1 / 61

Hard Probes (theory)

N. Armesto. Hard Probes (theory). International School on Quark-Gluon Plasma and Heavy Ion Collisions : past, present, future Torino, May 11th-17th 2005. N éstor Armesto Departamento de Física de Partículas and Instituto Galego de Altas Enerxías Universidade de Santiago de Compostela.

keaton
Download Presentation

Hard Probes (theory)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. N. Armesto Hard Probes (theory) International School on Quark-Gluon Plasma and Heavy Ion Collisions : past, present, future Torino, May 11th-17th 2005 Néstor Armesto Departamento de Física de Partículas and Instituto Galego de Altas Enerxías Universidade de Santiago de Compostela Acknowledgements: F.Arleo, R.Baier, A.Capella, A.Dainese, D.d’Enterria, E.G. Ferreiro, P.Jacobs, A.Morsch, C.Pajares, C.A.Salgado, J.Schukraft and U.A.Wiedemann. 1

  2. N. Armesto Contents 1. Introduction. 2. Basics of pQCD. 3. Medium-induced gluon radiation. 4. Quarkonium (very brief). 5. Final remarks. • I will concentrate on point 3 (see also Peter Jacobs' lectures). Other hard probes as open and hidden heavy flavor will be treated in other lectures. See: Yellow Report on Hard Probes in HIC at the LHC, CERN-2004-009 (hep-ph/0308248,0310274,0311048); http://event-hardprobes04.web.cern.ch. 2 Hard Probes (theory)

  3. Strategy: results with no medium (pp) and cold nuclear matter effects (pA) understood in pQCD define the benchmark for the probe; results in hot medium (AB) and their difference with defined expectation provides a (perturbative or non-perturbative) characterization of the medium. N. Armesto 1. Introduction: • Hard probes (of the medium created in a HIC): those whose benchmark (result of the probe in cold nuclear matter) can be studied using perturbative QCD, for which a hard scale is required (pT, mQ,...>>1/Rh). 3 Hard Probes (theory)

  4. N. Armesto Summary of probes: Jet quenching/heating Quarkonium suppression Control of the benchmark: DY, prompt photons 4 Hard Probes (theory): 1. Introduction

  5. N. Armesto 2. Basics of pQCD: • Fields: quarks and gluons. • Coupling constant: asymptotic freedom. • Confinement. • Factorization in hard processes. • Initial state ingredients. • Hard scattering elements. • Final state: fragmentation in vacuum. See e.g. Ellis et al, QCD and Collider Physics, Cambridge Univ.; Muta, Foundations of QCD, World Scientific; Yndurain, The theory of quark and gluon interactions, Springer-Verlag; Pich, hep-ph/9505231. 5 Hard Probes (theory)

  6. N. Armesto Fields: quarks and gluons • QCD: quantum field theory with SU(NC=3) as local gauge group. The fields in the QCD Lagrangian are: A)Matter fields: NC quarks being point-like spin-½ particles. Evidences: quark model, DIS experiments, two-jet events,... B)Exchange bosons: NC2-1gluons being massless spin-1particles. Evidences: three-jet events, scaling violations,... 6 Hard Probes (theory): 2. Basics of pQCD

  7. N. Armesto Coupling constant: asymptotic freedom Renormalization: fields, masses and the coupling constant acquire a dependence on a (momentum) scale. Due to gluon self-interactions (absent in QED), the coupling constant decreases with increasing momenta: large/ small at small /large momenta. , 7 Hard Probes (theory): 2. Basics of pQCD

  8. N. Armesto Confinement: • The fields q, g in the Lagrangian are not the particles in Nature (pions, protons,...). • The strong interaction is short rangebut QCD gluons (as QED photons) are massless. (106 $) problem of confinement • Hadrons: colorless combinations. • Valence description: 'dressed' constituent quarks. • Mass: dynamically generated. • Q-Qbar potential (until V>2mq): • Looking for deconfinement in HIC: QGP search. • K0 at large T: bound states (quarkonium) are dissolved (H.Satz’s lecture). 8 Hard Probes (theory): 2. Basics of pQCD

  9. N. Armesto Factorization in hard processes I: • Asymptotic freedom allows the use of pQCD for processes with a large scale (m, transverse momentum,...) involving the QCD fields q,g. • For inclusive processes, factorization(Collins, Soper, Sterman, '85) is the tool which makes it possible to use pQCD for hadronic processes. Basis: very different scales in h (~1/Rh) and in the hard scattering. 9 Hard Probes (theory): 2. Basics of pQCD

  10. N. Armesto Factorization in hard processes II: • Hard scattering elements computable in perturbation theory. • f: flux of 'initial' partons in the hadron or nucleus: (DGLAP) evolution with scale computable in perturbation theory. • D: projection of 'final' partons onto the observed particle: (DGLAP) evolution with scale computable in perturbation theory. Note 1: separation initial-final meaningless if there is cross-talk. Note 2: this factorization is called collinear, other schemes exist. Note 3: corrections to factorization in the form of powers 1/scale. 10 Hard Probes (theory): 2. Basics of pQCD

  11. N. Armesto Initial state ingredients I:(see Marzia Nardi's talk; Roberts, The structure of the proton, Cambridge Univ.) Parton fluxes (densities) measured in DIS: : scale, large for pQCD. : Momentum fraction of the parton in the hadron Densities at initial scale parameterized, evolution with scale given by DGLAP: global LO and NLO fits to nucleon data (MRST, CTEQ, GRV): gluon at small x rather uncertain, problem for extrapolations for LHC. 11 Hard Probes (theory): 2. Basics of pQCD

  12. N. Armesto Initial state ingredients II: Strategy: parameterize ratios at initial scale, evolution with scale given by DGLAP: global fits to nuclear data (EKS (LO), HKM (NLO), dFS (NLO)) (YR: hep-ph/0308248). Nuclear case: so partons fluxes in nuclei are not the superposition of those in hadrons (even isospin corrected). 12 Hard Probes (theory): 2. Basics of pQCD

  13. N. Armesto Hard scattering elements: Fixed order, collinear hard scattering elements available (at NLO, at least) for: Available Monte Carlo simulators (PYTHIA, HERWIG,...) use LO hard scattering elements + parton showers (i.e. parton radiation from initial and final state partons: they correspond to no fixed order in PT) (see e.g. Frixione, Webber, hep-ph/0202244; Nagy, Soper, hep-ph/0503053). Note: most HIC simulators (e.g. HIJING) use PYTHIA for hard processes. 13 Hard Probes (theory): 2. Basics of pQCD

  14. N. Armesto Final state: fragmentation in vacuum I Define a (collinear and IR) safe observable at partonic level (e.g. jets) (Sterman, Weinberg, PRL39(77)1436), OR use D(z,Q): fragmentation function, gives the probability parton k ---> hadron a with a momentum fraction z, at a scale Q: whitening of a parton by radiation. a Strategy: parameterize at some low scale, evolve with scale using DGLAP, fit to available (electron-positron) data (NLO: KKP, Kretzer); ff harder for massive (leading takes more than 70%) than for massless quarks (less than 40%). 14 Hard Probes (theory): 2. Basics of pQCD

  15. N. Armesto Final state: fragmentation in vacuum II If there are no final state medium effects, for scales large enough initial state effects and power suppressed contributions vanish: As the number of nucleon-nucleon collisions is proportional to AB times the nuclear overlap, at large enough scales we expect collision scaling, any deviation should be due to medium effects. 15 Hard Probes (theory): 2. Basics of pQCD

  16. N. Armesto 3. Medium-induced gluon radiation: • History. • Qualitative arguments. • Formalism. • Effects of radiation. • Features versus (RHIC) data. • To explore further. Reviews: Baier, Schiff, Zakharov, hep-ph/0002198; Gyulassy, Vitev, Wang, Zhang, nucl-th/0302077; Kovner, Wiedemann, hep-ph/0304151. Recent: Wiedemann, hep-ph/0503119; Vitev, hep-ph/0503221. 16 Hard Probes (theory)

  17. N. Armesto History I: • 1982: Bjorken(FERMILAB-PUB-82-059-THY) postulates the energy degradation of leading particles in jets and their disappearance in a dense medium, by elastic scattering (collisional energy loss). • Later works showed that elastic scattering lead to small energy loss e.g. dE/dx~0.1 GeV/fm for a 20 GeV parton for Tplasma=250 MeV. • Radiative energy loss (inelastic scattering) was proposed (Gyulassy, Plumer, PLB243(90)432): Bethe-Heitler to Bethe-Bloch in QED. • Gyulassy and Wang(NPB420(94)583): multiple collisions of partons with the medium in a QED form: interference in radiation (LPM effect). 17 Hard Probes (theory): 3. Medium-induced gluon radiation

  18. PHENIX, PRL91(03)072303 N. Armesto History II: • Baier-Dokshitzer-(Mueller-)Peigne-Schiff(PLB345(95)277) identified the dominant role in QCD of the rescattering of the gluon. • A general path-integral formalism was developed (Zakharov, JETPL63(96)952): the BDMPS results and the opacity expansion were recovered (Wiedemann, NPB588(00)303; Gyulassy, Levai, Vitev, NPB594(01)371; also the twist expansion in Wang, Guo, NPA696(01)788). • RHIC discovers high transverse momentum particle suppresion (PHENIX, PRL88(02)022321; STAR, PRL91(03)172302; PHOBOS, PLB578(04)297; BRAHMS, PRL91(03)072305; STAR, PRL90(03)082302). 18 Hard Probes (theory): 3. Medium-induced gluon radiation

  19. N. Armesto Qualitative arguments: I: vacuum; definitions. II: phase arguments. III: regimes of radiation. IV: energy loss. 19 Hard Probes (theory): 3. Medium-induced gluon radiation

  20. N. Armesto Qualitative arguments I:(Baier, Schiff, Zakharov, hep-ph/0002198; Baier, NPA715(03)209) x=w/E<<1 • Vacuum: • Take a medium of length L and density r (usually modelled as a collection of Yukawa-type potentials with Debye screening mass m – GW model). • Definitions: s proportional to aS the cross sections with the medium. l=1/(rs) the mean free path. m2the typical squared momentum transferred from the medium to the parton. qhat=m2/l the BDMPS transport coefficient. 20 Hard Probes (theory): 3. Medium-induced gluon radiation

  21. N. Armesto Qualitative arguments II: • In high-energy multiple scattering, the rescattered particle acquires a phase • What matters is the phase accumulated by the gluon to decohere from the radiating particle: jaccumulated>1, so w<wc is the dominant region, but small w are suppressed by oscillations in the phase. • From the phase: the time to decohere the gluon: and the number of coherent scatterings is 21 Hard Probes (theory): 3. Medium-induced gluon radiation

  22. N. Armesto Qualitative arguments III: Take E>wc (L<l[E/ELPM]1/2), and ELPM=m2l=2wc(l/L)2and ignore logs and constants. We have three regimes in the spectrum: A)w<ELPM or tcoh<l: Bethe-Heitler, incoherent regime, 1 scattering. B)ELPM<w<wc or l<tcoh<L: LPM regime, Ncoh<1, suppression from Bethe-Heitler. C)w>wc or tcoh>L: factorization regime, enhancement from LPM. 22 Hard Probes (theory): 3. Medium-induced gluon radiation

  23. N. Armesto Qualitative arguments IIIb: tcoh=(w/qhat)1/2: time to liberate the gluon, <(E/qhat)1/2. l L A) w<ELPM or tcoh<l: Bethe-Heitler, incoherent, 1 scattering. C)w>wc or tcoh>L: factorization regime. Difference QED/QCD: in QED, just the radiating parton accumulates, through rescattering, phase to decohere the radiated photon; in QCD, the radiated gluon also accumulates phase  additional factor L. 23 Hard Probes (theory): 3. Medium-induced gluon radiation

