In-Medium Fragmentation Functions via Direct  Measurements at STAR Experiment Ahmed M. Hamed for the STAR Collaboration Winter Workshop on Nuclear Dynamics, Ocho Rios, Jamaica Januray 2-9, 2010 Texas A&M University 1

Hard scattering in vacuum-QCD Probe the medium through the modification in Fragmentation Functions (FF)  In-Vacuum vs. In-Medium FF. 2 D vac c/h (z) ‏ p+p or peripheral Au+Au Hard Scattering in vacuum-QCD . ab h c Motivation  Global QCD analysis supports factorization and universality in the kinematical domain accessed by e + e -, ep, and pp experiments. High-pT hadron productions in vacuum-QCD What about hadron productions at high-pT in medium (nuclei collisions)? q-jet g-jet Eur. Phys. J. C 13, 573 (2000)‏ Z. Phys. C 69, 543 (1996)‏ LEP data

3  Modification of parton densities in nuclei. “Cold Nuclear Matter CNM” Hard scattering in medium and at RHIC Hadron productions in nuclear medium can differ significantly from vacuum. Phys. Rev. Lett. 40, 1624 (1978). Possible origins of the observed differences:  Interaction b/w the nuclear medium and partons “before fragmentation”.  Interaction b/w nuclear medium and hadrons “after fragmentation”. Central Au+Au Gluon radiation is induced by multiple scattering Hard Scattering in the medium med c/h D (z) ‏ a b c h o nPDFs do not spoil the requirements for factorization up to NLO according to DIS off nuclei and Drell-Yan process on nuclear target  nPDF is universal. nPDFs  Similar level and pattern of suppression for different hadrons in Au+Au compared to p+p.  suppression at partonic level.  Similar level and pattern of suppression for different partons in Au+Au compared to p+p.  Not understood yet!  Direct photons follow binary scaling in contrast to hadrons.  Di-hadron correlations: Strong modification in the FF of the recoil jet in Au+Au but not in p+p, and d+Au. Observations from Hard Scattering at mid- rapidity at RHIC Why these observations are not JUST CNM effect? o What about the nFFs? On progress!

4 Hard scattering at RHIC and a “golden probe”  assumes that factorization holds, one could extract medium parameters like:  s,  0, q,etc..   Indicates a medium formation with much higher energy density than that of CNM. Different models successfully describe the data with very different medium parameters ( q~3-19 GeV 2 /fm).  Phenomenological studies for RHIC data But Remember in previous slide: nPDF doesn’t spoil the factorization requirements and the question for nFF is awaiting for future measurements! Which measurements are free from uncertainties accompanying fragmentation? LO production processes of  dir Why  dir –jet measurement is golden probe? The  dir -jet coincidence measurement is “golden probe” to study the parton energy loss in the medium created at RHIC.

5 Direct gamma-jet coincidence as a “golden probe” P(  E)  F( E, L, C R, f )‏ Conjecture of energy loss functional form Is it possible to perform high-statistics measurements with practical facilities? o Measurements of path length dependence of energy loss (  -jet vs  0 -jet)‏ o Measurements of energy dependence of energy loss (  -jet in AuAu and pp)‏ The outgoing high-p T  dir balances the transverse momentum of the other outgoing parton assuming negligible k T effect (several hundred MeV “theoretically” and ~3GeV as PHENIX reported). In-medium  The mean free path of  dir is large enough that its momentum is preserved, regardless of the position of the hard scattering vertex inside the medium.  Samples a uniform spatial distribution of the hard scattering vertex inside the medium   “no surface bias and no tangential emission bias”  dir -jet coincidence measurements provide: hh 00 Surface bias hh 00 Tangential-emission bias  hh Uniform spatial distribution of the hard scattering vertex P(  E)  F( E )‏ P(  E)  F( L, C R )‏ If Compton scattering is the dominant process for  dir productions Color factor C R 00 00 Away-side q q/g “independent variables”

Background estimation I Very challenging measurements due to the signal/background ratio.  High-pt direct photons are produced at a rate comparable to that of single particles. 6 Assuming m T -scaling for the not measured particles in p+p and factor of 5 suppression in central Au+Au.   /  0   em The Compton-scattering process S/bg at  S=200 GeV at mid- rapidity at p T  8 GeV/c p+pAu+Au (central)‏  dir /  0 ~1:5~1:1  dir /  ~1:1.25~1:0.25  dir /  frag ~1:0.4?  dir /  ~1:0.451:0.09  dir /  ` ~1:0.251:0.05  dir /  0 ~1: : Why  frag is so special among other sources of bg? hep-ph/ (  0 represents ~80% of the total bg.)‏

