlations with the balancing heavy quark identified by the D meson(Red circle and STAR) [30]. The azimuthal correlation distribution was studied usingPYTHIA simulations and simulations including NLO process [30, 31], the charm andbottom quark contribution can be separately estimated by comparing the azimuthalcorrelation function from simulation and data. PHENIX also presents similar analysis toseparate charm and bottom contribution in non-photonic electron measurement (purplecircles). A clear peak structure has been seen around 1.2 GeV/ c in the invariantmass distribution of triggered non-photonic electron and correlated charged hadrons.By comparing to the data, the difference of the invariant mass peaks of triggeredelectrons and correlated charged hadrons from simulation can be used to estimate thecontributions from bottom and charm quark for the same electron p T [32]. All theexperimental results are consistent with the FONLL calculation shown as the curves [2]. verview of charm production at RHIC Table 1.
Charm production cross sections before and after bottom subtraction inminbias and central Au+Au collisions at 200 GeV. The first error is statistical, thesecond is systematical. collisions before bottom subtraction after bottom subtraction0-12% central Au+Au 297 ± ± µb ± ± µb ± ± µb ± ± µb The upper limit of the FONLL calculation was used to estimate the maximumcontribution of electrons from bottom decays in the non-photonic electron spectra,which were used to extract charm cross section in a combined fit. In Fig. ?? , the solidsquares and solid circles are the non-photonic electron spectra in 0-12% central and0-80% minbias Au+Au collisions at 200 GeV, respectively. The open symbols presentthe non-photonic electron spectra after the subtraction of the bottom contribution fromthe upper limit of FONLL calculation. Then the bottom-excluded non-photonic electronspectra were used in the new combined fit to extract the charm production cross section.Table 1 shows the charm production cross sections before and after bottom subtraction inminbias and central Au+Au collisions at 200 GeV. The difference is within ∼ p T muon measurement sample most fraction of the charm cross section [14], thehigh p T bottom contribution does not change it. (GeV/c) T p - d y ) ( G e V / c ) T dp T p p ev N ) / ( N ( d -6 -4 -2 · D 0-80% – e 250] · – ePower-law fitBlast-wave fit 250] · – m – m P.L.-fit b/(c+b) upperB.W.-fit b/(c+b) upper
Figure 5.
Combined fit to extract charm production cross section using D , µ andnon-photonic electron spectra before (solid squares and circles) and after (open squaresand circles) bottom contribution subtraction.
6. Conclusions
The results of charm production from analysis of D meson reconstruction and leptonsfrom heavy flavor semileptonic decays at RHIC were reported. The charm productioncross section was found to scale with number of binary collisions both in STAR andPHENIX, which indicates that charm quark produced at early stage of the system. Butthe discrepancy remains between STAR and PHENIX. The blast-wave fits and the direct verview of charm production at RHIC p T bottom contribution does not affect the charmproduction cross section. References [1] Z. Lin and M. Gyulassy, Phys. Rev. C , 2177 (1995).[2] M. Cacciari, P. Nason and R. Vogt, Phys. Rev. Lett. , 122001 (2005).[3] G.D. Moore, D. Teaney, Phys. Rev. C , 064904 (2005).[4] Y. Dokshizer et al. Phys. Lett. B 519 (2001) 199.[5] J. Adams et al. , Phys. Rev. Lett. , 152301 (2005);[6] J. Adams et al. , Phys. Rev. Lett. , 062301 (2005).[7] A. Shabetai, these proceedings.[8] Y. Zhang, J. Phys. G , S529 (2006); B. I. Abelev et al. , e-print arXiv: nucl-ex/0805.0364.[9] Y. Akiba, Heavy Quark Workshop, LBNL, 2007.[10] B. I. Abelev et al. , Phys. Rev. Lett. , 192301 (2007).[11] S. S. Adler et al. , Phys. Rev. Lett. , 032301 (2006); S. S. Adler et al. , Phys. Rev. Lett. ,172301 (2007).[12] A. Adare et al. , Phys. Rev. Lett. , 252002 (2006).[13] S. S. Adler et al. , Phys. Rev. Lett. , 082301 (2005).[14] H. Liu et al. , Phys. Lett. B , 441 (2006).[15] S. S. Adler et al. , Phys. Rev. D , 092002 (2007); D. Hornback, these proceedings.[16] S. Afanasiev et al. , e-print arXiv:nucl-ex/0802.0050.[17] R. Vogt, Int. J. Mod. Phys. E , 211 (2003); R. Vogt, e-print arXiv: hep-ph/0709.2531.[18] J. Raufeisen and J. C. Peng. Phys. Rev. D , 054008 (2003); E. L. Bratkovskaya et al. , Phys.Rev. C , 054905 (2003); T. Sj¨ostrand et al. , Computer Physics Commun. , 238 (2001).[19] H. Hees, V. Greco and R. Rapp, Phys. Rev. C , 034913 (2006).[20] E. Schnedermann, J. Sollfrank, and U. Heinz, Phys. Rev. C , 2462 (1993).[21] J. Adams et al. , Phys. Rev. Lett. , 112301 (2004).[22] J. Adams et al. , Phys. Rev. Lett. , 182301 (2004).[23] T. Hirano et al. , e-Print: arXiv:nucl-th/0710.5795.[24] R. Rapp and H. van Hees, J. Phys. G , S351 (2006).[25] A. Adil and I. Vitev, Phys. Lett. B , 139 (2007).[26] A. Dion, these proceedings.[27] J. Adams et al. , Phys. Rev. Lett. , 152301 (2006).[28] G. Wang, these proceedings.[29] X. Lin et al. , J. Phys. G , S821 (2007).[30] A. Mischke et al. , J. Phys. G , 044022 (2008); A. Mischke, these proceedings.[31] S. Frixione and B.R. Webber, J. High Energy Phys. , 029 (2002); S. Frixione, P. Nason andB.R. Webber, J. High Energy Phys.0308