Padova, Andrea Dainese 1 Parton energy loss in heavy-ion collisions from RHIC to LHC Andrea Dainese INFN Legnaro

Padova, Andrea Dainese 2 Layout The discovery of “jet quenching” at RHIC High-p T particle production in nucleus-nucleus collisions, according to perturbative QCD Calculating parton energy loss (BDMPS framework) Light-flavour hadron suppression in the Parton Quenching Model at RHIC and LHC Energy loss for heavy quarks RHIC: electrons R AA vs data LHC: testing E loss with heavy-to-light ratios Conclusions

Padova, Andrea Dainese 3 Discovery at RHIC: high-p T suppression Nuclear modification factor of p T distributions: PHENIX  0 (0-10%) factor 5 suppression! compilation by D.d’Enterria

Padova, Andrea Dainese 4 What about jets? Jets via di-hadron correlations: highest-p T track trigger: highest-p T track, (4--6 GeV)  distribution: 2 GeV < p T < p T trigger pp  2 back-to-back jets STAR Coll., PRL 90 (2003) slide courtesy of P.Jacobs near sideaway side

Padova, Andrea Dainese 5 Discovery at RHIC: no away-side jet in central Au-Au Quantified via ratio of integrals: ~1 in peripheral AA ~0 in central AA STAR Coll., PRL 90 (2003)

Padova, Andrea Dainese 6 Is it final-state energy loss? … or saturation of the parton densities in the initial nuclei? Control experiment, without medium: d-Au no high-p T suppressionthe away-side jet is there Final-state effect PHENIX Coll., PRL 91 (2003) STAR Coll., PRL 91 (2003)

Padova, Andrea Dainese 7 Is it final-state energy loss? … or saturation of the parton densities in the initial nuclei? “Control experiment”, with medium-blind probe:  ’s in Au-Au no suppression, but N coll scaling Final-state effect figure by D. d’Enterria

Padova, Andrea Dainese 8 High-p T particle prod. in AA collisions A schematic view: Ingredients: pp baseline (pQCD) initial-state effects:  PDF (anti)shadowing  k T broadening (Cronin) final-state effects:  energy loss  in-medium hadronization (coalescence) medium formed in the collision Au q q h h q p p q q h h pp  h+X x f g Pb / f g p LHC RHIC SPS R AA 1 Q 2 = 5 GeV 2 pTpT R AB 1 ~2-4 GeV/c kL  kTkL  kT Cronin enhancement

Padova, Andrea Dainese 9 Parton Energy Loss Partons travel ~4 fm in the high-density medium Bjorken (`82): energy loss due to elastic scattering … Bjorken, FERMILAB-Pub-82/59-THY (1982).

Padova, Andrea Dainese 10 Parton QCD Energy Loss Partons travel ~4 fm in the high colour-density medium medium-induced gluon radiation Successive calculations (`92  ): a QCD mechanism dominates, medium-induced gluon radiation Coherent wave-function gluon acummulates k T due to multiple inelastic scatterings in the medium  it decoheres and is radiated hard parton path length L Gyulassy, Pluemer, Wang, Baier, Dokshitzer, Mueller, Peigne’, Schiff, Levai, Vitev, Zhakarov, Salgado, Wiedemann, … kTkT

Padova, Andrea Dainese 11 Calculating Parton Energy Loss Baier, Dokshitzer, Mueller, Peigne‘, Schiff, NPB 483 (1997) 291. Zakharov, JTEPL 63 (1996) 952. Salgado, Wiedemann, PRD 68(2003) BDMPS-Z formalism path length L kTkT  Radiated-gluon energy distrib.: transport coefficient sets the scale of the radiated energy related to constraint k T < , controls shape at  <<  c Casimir coupling factor: 4/3 for q, 3 for g STATIC MEDIUM (BDMPS case)

