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

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

Hard scattering in longitudinal plane Generally, momentum fraction x 1  x 2. (Not in PHENIX –0.35<  <0.35) Hard scattering Hard scattering in transverse plane Point-like partons  elastic scattering Partons have intrinsic transverse momentum k T

Jet Fragmentation (width of the jet cone) Partons have to materialize (fragment) in colorless world jet jet fragmentation transverse momentum j T and k T are 2D vectors. We measure the mean value of its projection into the transverse plane  |j Ty |  and  |k Ty | .  |j Ty |  is an important jet parameter. It’s constant value independent on fragment’s p T is characteristic of jet fragmentation (j T -scaling).  |k Ty |  (intrinsic + NLO radiative corrections) carries the information on the parton interaction with QCD medium. p+pp+AA+A

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

 0 in pp: well described by NLO Ingredients (via KKP or Kretzer) Ingredients (via KKP or Kretzer)  pQCD  Parton distribution functions  Fragmentation functions p+p->  0 + X Hard Scattering Thermally- shaped Soft Production hep-ex/ S.S. Adler et al. “Well Calibrated”

Fate of jets in heavy ion collisions? p p ? Au+Au idea: p+p same  s NN = 200 GeV as reference ?: 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 p T particles)  “kills” jet partner on other side

Intrinsic k T, Cronin EffectParton Distribution FunctionsShadowing, EMC Effect Fragmentation Function leading particle suppressed Partonic Energy Loss c d hadrons a b Hard-scattering cross-section (pQCD context…) High p T Particle Production in A+A

Jet fragment shape parameters j T, k T

Parton distribution functions (hep-ex/ ) RHIC

Do we understand hadron production in elementary collisions ? (Ingredient I: PDF) RHIC

Ingredient II: Fragmentation functions KKP (universality), Bourrely & Soffer (hep-ph/ ) 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, E inc, and flavor zz

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

 0 in pp: well described by NLO (& LO) Ingredients (via KKP or Kretzer) Ingredients (via KKP or Kretzer)  pQCD  Parton distribution functions  Fragmentation functions..or simply PYTHIA…..or simply PYTHIA… p+p->  0 + X Hard Scattering Thermally- shaped Soft Production hep-ex/ S.S. Adler et al. “Well Calibrated”

pp at RHIC  Strangeness formation in QCD 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  production). s is not just another light quark nucl-ex/

How strong are the NLO corrections in LO calculations (PYTHIA) ? K.Eskola et al. 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

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

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

mt scaling in pp

Breakdown of m T scaling in pp ?

m T slopes from PYTHIA 6.3 Gluon dominance at RHIC PYTHIA: Di-quark structures in baryon production cause m t -shift Recombination: 2 vs 3 quark structure causes m t shift

Baryon/meson ratios – p+p collisions PLB 637 (2006) 161 Bell shape from fragmentation is visible

Collision Energy dependence of baryon/meson ratio Ratio vs p T 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

Recombination vs. Fragmentation (a different hadronization mechanism in medium than in vacuum ?) Recombination at moderate P T Recombination at moderate P T Parton pt shifts to higher hadron pt. Fragmentation at high P T: Fragmentation at high P T: Parton pt shifts to lower hadron p T recombining partons: p 1 +p 2 =p h fragmenting parton: p h = z p, z<1 Recomb. Frag.

Baryon production mechanism through strange particle correlations …  Test phenomenological fragmentation models OPAL ALEPH and DELPHI measurements: Yields and cos  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  bar pairs are produced predominantly in the same jet, i.e. short range compensation of quantum numbers.

Flavor dependence of yield scaling 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) PHENIX D-mesons up, down strange charm

Charm cross-section measurements in pp collisions in STAR  Charm quarks are believed to be produced at early stage by initial gluon fusions  Charm cross-section should follow number of binary collisions (N bin ) scaling Measurements direct D 0 (event mixing) c→  +X (dE/dx, ToF) c→e+X (ToF) (EMC) p T (GeV/c) 0.1    4.0  1.5 constraint , d  /dp T  d  /dp T

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

RHIC: FONLL versus Data Matteo Cacciari (FONLL): Matteo Cacciari (FONLL): factor 2 is not a problem factor 2 is not a problem factor 5 is !!! factor 5 is !!!  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. hep-ex/ nucl-ex/

Conclusions for RHIC pp data We are mapping out fragmentation and hadronization in vacuum as a function of flavor. We are mapping out fragmentation and hadronization in vacuum as a function of flavor. What we have learned : 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) ? What will happen at the LHC ? What has happened in AA collisions (hadronization in matter) ?

