1. 7-Mar-161 Fragmentation function from the direct photon associated distributions. Jan Rak Jan Rak Jyväskylä University & Helsinki Institute of Physics, Finland

2. 7-Mar-162 MotivationMotivation Great success of RHIC: perfect liquid, sQGP Measured for variety of species  0,  , ,  dir, p, K S, , , J/ ,  … and CMS energies  s=17, 22.4, 62.4, 130, 200 GeV/c 7-Mar-16Jan Rak2 Jet quenching -light mesons suppressed by factor of 5, direct-  unsuppressed => FS nature of observed suppression. Density of scattering centers Range of color force Transp. Coef. Scatt. power of QCD med:

3. 7-Mar-163 Fun with the String Theory Great success of RHIC: test bench for string theory (AdS/CFT) AdS/CFT Correspondence AdS/CFT Correspondence (Maldacena 1998) Strongly interacting matter X AdS/CFT duality (Phys. Rev. Lett., 2005, 94,111601) Strongly interacting matter X AdS/CFT duality (Phys. Rev. Lett., 2005, 94,111601)

4. 7-Mar-164 Some open questions however, even “simple” inclusive observable left us with with questions: Light and heavy quarks suppression Quarks and gluons suppression Direct photon suppression at high p T Mark Thomas Heinz

5. 7-Mar-165 p T broadening DIS x HI Pasquale Di Nezza HERMES away-side widths similar for central and peripheral d+Au 0.24+-0.07 rad Au+Au 20-40% 0.20+-0.02 rad Au+Au 0-5% 0.22+-0.02 rad away-side widths similar for central and peripheral d+Au 0.24+-0.07 rad Au+Au 20-40% 0.20+-0.02 rad Au+Au 0-5% 0.22+-0.02 rad STAR Phys.Rev.Lett.97:2006 8 < p T (trig) < 15 GeV/c

6. 7-Mar-166 Direct photon correlations Two particle correlations more detailed view into a nature of parton interactions with QCD medium. Access to parton intrinsic momentum k T -> soft pQCD radiation, jet shape parameters j T -> induced radiation, fragmentation function -> energy loss. –Di-hadron correlations and conditional yields –Direct photons-hadron correlations in p+p @  s=200 GeV and 14 TeV Direct photon-hadron correlations Jet reconstruction difficult/impossible small acceptance and in A+A collisions. Photon energy balances the outgoing parton fixes the energy scale?

7. 7-Mar-167 D(z) measurement without jet reconstruction D(z) measurement without jet reconstruction Assumption: Leading particle fixes the energy scale of the trigger & assoc. jet => leading particle - trigger p Tt xEzxEz p out kTkT away-side fragments - associated particles p Ta JTJT

8. 7-Mar-168 Azimuthal correlation function in p+p @  s=200 GeV d+Au Phys.Rev.D74:072002,2006 NN AA  N   j T  jet fragmentation transverse momentum  F   k T  parton transverse momentum Y A  folding of D(z) and final state parton dist. p + p  jet + jet 

9. 7-Mar-169 Jet shape evolution with trigger and assoc. p T Au+Au / p+p  s = 200 GeV arXiv:0705.3238 [nucl-ex] Per-trigger yield vs.  for various trigger and partner p T (p A T  p B T ), arranged by increasing pair momentum (p A T + p B T ) Flat region: celebrated b2b disappearance Punch through region (HR): reappearance at high-p T Shoulder region (SR): Medium induced “Mach cone” Low p T : Enhancement in SR & suppression in HS High p T : Reappearance of away-side jet not due to merging of side peaks

10. 7-Mar-1610 Two-particle correlations in p+p Fragmentation function D(z) and Intrinsic momentum k T Fragmentation function D(z) and Intrinsic momentum k T

11. 7-Mar-1611 Soft + hard QCD radiation k T phenomenology Back-to-back balanced Soft QCD radiation Hard NLO radiation Compton photo-production

12. 7-Mar-1612 Correl. fcn width - k T and acoplanarity Lorentz boost => p T,pair || k T,t || k T,a colinearity partonic hadronic Lab frame Hard scattering rest frame

13. 7-Mar-1613 Associated yield Assumption ( Phys.Rev.D74:072002,2006 for details) : Invariant mass of mass-less partons in hard scattering CMS and in LAB is the same -> non-Gaussian k T -smearing.