Padova, Andrea Dainese 12 Calculating Parton Energy Loss Probe the medium gluons volume-density and interaction cross section Finite parton energy (qualitatively)  If E <  c (e.g. small p T parton with large L):  dependence on parton energy  : smaller sensitivity to density 

Padova, Andrea Dainese 13 Application: Parton Quenching Model Dainese, Loizides, Paic, EPJC 38 (2005) 461. BDMPS + Glauber-based medium geometry and density profile + PYTHIA for parton generation and fragmentation The procedure in short: 1)generate parton (q or g) with PYTHIA (or back-to-back pair) 2)calculate its L and average along the path 3)use quenching weights (from  dI/d  ) to get energy loss 4)quench parton and then hadronize it (independent fragm.) PYTHIA Fragmentation pTpT p T –  pTpT dN/dp T

Padova, Andrea Dainese 14 Model vs RHIC “light” data Density ( ) “tuned” to match R AA in central Au-Au at 200 GeV matches p T -indepence of suppression at high p T Dainese, Loizides, Paic, EPJC 38 (2005) 461. (Quark Matter 05) Similar results by Eskola, Honkanen, Salgado, Wiedemann

Padova, Andrea Dainese 15 Model vs RHIC data Centrality dependence of R AA p T > 4.5 GeV Centrality evolution according to Glauber-model collision geometry Dainese, Loizides, Paic, EPJC 38 (2005) 461.

Padova, Andrea Dainese 16 Testing L-dependence? R AA for 63 Cu- 63 Cu R AA STAR preliminary Charged hadrons

Padova, Andrea Dainese 17 Testing L-dependence? v 2 at high p T from E loss The azimuthal asymmetry --v 2 or R AA (  )-- of high-p T particle yields in non-central collisions tests the path-length dependence of E loss (almond-shaped medium) PHENIX  0 v 2 v 2 from E loss: Dainese, Loizides, Paic, EPJC 38 (2005) 461

Padova, Andrea Dainese 18 Extrapolation in c.m.s. energy Intermediate RHIC energy  s = 62 GeV energy extrapolation works reasonably well Extrapolation in  s: assuming  N gluons /volume  (  s) 0.6 (EKRT saturation model) First test: EKRT: Eskola, Kajantie, Ruuskanen, Tuominen, NPB 570 (2000) 379. PHENIX Coll., JPG 31 (2005) S473.

Padova, Andrea Dainese 19 Model prediction for LHC Extrapolation to LHC according to saturation model gives: Most partons are absorbed Already at RHIC, only those from the surface can escape … surface emission dominates

Padova, Andrea Dainese 20 Model vs RHIC data Disappearence of the away-side jet near side away side STAR Coll., nucl-ex/

Padova, Andrea Dainese 21 Observation of true di-jets in Au-Au STAR

Padova, Andrea Dainese 22 Di-jets associated yields (I AA )

Padova, Andrea Dainese 23 Tangential di-jets?

Padova, Andrea Dainese 24 Putting the pieces together

Padova, Andrea Dainese 25 Limited sensitivity of R AA Strong suppression requires very large density Surface emission scenario R AA determined by geometry rather than by density itself  Limited sensitivity to  Need more differential observables: massive partons study of jet shapes … Eskola, Honkanen, Salgado, Wiedemann, NPA 747 (2005) 511. ? large  R AA indep. of

Padova, Andrea Dainese 26

Padova, Andrea Dainese 27 Lower E loss for heavy quarks ? In vacuum, gluon radiation suppressed at  < m Q /E Q  “dead cone” effect Dead cone implies lower energy loss (Dokshitzer-Kharzeev, 2001) : energy distribution  d  /d  of radiated gluons suppressed by angle- dependent factor suppress high-  tail Q Dokshitzer, Khoze, Troyan, JPG 17 (1991) Dokshitzer and Kharzeev, PLB 519 (2001) 199. Dokshitzer Gluonsstrahlung probability