 0 in pp: well described by NLO Ingredients (via KKP or Kretzer) Ingredients (via KKP or Kretzer)  pQCD  Parton distribution functions  Fragmentation functions p+p->  0 + X Hard Scattering Thermally- shaped Soft Production hep-ex/ S.S. Adler et al. “Well Calibrated”

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

Modification of fragmentation functions (hep-ph/ )

STAR, nucl-ex/ energy loss pQCD + Shadowing + Cronin pQCD + Shadowing + Cronin + Energy Loss R AA and high-pT suppression Deduced initial gluon density at   = 0.2 fm/c dN glue /dy ≈  ≈ 15 GeV/fm 3, eloss = 15*cold nuclear matter (compared to HERMES eA) (e.g. X.N. Wang nucl-th/ )

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: Induced Gluon Radiation  ~collinear gluons in cone  “Softened” fragmentation Modification according to Gyulassy et al. (nucl-th/ ) Quite generic (universal) but attributable to radiative rather than collisional energy loss zz

Jet quenching I: hadrons are suppressed, photons are not

37   nucl-ex/ Energy dependence of R AA R AA at 4 GeV: smooth evolution with √s NN Agrees with energy loss models

Radiative energy loss in QCD BDMPS approximation: multiple soft collisions in a medium of static color charges  E independent of parton energy (finite kinematics  E~log(E))  E  L 2 due to interference effects (expanding medium  E~L) Medium-induced gluon radiation spectrum: Total medium-induced energy loss: Transport coefficient: Baier, Schiff and Zakharov, AnnRevNuclPartSci 50, 37 (2000)

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 q 2 domain.

Mechanisms High energy limit: energy loss by gluon radiation. Two limits: (a) Thin medium: virtuality q 2 controlled by initial hard scattering (LQS, GLV) (b) Thick medium: virtuality q 2 controlled by rescattering in medium (BDMPS) Trigger on leading hadron (e.g. in R AA ) 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). q q L qq g L

Extracting qhat from hadron suppression data R AA : qhat~5-15 GeV 2 /fm

What does qhat measure? Equilibrated gluon gas: number density  ~T 3 energy density  ~T 4  qhat+modelling  energy density pQCD result: c~2 (  S ? quark dof? …) sQGP (multiplicities+hydro): c~10 R. Baier, Nucl Phys A715, 209c Hadronic matter QGP ~RHIC data Model uncertainties

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

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

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

R AA for  0 : medium density I C. Loizides hep-ph/ v2 I. Vitev W. Horowitz Use R AA to extract medium density: I. Vitev: 1000 < dN g /dy < 2000 W. Horowitz: 600 < dN g /dy < 1600 C. Loizides: 6 < < 24 GeV 2 /fm Statistical analysis to make optimal use of data Caveat: R AA folds geometry, energy loss and fragmentation

Different partons lose different amounts of energy 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. Yu.Dokshitzer

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

Particle dependencies: R AA of strangeness A remarkable difference between R AA and R CP 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

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

An important detail: the medium is not totally opaque There are specific differences to the flavor of the probe plus: heavy quarks also show effects of collisional e-loss Theory: there are two types of e-loss: radiative and collisional, plus dead-cone effect for heavy quarks Flavor dependencies map out the process of in-medium modification Experiment: there are baryon/meson differences

BUT: heavy quarks show same e-loss than light quarks R AA of electrons from heavy flavor decay R AA of electrons from heavy flavor decay Describing the suppression is difficult for models  radiative energy loss with typical gluon densities is not enough (Djordjevic et al., PLB 632(2006)81)  models involving a very opaque medium agree better (qhat very high !!) (Armesto et al., PLB 637(2006)362)  collisional energy loss / resonant elastic scattering (Wicks et al., nucl-th/ , van Hees & Rapp, PRC 73(2006)034913)  heavy quark fragmentation and dissociation in the medium → strong suppression for charm and bottom (Adil & Vitev, hep-ph/ )

Constraining medium viscosity  /s Simultaneous description of Simultaneous description of STAR R(AA) and PHENIX v2 for charm. (Rapp & Van Hees, PRC 71, 2005) Ads/CFT ==  /s ~ 1/4  ~ 0.08 Ads/CFT ==  /s ~ 1/4  ~ 0.08 Perturbative calculation of D (2  t) ~6 Perturbative calculation of D (2  t) ~6 (Teaney & Moore, PRC 71, 2005) ==  /s~1 transport models require transport models require  small heavy quark relaxation time  small diffusion coefficient D HQ x (2  T) ~ 4-6  this value constrains the ratio viscosity/entropy ratio viscosity/entropy   /s ~ (1.3 – 2) / 4   within a factor 2 of conjectured lower quantum bound  consistent with light hadron v 2 analysis  electron R AA ~  0 R AA at high p T - is bottom suppressed as well?

Energy density of matter high energy density:  > J/m 3 P > 1 Mbar I > 3 X W/cm 2 Fields > 500 Tesla QGP energy density  > 1 GeV/fm 3 i.e. > J/cm 3