7 Background estimation II Example of Bremsstrahlung diagrams Fragmentation photons  frag  frag seems to be accompanied by additional hadrons. In Au+Au The sub-process of  frag is of order of O(  s 2 ) but its yield is comparable to  dir LO process O(  s  em ). The relative contributions of  dir and  frag are strongly depend on the region explored in the PDF  collider energy and kinematics.  frag /  dir ~30-40% at p  T  8 GeV/c at mid-rapidity at RHIC energy. The  frag contribution is expected to fall off more rapidly in x T than the other lowest order of  dir. Enhancement: jet-plasma photons Suppression: quark suppression How STAR select events rich in  ? “more problematic at LHC than at RHIC”  em /  s

8 STAR detector and on-line event selections Bht2-mb: ZDC coincidence, and E T(tower)  5.76 Tagger for express stream: Based on bht2-mb, with additional higher E T (cluster)  7.44GeV. “Cluster_size  2 towers” SpeciesRun Year  S NN Integrated luminosity p+p GeV11pb -1 Au+Au GeV 535  b -1 The 535  b -1 of Au+Au corresponds to 20.8 pb -1 of p+p. 1  -triggered event each 5000 mb event L2gamma trigger in AuAu (2007)‏ How to construct azimuthal correlation in event-by-event at STAR?

Correlate photon candidates “triggers” (BEMC-BSMD) with associated tracks (TPC) BEMC TPC STAR detector Offline event selections Offline: event selection and analysis Beam axis  vertex within  55 cm of the center of TPC. 180°  tracking efficiency as a function of multiplicity through embedding (   ). Systematic uncertainties: A detailed study of shower profile, primary vertex, charge-rejection cuts., and energy scale uncertainty.  single particle simulation of (  /  0 ) and embedding to study the shower profile. How to distinguish between  /  0 at STAR  at least one cluster with E T  8GeV, Esmd  0.5GeV, Esmd  0.5GeV, and no track with p  3GeV/c pointing to that cluster.   9 00 2

10 STAR BEMC and BSMD  i : strip energy r i : distance relative to energy maxima Cross section in  The shower shape is quantified with the cluster energy, measured by the BEMC, normalized by the position-dependent energy moment, measured by the BSMD strips. E cluster  i  i r i 1.5 i=0,…7 in  and  The two photons originated from  0 hit the same tower at p T >8GeV/c   What is the efficiency/rejection power of the Transverse Shower Profile “TSP” cut?

[cm -1.5 ] Shower shape analysis  Rejection power: > 99% direct photons rejections and ~60% for rejecting  0.  sample free of  dir. 11  The tower energy asymmetry cut to purify the  rich sample in case of  0 decay across the module in   Frag. Photons, photons from asymmetric decay of  0, photon from decay of , and other hadrons?  Transverse shower profile shows no strong dependence on the trigger energy. How the correlation functions look like for  /  0 after using TSP? STAR Preliminary [cm -1.5 ]

Correlation functions 12 How to test the purity of  0 -rich sample against  dir ? nucl-ex/   rich sample has lower near-side yields compared to those of the  0 rich, but not zero!  Shower-shape analysis is only effective for rejecting two close  showers, leaving background  from asymmetric decays of  0, ,  frag.  The level of uncorrelated bg is dramatically suppressed relative to the signal over the measured rang of p T assoc  “negligible v2 contribution”. Fitting the correlation with two Gaussian and straight line to extract the near “|  |  0.63 rad” - and away-side “|  -  |  0.63 rad” yields over |  |  1.9. Correlation functions without bg subtraction

Near and away-side associated yields per  0 -rich sample (  dir free) 13 z T dependence of  0 -h  and h  -h  near and away-side yields. D(z T ) = 1/N trig dN/d(  ) over |  |  1.9 for |  |  0.63 rad and |  -  |  0.63 rad A general agreement of ~ 20-30% b/w the results from  0 -h  and h  -h  is clearly seen in both near and away-side yields  the  0 -rich sample is free of  dir. For  0 -h  : Correlated systematic ~7-13% and point-to-point uncertainties are less than 5% How to extract the yield associated with  dir ? nucl-ex/

values reasonable?Are Obtaining the FF with  dir “novel method” 14 Standard Statistical Method: 1. Measure inclusive photons. 3. Subtract photons from decay of    etc. 2. Reconstruct other sources of photons “hadrons”! We don’t tag event rich in  dir and we don’t obtain information about the FF of the away side. Novel method Statistical measurement of  -jet yields All sources of bg are approximated to the measured  0 Shower shape analysis doesn’t measure all bg, it measures only the  0 in its symmetric decay mode. Imposing the condition of zero-near side yield associated with  dir Do the other sources of bg have similar correlations with charged hadrons as that of the measured  0 ?  10% of all  0 (8-16GeV/c) decay asymmetrically with one gamma has p T > 8 GeV/c within STAR-BEMC acceptance.  causes similar level of background as asymmetric  0. (a measure of bg in the  rich sample)‏ Are R values reasonable?