Padova, Andrea Dainese 28 Lower E loss for heavy quarks ? Detailed massive calculation shows that: Armesto, Salgado, Wiedemann, PRD 69 (2004) Medium-induced gluon radiation fills the dead cone Still, k T -integrated radiation is suppressed, but only for quite large m/E (i.e. large m, low p T )* R = 10 5 *Warning: large uncertainties kTkT m/E = 0.1 massive massless dead cone

Padova, Andrea Dainese 29 Model for heavy quarks Initially only charm Baseline at RHIC: PYTHIA, with EKS98 shadowing, tuned to match p T - shape of D cross section measured in d-Au by STAR (QM04) Heavy-quark E loss using (m/E)- dependent QW extracted from  0,h  R AA (central) Thermalize charms that lose all energy dN/dm T  m T exp(-m T /T), T = 300 MeV Armesto, Dainese, Salgado, Wiedemann, PRD 71 (2005) EKS98: Eskola, Kolhinen, Salgado, EPJC 9 (1999) 61. baseline dN/dp T baseline R AA

Padova, Andrea Dainese 30 Charm R AA at RHIC effect of the mass thermalized component Small effect of mass for charm (~50% for D, ~30% for e) at low p T [large uncertainties!] Basically no effect in “safe” p T -region Armesto, Dainese, Salgado, Wiedemann, PRD 71 (2005) (extracted from light-hadron data) larger uncertainties other contributions become important

Padova, Andrea Dainese 31 Charm + beauty + DY electrons at RHIC (pQCD baseline revised, and its uncertainties) FONLL calculation: Cacciari, Nason, Vogt, PRL95 (2005) Drell-Yan from: Gavin et al., hep-ph/ Comparison: Armesto, Cacciari, Dainese, Salgado, Wiedemann, hep-ph/ FONLL: electron spectrum may be ~50% c + ~50% b for 3 < p T < 8 GeV Drell-Yan component investigated as well: < 10% up to 10 GeV Large uncertainty on b/c crossing point in p T : from scales/masses variation it changes from 3 to 9 GeV Note: still, electron cross section in pp at 200 GeV underestimated at high p T PHENIX hep-ex/

Padova, Andrea Dainese 32 R AA of c and b electrons at RHIC Armesto, Cacciari, Dainese, Salgado, Wiedemann, hep-ph/ Due to larger mass of b quark electron R AA increased to ~0.4 Mass uncertainty (in E loss) and scales uncertainty (in pQCD  b/c crossing) were studied c b c+b Theory predicts e R AA (~0.4) larger than  R AA (~0.2) e spectra in principle sensitive to mass hierarchy Perturbative uncertainty on the pp baseline comparable to model-intrinsic uncertainty in determination of Preliminary STAR data not conclusive for comparison with theory

Padova, Andrea Dainese 33 Heavy Quark Energy Loss at LHC ~100 cc pairs and ~5 bb pairs per central Pb-Pb collision Experiments will measure with good precision R AA for D and B, and for their decay leptons What can we learn from a comparative quenching study of massive and massless probes at the LHC?

Padova, Andrea Dainese 34 Heavy Flavour R AA at LHC Baseline: PYTHIA, with EKS98 shadowing, tuned to reproduce c and b p T distributions from NLO pQCD (MNR) (m/E)-dep. E loss with MNR: Mangano, Nason, Ridolfi, NPB 373 (1992) 295. Armesto, Dainese, Salgado, Wiedemann, PRD 71 (2005) * EKRT Saturation model: Eskola, Kajantie, Ruuskanen, Tuominen, NPB 570 (2000) 379.