  24. N. Armesto Qualitative arguments IV: Now the energy loss The dominant contribution is w<wc: so we get the BDMPS result so the energy loss becomes independent of E and proportional to CF and L2. Note: in QED so 24 Hard Probes (theory): 3. Medium-induced gluon radiation

  25. N. Armesto Formalism: I, II: formula and ingredients. III: limitations. IV: what we can compute. 25 Hard Probes (theory): 3. Medium-induced gluon radiation

  26. N. Armesto Formalism I: The most complete formalism (Zakharov, Wiedemann) uses apath integral: • It resums all nuclear corrections LO in , leading (NL) in 1/E in the norm (phase). indicates the opacity which characterizes the medium. 26 Hard Probes (theory): 3. Medium-induced gluon radiation

  27. N. Armesto Formalism II: • The strength of the medium-induced radiation is determined by the displacement of the radiating charge. : FT of the elastic cross section (high energies, so only transverse coordinates). • Interference and mass effects: 27 Hard Probes (theory): 3. Medium-induced gluon radiation

  28. N. Armesto Formalism III: • Limitation I: except for a (1/E)-NL contribution allowed in the phase, this is an eikonal formalism, so DE<<E (the radiating parton does not deviate). Kinematical restrictions kT<w and w<E imposed a posteriori. • Limitation II: exact solution to the path integral does not exist, just two approximations: : saddle point (BDMPS), Brownian motion. Opacity expansion (in powers of (ns)N): first terms usually dominate (GLV) and give corrections to Brownian motion. • Approaches: numerically similar (Salgado, Wiedemann, PRD68(03)014008). 28 Hard Probes (theory): 3. Medium-induced gluon radiation

  29. N. Armesto Formalism IV: Within these limitations, we can compute everything: 1) Double differential spectrum of radiated gluons: gluon number and energy distributions associated with a high energy radiating parton. 2) Energy spectrum: 3) Energy loss: influence over single particle spectra. Note 1: what we get are partons (gluons), not hadrons, so either study 'safe' observables (jets) or go to hadrons with LPHD or ff. Note 2: dilution of the medium due to expansion taken into account by the redefinition , 29 Hard Probes (theory): 3. Medium-induced gluon radiation

  30. N. Armesto Effects of radiation: I, II: degradation of the leading particle; how to compute single particle spectra. III: jet heating and jet shapes. IV: effect of the mass of the radiating parton. V: effect of the color charge of the parent parton. VI: dilution of the medium. VII: flow effects? 30 Hard Probes (theory): 3. Medium-induced gluon radiation

  31. N. Armesto Effects of radiation I: Gluon radiation implies an energy degradation of the leading particle. To compute single-inclusive particle spectra: two ways: A) (BDMS, JHEP 0109(01)033). It clearly shows the influence of the spectrum: the harder it is, the stronger the quenching effects. The spectrum also determines the high pT behavior: for fixed DE(~pT at h=0), 31 Hard Probes (theory): 3. Medium-induced gluon radiation

  32. N. Armesto Effects of radiation II: B) (Wang, Guo, NPA696(01)788). It shows the influence of the ff at z-->1: the harder it is (e.g. for heavy flavor), the stronger the effect. • Quenching weights (BDMS, JHEP 0109(01)033; SW, PRD'03): probability to lose a fraction of energy e, computed under the assumption of multiple independent emissions: 32 Hard Probes (theory): 3. Medium-induced gluon radiation

  33. N. Armesto Effects of radiation III: Jet heating: increase of associated hadron multplicity and broadening of the associated parton shower (BDMS, PRC64(01)057902; SW, PRL93(04)042301). RHIC: particle multiplicity associated with a high pT trigger (see Peter Jacobs' lectures). LHC: energy distribution within a cone of size R, still unclear whether the jet will survive (full Monte Carlo simulations needed). 33 Hard Probes (theory): 3. Medium-induced gluon radiation

