pQCD A.) pQCD components in elementary collisions B.) modification in AA collisions

1. pQCDA.) pQCD components in elementary collisionsB.) modification in AA collisions

2. High pT Particle Production (the factorization theorem) hadrons Parton Distribution Functions hadrons Hard-scattering cross-section leading particle Fragmentation Function High pT (> 2.0 GeV/c) hadron production in pp collisions for √s > 60 Gev: ~ Jet: A localized collection of hadrons which come from a fragmenting parton c a Parton Distribution Functions Hard-scattering cross-section Fragmentation Function b d “Collinear factorization”

3. Hard scattering in longitudinal plane Hard scattering in transverse plane Generally, momentum fraction x1x2. (Not in PHENIX –0.35<<0.35) Point-like partons  elastic scattering Partons have intrinsic transverse momentum kT Hard scattering

4. jet fragmentation transverse momentum jet p+p p+A A+A Jet Fragmentation (width of the jet cone) Partons have to materialize (fragment) in colorless world jT and kT are 2D vectors. We measure the mean value of its projection into the transverse plane |jTy| and |kTy| . |jTy|is an important jet parameter. It’s constant value independent on fragment’s pT is characteristic of jet fragmentation (jT-scaling). |kTy| (intrinsic + NLO radiative corrections)carries the information on the parton interaction with QCD medium.

5. In Practice parton momenta are not known  Simple relation Fragmentation Function (distribution of parton momentum among fragments) jet In Principle Fragmentation function

6. Thermally-shaped Soft Production “Well Calibrated” Hard Scattering p0 in pp: well described by NLO p+p->p0 + X • Ingredients (via KKP or Kretzer) • pQCD • Parton distribution functions • Fragmentation functions hep-ex/0305013 S.S. Adler et al.

7. Fate of jets in heavy ion collisions? idea: p+p collisions @ same sNN = 200 GeV as reference p p ?: what happens in Au+Au to jets which pass through medium? • Prediction: scattered quarks radiate energy (~ GeV/fm) in the colored medium: • decreases their momentum (fewer high pT particles) • “kills” jet partner on other side ? Au+Au

8. High pT Particle Production in A+A Parton Distribution Functions Intrinsic kT , Cronin Effect Shadowing, EMC Effect Hard-scattering cross-section c a Partonic Energy Loss b d hadrons FragmentationFunction leading particle suppressed (pQCD context…)

9. Jet fragment shape parameters jT, kT

10. Parton distribution functions(hep-ex/0305109) RHIC

11. Do we understand hadron productionin elementary collisions ? (Ingredient I: PDF) RHIC

12. z z Ingredient II: Fragmentation functionsKKP (universality), Bourrely & Soffer (hep-ph/0305070) Non-valence quark contribution to parton fragmentation into octet baryons at low fractional momentum in pp !! Quark separation in fragmentation models is important. FFs are not universal. Depend on Q, Einc, and flavor

13. How to measure PID ? • Initial PID: charged hadrons vs. neutral pions • Detailed PID: • dE/dx (0.2-0.8 GeV/c) • TOF / RICH / TRD (1.5-5 GeV/c) • rdE/dx (5-20 GeV/c) • V0 topology (only statistics limited)

14. Thermally-shaped Soft Production “Well Calibrated” Hard Scattering p0 in pp: well described by NLO (& LO) p+p->p0 + X • Ingredients (via KKP or Kretzer) • pQCD • Parton distribution functions • Fragmentation functions • ..or simply PYTHIA… hep-ex/0305013 S.S. Adler et al.

15. pp at RHIC:Strangeness formation in QCD nucl-ex/0607033 Strangeness production not described by leading order calculation (contrary to pion production). It needs multiple parton scattering (e.g. EPOS) or NLO corrections to describe strangeness production. Part of it is a mass effect (plus a baryon-meson effect) but in addition there is a strangeness ‘penalty’ factor (e.g. the proton fragmentation function does not describe L production). s is not just another light quark

16. How strong are the NLO correctionsin LO calculations (PYTHIA) ? • K.Eskola et al. (NPA 713 (2003)): Large NLO corrections not unreasonable at RHIC energies. Should be negligible at LHC (5.5 or 14 TeV). STAR LHC

17. New NLO calculation based on STAR data (AKK, hep-ph/0502188, Nucl.Phys.B734 (2006)) K0s apparent Einc dependence of separated quark contributions.