Padova, Andrea Dainese 35 Colour-charge and mass dep. of E loss with Heavy-to-Light ratios at LHC Heavy-to-light ratios: Compare g  h, c  D and b  B mass effect For 10 < p T < 20 GeV, charm behaves like a m=0 quark, light-flv hadrons come mainly from gluons R D/h enhancement probes colour-charge dep. of E loss R B/h enhancement probes mass dep. of E loss Armesto, Dainese, Salgado, Wiedemann, PRD71 (2005)

Padova, Andrea Dainese 36 Beauty-to-Charm ratio: R B/D Compare c and b  same colour charge Mass effect  Enhancement of factor ~2, independent of (for ) Challenging from experimental point of view…

Padova, Andrea Dainese 37 Summary One of the most exciting discoveries at RHIC ! We are dealing with energy loss in an extremely opaque medium, but …  theoretically, we are just starting to learn how to probe the medium; still large uncertainties (see also next talk)  experimentally, going to more differential observables  vs system size / azimuthal angle (path-length dependence)  vs quark mass -- c (b) SUPPRESSED at RHIC, but need to disentangle c and b to clarify picture The LHC will be a `hard / heavy probes machine’ and quenching studies will play a central role Example: Heavy-to-light ratios as probes of E loss…  … colour-charge dependence (R D/h )  … parton-mass dependence (R B/h, R B/D ?)

Padova, Andrea Dainese 38 EXTRA SLIDES

Padova, Andrea Dainese 39 Parton energy loss at SPS (  s  17 GeV)? R CP (K) vs E loss calculations E loss (Wang) NA49, QM2005 NA57 PLB623 (2005) 17 Wang calculation: pQCD + Cronin + (anti-)shadowing + energy loss (gluon density scaled by dN ch /dh) Good agreement between data and both Wang and PQM calculations ( )

Padova, Andrea Dainese 40 Open points (2): the opacity problem Can we really probe the medium? Need to relate extracted to an energy density  QCD estimate for ideal QGP: A recent analysis* of RHIC data, similar to that presented, extracts energy density  5 larger than that estimated from produced transverse energy dE T /dy (Bjorken estimate) Opacity problem: the interaction of the hard parton with the medium is much stronger than expected (Baier) Baier, NPA 715 (2003) 209. * Eskola, Honkanen, Salgado, Wiedemann, NPA 747 (2005) 511.

Padova, Andrea Dainese 41 Collisional energy loss revisited Earlier estimates: collisional (elastic) energy loss is negligible relative to radiative effects New estimate: Boltzmann transport + 1-D Bjorken expansion Mustafa and Thoma, Acta Phys.Hung. A22, 93 (2005) Q(p  ) = R AA Can we really ignore collisional energy loss? R AA = for reasonable pathlength, similar to radiative E-loss

Padova, Andrea Dainese 42 Reappearance of di-jets: surface emission of tangential partons? p T (assoc) > 5 GeV/c 1/N trig dN/d  STAR Preliminary 8 < p T (trig) < 15 GeV/c

Padova, Andrea Dainese 43 Medium Expansion The density of scattering centres is time-dependent: Dynamical scaling law: same spectrum obtained for equivalent static trasport coefficient Calculations for a static medium apply to expanding systems Salgado and Wiedemann, PRL 89 (2002)  = 1.5, 1.0, 0.5, 0

Padova, Andrea Dainese 44 Static vs Bjorken Expansion

Padova, Andrea Dainese 45 Static vs Bjorken: numbers

Padova, Andrea Dainese 46 The azimuthal asymmetry --v 2 or R AA (  )-- of D and B mesons in non-central collisions tests: at low/moderate p T : recombination scenario, v 2 of c/b quarks, hence degree of thermalization of medium at higher p T : path-length dependence of E loss (almond-shaped medium => v 2 ~ )  = 0  =  /2 PHENIX  0 v 2 Quark Matter 05 v 2 from E loss: Dainese, Loizides, Paic, EPJC 38 (2005) 461 Armesto, Cacciari, Dainese, Salgado, Wiedemann, hep-ph/ , PLB to appear STAR results withdrawn; new analysis in progress v 2 at high p T from E loss