  34. N. Armesto Effects of radiation IV: Mass effects on radiation: in vacuum we have the dead cone effect • Dokshitzer, Kharzeev(PLB519(01)199) proposed that the same effect should suppress medium-induced radiation. • Technically: dead cone + rescattering, numerical results (Djordjevic, Gyulassy, NPA733(04)265; Zhang, Wang, Wang, PRL93 (04)072301; ASW, PRD69(04)114003). 34 Hard Probes (theory): 3. Medium-induced gluon radiation

  35. N. Armesto Effects of radiation V: • Color effect: gluons, CF=3, lose more energy than quarks, CF=4/3 --> look for particle ratios sensitive to this, as pbar/p or Lbar/L (Wang, PRC58(98)2321; Wang, Wang, PRC71(05)014903) or heavy-to-light ratios (e.g. D/h) (Dainese et al, PRD71(05)054027). Several effects to be taken into account in realistic predictions: • Color charge. • Mass effects on partonic spectrum. • Id. on fragmentation. • Id. on energy loss. 35 Hard Probes (theory): 3. Medium-induced gluon radiation

  36. N. Armesto Effects of radiation VI: • Dilution of the medium due to expansion: redefinition (SW, PRL89(02)092303; BDMS, PRC58(98)1706; Gyulassy, Vitev, Wang, PRL86(01)2537). • In principle, the transport coefficient measures the energy density of the medium 36 Hard Probes (theory): 3. Medium-induced gluon radiation

  37. N. Armesto Effects of radiation VII: • If hard partons are not produced in a frame comoving with the medium, radiative energy loss may be sensitive to more than energy density: (for e=3p) can be large (5p for h=1). Momentum exchanges becomes anisotropic Space-time picture of the medium? (ASW, PRL93(04)242301; hep-ph/0411341). 37 Hard Probes (theory): 3. Medium-induced gluon radiation

  38. N. Armesto Features versus data: I. Where to look for. II. Problems at RHIC and LHC: energy of the parent. III, IV. Description of the medium. V. Full formula. VI. Single particle spectra for light flavors. VII. What about the transport coefficient? VIII. Heavy flavors. 38 Hard Probes (theory): 3. Medium-induced gluon radiation

  39. N. Armesto Features versus data I: Where to look for all this? Which pT is high enough? (Wiedemann, QM04) V Hadronization outside medium, partonic dynamics inside, tomography? Multiplicities, saturation? Hadronization inside medium, particle species dependence 39 Hard Probes (theory): 3. Medium-induced gluon radiation

  40. N. Armesto Features versus data II: Problem: how to determine the energy of the radiating parton? • At the LHC: try to reconstruct the jet energy or considers jets balanced by a particle which can be identified (e.g. g-jet configuration). • At RHIC: low energy jets do not stand over background, energy reconstruction problematic, so look at the hardest particle. But this implies a trigger bias: a) The hardest fragmentation: b) Surface emission (small L): c) Low energy loss for fixed L: d) Initial pT broadening towards the trigger (not collinear): 40 Hard Probes (theory): 3. Medium-induced gluon radiation

  41. N. Armesto Features versus data III: Two parameters describe the medium: geometry and product density times cross section, given generically by L and qhat, or combinations like wc=L2qhat/2 and R=wcL. Until now, the most discussed observable is single-particle ratios: Geometry: to test the L2 dependence proper of the LPM effect (different from the linear dependence in absorption models): a) Centrality evolution of the ratios. b) Dependence with the azimuth. Density times cross section: to test our understanding of the created medium that we try to characterize: a) Magnitude of the suppression. b) Evolution of the suppression with collision energy. 41 Hard Probes (theory): 3. Medium-induced gluon radiation

  42. N. Armesto Features versus data IV: (GVW, PRL86(01)2537; Dainese et al, EPJC38(05)461; Eskola et al, NPA747(05)511) Production point s=(x0,y0) sampled according to TA(s)TB(b-s) i.e. number of nucleon-nucleon collisions. Trajectory: • Then: 42 Hard Probes (theory): 3. Medium-induced gluon radiation