14. 7-Mar-1614 LEP data M.J.Tannenbaum Approximation - Incomplete Gamma function when assumed power law for final state PDF and exp for D(z) yield Trigger associated spectra are insensitive to D(z)

15. 7-Mar-1615 Unavoidable z-bias in di-hadron correlations z-bias; steeply falling/rising D(z) & PDF(1/z)  z trig   z assoc  Varying p Tassoc with p Ttrigger kept fixed leads to variation of both trigger and associated jet energies. Fixed trigger particle momentum does not fix does not fix the jet energy! Angelis et al (CCOR): Nucl.Phys. B209 (1982) Angelis et al (CCOR): Nucl.Phys. B209 (1982)

16. 7-Mar-1616  k 2 T  and  z t  in p+p @ 200 GeV from  0 -h CF Phys.Rev.D74:072002,2006 For D(z) the LEP date were used. Main contribution to the systematic errors comes from unknown ratio gluon/quark jet => D(z) slope. Base line measurement for the k T broadening - collisional energy loss. Direct width comparison is biased. Still, we would like to extract FF from our own data -> direct photon-h correl.

17. 7-Mar-1617 High p T : ref. for HI, resummation, detailed NLO tests High p T : ref. for HI, resummation, detailed NLO tests PHENIX measured  p T  pair =3.36  0.09  0.43GeV/c extrapolation to LHC  k 2 T  36 GeV 2 /c 2

18. Parton evolution - j T 3/7/201618 H.J. Pirner talk from yesterday A. Basseto, M. Ciafaloni, G. Marchesini And Nucl Phys B 163 (1980) 477

19. 7-Mar-1619 D(z) from gamma tagged correlation D(z) from gamma tagged correlation leading particle - trigger p Tt xEzxEz p out kTkT away-side fragments - associated particles p Ta h-h: Leading particle does not fix Energy scale. Direct gamma - trigger p Tt xEzxEz p out kTkT away-side fragments - associated particles p Ta  -h: direct gamma does fix Energy scale if no k T

20. 7-Mar-1620 00 Direct  PHENIX  s=200 GeV  0 and dir-  assoc. distributions Run 5 p+p @ 200 GeV Statistical Subtraction Method Arbitrary Normalization Matthew Nguyen APS Spring Meeting, April 15, 2007 Exponential slopes still vary with trigger  p T . If dN/dx E  dN/dz then the local slope should be p T  independent. FF slope

21. 7-Mar-1621 Pythia Initial/Final st. radiation & k T Initial/Fina state radiation OFF,  k 2 T  =0 GeV/c Initial/Fina state radiation ON,  k 2 T  =5 GeV/c

22. 7-Mar-1622  -h correlation and k T bias Can one extract the Fragmentation Function from  -h associated distribution despite the k T bias?  Solve for net-pair momentum

23. 7-Mar-1623  -h correlation and k T bias And assuming 2D Gaussian distribution for p T,pair => Conditional probability for detecting given photon-associated particle pair:

24. 7-Mar-1624 Folding with a Fragmentation function  -h h-h Di-hadron correlation slopes is incresing with p T as in the data gamma-hadron correlation slopes are converging at high photon-p T

25. 25 points are p+p 14 TeV PYTHIA xE distribution, dashed line KKP FF parameterization Nucl. Phys., 2001, B597, 337-369  - gluon jet (Annihilation) 17 %  - u quark jet (Compton) 66 %

26. Comparison to PYTHIA 3/7/201626  -h h-h When we used PYTHIA FF slopes for quarks and gluons we got quite satisfactory agreement.

27. 7-Mar-1627 SummarySummary I discussed: di-hadron and direct photon-h correlations - base line measurement for nuclear modification study: k T and initial/final state QCD radiation, resummation vs NLO j T near-side jet shape modifications fragmentation function - can be measured using jets - not from the first data. Despite our expectation FF is not accessible in di-hadron correlations. FF can be extracted from direct photons correlation only at relatively small trigger- photon momenta. k T -bias still present - pushes the minimum photon-trigger p T above 10 GeV/c at RHIC and 20 GeV/c at LHC. What we need is just data…

28. 7-Mar-1628 Final state parton dist and FF from data of pQCD? Effective FS parton distribution: Fragmentation function:  0 invariant cross section provides a constrain: