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

2. 2  Motivation, Hard scattering in vacuum-QCD, in medium, and at RHIC.  Offline event selection & analysis technique.  Direct photons & background estimation.  Results and Summary  STAR detector and on-line data selections.  STAR detector and Shower profile analysis.  Correlation functions.  The associated yield with a trigger-sample (  0 -rich) free of direct photons.  Novel method for obtaining fragmentation functions per direct gamma trigger.  Discussion on the remaining background.  Fragmentation functions per direct gamma trigger in vacuum-QCD and at RHIC. Table of contents  Parton energy loss discussion.

3. Motivation and Hard scattering in vacuum-QCD Probe the medium through the modification in Fragmentation Functions (FF)  In-Vacuum vs. In-Medium FF.  Hadronization process: great challenges for the theory of Strong Interaction.  Global QCD analysis supports factorization and universality in the kinematical domain accessed by e + e -, ep, and pp experiments. 3 To the LO and in the asymptotic limit of very large jet energy: g-jet q-jet ~ 2.25(ratio of Casimir factors)‏ D vac c/h (z) ‏ p+p or peripheral Au+Au Hard Scattering in vacuum-QCD . ab h c exponential fit in the 0.2  z  1 region Motivation

4. 4  Modification of parton densities in nuclei. “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 For CNM Up to NLO: DIS off nuclei and Drell-Yan process on nuclear target: Factorization and universality are still valid in nuclear environment. nPDFs do not spoil the requirements for factorization, How about the final-state nuclear effects (nFFs)? 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. Hard Scattering results at RHIC

5. 5 Direct gamma-jet coincidence as a “golden probe” o Measurements of energy dependence of energy loss (  -jet in AuAu and pp)‏ o Measurements of path length dependence of energy loss (  -jet vs  0 -jet)‏  hh hh 00  dir -jet coincidence measurements: P(  E)  F( E, L, C R, f )‏ Energy loss functional form In theory assuming that factorization holds  Medium parameters like:  s,  0, q,etc..  Phenomenological studies for RHIC data indicate 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).  provides an insight into the dynamics of hadronic constituents which is not obscured by their fragmentation. LO are the dominant processes: negligible k T effect Assuming: Full jet  leading hadron No strong dependence on: Flavor “parton type” Species “hadron type”

6. 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: perform high-statistics measurements with practical facilities. 6 Assuming m T -scaling for the not measured particles in p+p and factor of 5 suppression in central Au+Au.  /  0   em (  0 represents ~80% of the total bg.)‏ The inverse 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 ~1:0.00011:0.00002

7. 7 Background estimation II Example of Bremsstrahlung diagrams Fragmentation photons  frag  frag seems to be accompanied by additional hadrons. PYHTIA study indicates the survival of  frag after the isolation cut. 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

8. 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+p2006200 GeV11pb -1 Au+Au2007200 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)‏

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

10. 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  

11. 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.

12. Correlation functions 12  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

13. 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%

14. 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)‏

15. 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.

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

17. 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 :

18. 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 inverse 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. 1. At given z T, the away-side yield per  0 trigger is significantly larger than that per  dir trigger. 2. 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”

19. 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

20. 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. The 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

21. 21 I AA of  dir shows no strong dependence on E. Then The dependence on other two factors is small as well. I AA (E) of  dir

22. 22 Summary, Conclusion, and Discussion 2. Assuming: Then, within the accessed kinematics range one concludes: 1. Negligible k T effect at such high p T (8-16GeV/c) of  dir. 2. Leading hadron is sufficient for FF measurements. 3. The remaining  frag causes negligible effect on the  dir measurements. 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. Parton energy loss doesn’t depend strongly on: 1. Parton initial energy 2. Path length within the medium 3. Color factor 4. Inverse Compton scattering is the dominant channel for  dir productions. If this is true and nothing is missing, then, what else determine the energy loss within the medium?