18. Non-strange baryon spectra in p+p Pions agree with LO (PYTHIA) Protons require NLO with AKK-FF parametrization (quark separated FF contributions) PLB 637 (2006) 161

19. mt scaling in pp

20. Breakdown of mT scaling in pp ?

21. mT slopes from PYTHIA 6.3 Gluon dominance at RHIC PYTHIA: Di-quark structures in baryon production cause mt-shift Recombination: 2 vs 3 quark structure causes mt shift

22. Baryon/meson ratios – p+p collisions Bell shape from fragmentation is visible PLB637 (2006) 161

23. Collision Energy dependence of baryon/meson ratio Ratio vs pT seems very energy dependent (RHIC < < SPS or FNAL), LHC ? Not described by fragmentation ! (PYTHIA ratios at RHIC and FNAL are equal) Additional increase with system size in AA Both effects (energy and system size dependence) well described by recombination

24. Recombination vs. Fragmentation(a different hadronization mechanism in medium than in vacuum ?) Recombination at moderate PT Parton pt shifts to higher hadron pt. Fragmentation at high PT: Parton pt shifts to lower hadron pT Recomb. fragmenting parton: ph = z p, z<1 recombining partons: p1+p2=ph Frag.

25. Baryon production mechanism through strange particle correlations … • Test phenomenological fragmentation models OPAL ALEPH and DELPHI measurements: Yields and cosQ distribution between correlated pairs distinguishes between isotropic cluster (HERWIG) and non-isotropic string decay (JETSET) for production mechanism. Clustering favors baryon production JETSET is clearly favored by the data. Correlated L-Lbar pairs are produced predominantly in the same jet, i.e. short range compensation of quantum numbers.

26. Flavor dependence of yield scaling up, down strange charm PHENIX D-mesons • participant scaling for light quark hadrons (soft production) • binary scaling for heavy flavor quark hadrons (hard production) • strangeness is not well understood (canonical suppression in pp)

27. Charm cross-section measurements in pp collisions in STAR • Charmquarks are believed to be produced at early stage by initial gluon fusions • Charm cross-section should follow number of binary collisions (Nbin) scaling

28. FONLL RHIC (from hep-ph/0502203 ): LO: NLO: LO / NLO / FONLL? • A LOcalculation gives you a rough estimate of the cross section • A NLOcalculation gives you a better estimate of the cross section and a rough estimate of the uncertainty • Fixed-Order plus Next-to-Leading-Log (FONLL) • Designed to cure large logs in NLO for pT >> mc where mass is not relevant • Calculations depend on quark mass mc, factorization scale mF (typically mF = mc or 2 mc), renormalization scale mR (typically mR = mF), parton density functions (PDF) • Hard to obtain large s with mR = mF (which is used in PDF fits) CDF Run II c to D data (PRL 91,241804 (2003): • The non-perturbative charm fragmentation needed to be tweaked in FONLL to describe charm. FFFONLL is much harder than used before in ‘plain’ NLO  FFFONLL≠ FFNLO

29. hep-ex/0609010 RHIC: FONLL versus Data • Matteo Cacciari (FONLL): • factor 2 is not a problem • factor 5 is !!! nucl-ex/0607012 • Spectra in pp seem to require a bottom contribution • High precision heavy quark measurements are tough at RHIC energies. Need direct reconstruction instead of semi-leptonic decays. Easy at LHC. • Reach up to 14 GeV/c D-mesons (reconstructed) in pp in first ALICE year.

30. Conclusions for RHIC pp data • We are mapping out fragmentation and hadronization in vacuum as a function of flavor. • What we have learned: • Strong NLO contribution to fragmentation even for light quarks at RHIC energies • Quark separation in fragmentation function very important. Significant non-valence quarks contribution in particular to baryon production. • Gluon dominance at RHIC energies measured through breakdown of mt-scaling and baryon/meson ratio. Unexpected small effect on baryon/antibaryon ratio • Is there a way to distinguish between fragmentation and recombination ? Does it matter ? • What will happen at the LHC ? What has happened in AA collisions (hadronization in matter) ?

31. Thermally-shaped Soft Production “Well Calibrated” Hard Scattering p0 in pp: well described by NLO p+p->p0 + X • Ingredients (via KKP or Kretzer) • pQCD • Parton distribution functions • Fragmentation functions hep-ex/0305013 S.S. Adler et al.