15 The level of bg in the  rich sample: ~55-30% from pp to central Au+Au, and doesn’t show strong dependence neither on p T trig nor on p T assoc. Do the other sources of bg have similar correlations with h  as that of the measured  0 ? STAR Preliminary [GeV/c] STAR Preliminary [GeV/c]

16 Do other sources of bg have similar correlations to that of measured  0 ? PYTHIA simulation indicates, within ~10% at the same p T trig, that the correlations of  triggers from asymmetric hadron decays are 1. Similar to those of symmetrically decaying  0 triggers. 2. Similar to the measured correlations of  0 -rich triggers. What about  frag ? PYTHIA

17  frag has different correlation with the charged particle compared to that of  0 with insensitivity to the charged rejection cut.. 1. The  frag which has near side yield are estimated using the  2 analysis, by comparing the shape of the near-side correlation of  rich to  0 rich triggers, and is taken into account in the systematic errors. 2. The  frag which has no near side yield within the integrated region “|  |  0.63 rad” remains in the  dir measurements. Do other sources of bg have similar correlations to that of measured  0 ? 2 classes of consideration for  frag : How the associated yields per  dir are compared to theory and to that of  0 ?

nucl-ex/ Fragmentation function per  dir 18 z T dependence of away-side associated-particle yields for  0 triggers and  dir triggers.  dir carries the total scattered constituent momentum while  0 carries only a fraction of it.  different proportions of q and g recoiling from  dir and  0 triggers if Compton scattering is the dominant channel for  dir productions. p+p Au+Au  different path length for the recoiling jet from  0 trigger and  dir trigger.  At given z T, the away-side yield per  0 trigger is significantly larger than that per  dir trigger.  The yields in p+p and Au+Au are well described by theoretical models: 1. Zhang et al., no  frag contributions. 2. Qin et al., significant contribution of  frag. Yields “upper panel” How to quantify the medium effect on the associated yields with  dir /  0 ?  dir vs.  0 Data vs. theory

19 “Lower panel”: Medium effect quantification as a function of z T I AA =D(z T ) pp /D(z T ) AuAu(0-10%) for the recoiling jet of  0 and  dir triggers:  similar level and pattern of suppression for I AA of  0 and  dir triggers and both are z T -independent  effect of fluctuations in energy loss dominates over the effect of geometry. I AA of  0 vs. I AA of  dir I AA of  0 vs. theory I AA of  dir vs. theory  agrees with Zhang et al. within the current uncertainties.  disfavors Renk-YaJEM  lost energy is distributed to very low pt and large angle.  agrees with Renk-ASW, Qin et al., and Zhang et al. within current uncertainties.  shows no strong rise at low z T. Probe the medium with Fragmentation function per  dir Why the geometry effect is expected to result in different I AA for  dir than that for  0 ? nucl-ex/

20 If strong path length dependence of energy loss, it is expected that I AA of  0 to be smaller than that of  dir 1. The recoiling jet from  0 travel on average longer distance within the medium than that of  dir 2. If the Compton scattering is the dominant channel for  dir productions, then recoiling jet of  0 is a mix of q/g while for  dir the dominate is q. 3. The energy of the recoiling jet from  0 is greater than that of  dir. I AA (  0 )  I AA (  dir )‏ I AA (  0 )  I AA (  dir )‏ Factors to determine the ratio b/w I AA (  0 ) and I AA (  dir )‏ If we determine the I AA (E) we can learn about the other two factors. I AA of  0 vs. I AA of  dir How I AA depends on E?  E  f(L)‏  E  f(C R )‏  E  f(E)‏

21 I AA of  dir shows no strong dependence on E. Then The dependence on the other two factors is small as well. I AA (E) of  dir Why this study is useful? nucl-ex/

22 Summary, Conclusion, Discussion, and Future 1. One more measurement for the QCD global analysis for nFF parameterization is presented. 3. One more measurement with a better constrain for the in-medium energy loss models is reported by the STAR experiment, where the detector is very-well suited for such measurements. o Parton initial energy o Path length within the medium o Color factor  Conclusion  Summary  Discussion 2. Does the fluctuation in energy loss smear out the expected geometrical effects? 3. Is the medium so dense that energy loss doesn’t depend on the parton initial energy?  Future STAR is planning to: 1. Measure anisotropic asymmetry of  dir /  0 w.r.t reaction plane. 2. Measure I AA in- and out- of reaction plane. 4. How can progress be made in extracting medium parameters? 2. Lost energy is spread throughout the medium at larger angle from the “jet-axis” and distributed to lower p T particles than measured in this analysis. 3. Study the low z T region either by increasing p T of the trigger or decreasing the p T of the associated. With assumption:  Negligible k T effect at such high p T of  dir,  Leading hadron is sufficient for modified FF measurements,  Residual contributions of  frag is negligible,  The Compton scattering is the dominate process for  dir productions, then within the accessed kinematics range and accuracy of these measurements one conclude that parton energy loss doesn’t strongly depend on: 1. Is the away-side surface-biased as well within the measured p t associated?

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