  43. N. Armesto Features versus data V: Full formula (also ADSW, PRD71(05)054027): • Geometry + one parameter (fixed e.g. in central AuAu) give full results. • Quenching weights publicly available: they may give DE>E (they were deduced in the high-energy approximation). Two recipes to mend this give the most extreme cases (see Dainese et al and Eskola et al) and guarantee a) Renormalize to DE<E or b) Set DE>E to DE=E. 43 Hard Probes (theory): 3. Medium-induced gluon radiation

  44. N. Armesto Features versus data VI: 4.5<pT<10 GeV 44 Hard Probes (theory): 3. Medium-induced gluon radiation

  45. N. Armesto Features versus data VII: Medium is opaque at RHIC: 4<qhat<14 GeV2/fm; surface emission (Muller, PRC67(03)061901; see Arleo, JHEP0211(02)044 for qhat). Extrapolation to other energies according to multiplicities: from top RHIC dNch/dh|h=0~600, factor 2.5 to 7 (even 15) to LHC. Now: So for e(t0)~100GeV/fm3, L~10t0, 0.75<a<1.5, c~8-19>>2 --> non-ideal QGP, links with the thermalization/viscosity problems. 45 Hard Probes (theory): 3. Medium-induced gluon radiation

  46. PHENIX: Averbeck, Moriond '05 RAA M. Djordjevic et al., hep-ph/0410372 N. Armesto et al. hep-ph/0501225 PT [GeV/c] N. Armesto Features versus data VIII: What about heavy flavor production? RHIC data in AuAu: electron spectra, weak correlation in pT with D/B (Batsouli et al, PLB557(03)23), and possible contribution from B decays; the region pTD<7 GeV is to be taken with care. 46 Hard Probes (theory): 3. Medium-induced gluon radiation

  47. N. Armesto To explore further: I. RHIC: heavy flavors. II. RHIC: jet-like shapes. III. RHIC: v2 at large pT. IV. LHC: jet shapes. V. LHC: heavy flavors. VI. Other alternatives. 47 Hard Probes (theory): 3. Medium-induced gluon radiation

  48. N. Armesto To explore further I: Run IV at RHIC: enormous increase in statistics (factor ~40), so new studies become possible: • Extend the study of electron spectra to large pT. • Look for topological decays D->Kp (as STAR in dAu). • ADSW, PRD71(05)054027: the region 7<pTD<12 GeV should be safe from hadronization uncertainties and sensitive to color and mass effects (but contamination from B decays has to be considered). 48 Hard Probes (theory): 3. Medium-induced gluon radiation

  49. p+p minbias Au+Au, 20-40% STAR preliminary 2 < pT(assoc) < pT(trig) || < 0.5 STAR preliminary N. Armesto To explore further II: Increasing interest at RHIC on particles distributions associated with a high pT trigger(see P. Jacobs' lectures). Several ideas: • Soft particles shift the radiation (Voloshin, nucl-th/0312065). • Flow may induce asymmetry in radiation (ASW, PRL93(04) 242301; hep-ph/0411341). • Difficult studies: need of Monte Carlo simulation (Hirano, Nara, PRC66(02)041901; PRC69(04)034908) coupled to the medium to be quantitative. STAR: Magestro at HP04 49 Hard Probes (theory): 3. Medium-induced gluon radiation

  50. N. Armesto To explore further III: v2 at RHIC at large pT: too large to be explained by jet quenching models (even by absorption models: Drees, Feng, Jia, PRC71(05)034909). Dainese et al, EPJC38(05)461 • Push by lowpT partons? (Molnar, nucl-th/0503051). • The introduction of a component of qhat proportional to the flow field (ASW, hep-ph/0411341) increases v2, but also mimics a higher energy density --> flow may be very important for the interpretation of high pT at RHIC. 50 Hard Probes (theory): 3. Medium-induced gluon radiation

More Related