32. Hadronization in QCD (the factorization theorem) hadrons Parton Distribution Functions hadrons Hard-scattering cross-section leading particle Fragmentation Function High pT (> 2.0 GeV/c) hadron production in pp collisions: ~ Jet: A localized collection of hadrons which come from a fragmenting parton c a Parton Distribution Functions Hard-scattering cross-section Fragmentation Function b d “Collinear factorization”

33. Modification of fragmentation functions(hep-ph/0005044)

34. RAA and high-pT suppression STAR, nucl-ex/0305015 pQCD + Shadowing + Cronin energy loss pQCD + Shadowing + Cronin + Energy Loss Deduced initial gluon density at t0 = 0.2 fm/c dNglue/dy ≈ 800-1200 e≈ 15 GeV/fm3, eloss = 15*cold nuclear matter (compared to HERMES eA)(e.g. X.N. Wang nucl-th/0307036)

35. Induced Gluon Radiation • ~collinear gluons in cone • “Softened” fragmentation Is the fragmentation function modification universal ? Octet baryon fragmentation function from statistical approach based on measured inclusive cross sections of baryons in e+e- annihilation: Modification according to Gyulassy et al. (nucl-th/0302077) Quite generic (universal) but attributable to radiative rather than collisional energy loss z z

36. Jet quenching I: hadrons are suppressed, photons are not

37. Energy dependence of RAA p 0 nucl-ex/0504001 RAA at 4 GeV: smooth evolution with √sNN Agrees with energy loss models

38. Baier, Schiff and Zakharov, AnnRevNuclPartSci 50, 37 (2000) Radiative energy loss in QCD BDMPS approximation: multiple soft collisions in a medium of static color charges Transport coefficient: Medium-induced gluon radiation spectrum: Total medium-induced energy loss: DE independent of parton energy (finite kinematics DE~log(E)) DE  L2 due to interference effects (expanding medium DE~L)

39. High-energy parton loses energy by rescattering in dense, hot medium. q q “Jet quenching” = parton energy loss Described in QCD as medium effect on parton fragmentation: Medium modifies perturbative fragmentation before final hadronization in vacuo. Roughly equivalent to an effective shift in z: Important for controlled theoretical treatment in pQCD: Medium effect on fragmentation process must be in perturbative q2 domain.

40. L q q g L q q Mechanisms High energy limit: energy loss by gluon radiation. Two limits: (a) Thin medium: virtuality q2 controlled by initial hard scattering (LQS, GLV) (b) Thick medium: virtuality q2 controlled by rescattering in medium (BDMPS) Trigger on leading hadron (e.g. in RAA) favors case (a). Low to medium jet energies: Collisional energy loss is competitive! Especially when the parent parton is a heavy quark (c or b).

41. Extracting qhat from hadron suppression data RAA: qhat~5-15 GeV2/fm

42. ~RHIC data QGP Hadronic matter  R. Baier, Nucl Phys A715, 209c What does qhat measure? • Equilibrated gluon gas: • number density ~T3 • energy density e~T4 qhat+modelling  energy density Model uncertainties • pQCD result: c~2 (aS? quark dof? …) • sQGP (multiplicities+hydro): c~10

43. RHIC data sQGP? ? QGP Pion gas Cold nuclear matter q-hat at RHIC

44. Salgado and Wiedemann PRD68 (2003) 014008 Medium-induced radiation spectrum GLV BDMPS   Baier, Dokshitzer, Mueller, Peigne, Schiff, Armesto, Salgado, Wiedemann, Gyulassy, Levai, Vitev BDMPS(ASW) vs. GLV Rough correspondence: (Wiedemann, HP2006)  30-50 x cold matter density

45. What do we learn from RAA? GLV formalism BDMPS formalism ~15 GeV Wicks et al, nucl-th/0512076v2 Renk, Eskola, hep-ph/0610059 DE=15 GeV Energy loss distributions very different for BDMPS and GLV formalisms But RAA similar! Need more differential probes

46. RAA for p0: medium density I I. Vitev C. Loizides hep-ph/0608133v2 W. Horowitz Use RAA to extract medium density: I. Vitev: 1000 < dNg/dy < 2000 W. Horowitz: 600 < dNg/dy < 1600 C. Loizides: 6 < < 24 GeV2/fm Statistical analysis to make optimal use of data Caveat: RAA folds geometry, energy loss and fragmentation

47. Yu.Dokshitzer 1.) heavy quark dead cone effect : Heavy quarks in the vacuum and in the medium (Dokshitzer and Kharzeev (PLB 519 (2001) 199)) the radiation at small angles is suppressed 2.) gluon vs. quark energy loss: Gluons should lose more energy and have higher particle multiplicities due to the color factor effect. Different partons lose different amounts of energy

48. …but everything looks the same at high pt…. up,down strange charm ?

49. Particle dependencies: RAA of strangeness A remarkable difference between RAA and RCP that seems unique to strange baryons. Ordering with strangeness content. ‘Canonical suppression’ is unique to strange hadrons This effect must occur ‘between’ pp and peripheral AA collisions

50. Strange enhancement vs. charm suppression ? Do strange particles hadronize different than charm particles ? But is it a flavor effect ? Kaon behaves like D-meson, we need to measure Lc