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Jets in Nuclear Collisions

Ivan Vitev. Jets in Nuclear Collisions. ISMD 2004, July 26 - August 1, 2004 Sonoma County, California, USA. Ivan Vitev , LANL. Outline of the Talk. Measurements of jets in nuclear collisions:  Determination of the jet properties from the near-side and

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Jets in Nuclear Collisions

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  1. Ivan Vitev Jets in Nuclear Collisions ISMD 2004, July 26 - August 1, 2004 Sonoma County, California, USA Ivan Vitev, LANL

  2. Outline of the Talk • Measurements of jets in nuclear collisions: •  Determination of the jet properties from the near-side and • away-side di-hadron correlations. • Baseline jet results in the vacuum: •  Quark and gluon jet widths •  Quark and gluon jet multiplicities • Modification of jet properties in cold and hot nuclear matter : • Elastic: Transverse momentum diffusion. Broadening of the • away-side correlation function. Acoplanarity • Inelastic: QCD radiative energy loss. Jet quenching • Modification of the jet multiplicities and the • back-to-back jet correlations • Coherent: Power corrections • Conclusions: Ivan Vitev,LANL

  3. Clean Jets in DIS and e+, e- C.C. example Jets in DIS Jets in p+p (Single clean jet) Ivan Vitev,LANL

  4. Jets in A+A Reactions The complication at the RHIC (STAR) The complication in heavy ion reactions Infinite multiplicities to deal with Globally correlated underlying event (v2) So far STAR uses a jet reconstruction algorithm Jets in nuclear collisions The complication at the Tevatron (D0) Ivan Vitev,LANL

  5. If then Di-hadron Correlations G.Altarelli, R.K.Ellis, G.Martinelli, Phys.Lett. 151B (1985) Hadron 1 Hadron 2 • Vacuum:intrinsic, NLO corrections, soft gluon resummation Relative to : • Medium:transverse momentm diffusion • Fragmentation:not collinear, a jT kick to the hadron Di-hadron correlation function: Relate the widths and the momentum measures Ivan Vitev, LANL

  6. Key result Relative to naive Analytic Multiplicity Results Double ordering See e.g. Field and Feynman, Dokshitzer et al. • The probability to emit n gluons: • Average gluon number: Experimentally 1.54 +/- … Z0 mass scale Ivan Vitev, LANL

  7. The final kT distribution of the jet. Gives by momentum • conservation information for the distribution of gluons (very broad) Key result Angular Distribution The LDLA • Definite shortcomings Normalization and mean kT2 • In the limit of small coupling The OPAL experiment: 17% of g-energy Within 4% of the jet axis 30% of q-energy Ivan Vitev,LANL

  8. + + Incoherent local Glauber. Elastic application Before the hard scatter After the hard scatter pT Diffusion in Nuclei Additionalapproximation for a Gaussian form L Summary Ivan Vitev, LANL

  9. d+Au and Au+Au J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068 <|kTy|>pA = 1.25 GeV <z><|kTy|>AA = 1.25 - 1.45 GeV p+A From: <z> = 0.75, <|kTy|>pp = 1.05 GeV A+A • The vacuum broadening is large • Cold nuclear matter – only a small effect • Hot nuclear matter – seems insufficient 2.5pTtrigg4.0, 1.0pTassoc2.5 Feedback? pp: <z><|kTy|> pp: <|jTy|> J.Rak, hep-ex/0403038 P.Constantin, N.Grau Ivan Vitev, LANL

  10. + + Medium Induced Non-Abelian Energy Loss Iterative solution Interplay of formation times and medium size M.Gyulassy, P.Levai, I.V., Nucl.Phys. B594 (2001); Phys.Rev.Lett.85 (2000) • Explicitly the Landau- • Pomeranchuk-Migdal • destructive interference • effect in QCD • Incorporatesfinite • kinematics and small • number of scatterings • Applicable for realistic • systems Inverse formation times Color current propagators Also see R. Baier et al., B. Zakharov, U. Wiedemann, X.N. Wang Ivan Vitev, LANL

  11. 17 GeV 62 GeV 200 GeV Radiative Spectra The basis for jet tomography – the extraction of the density of the medium Isospin symmetry Parton-hadron duality Small and finite - transport coefficient - effective gluon rapidity density B.Back et al., Phys.Rev.Lett. 88 (2002) Estimate: I.V., nucl-th/0404052 Ivan Vitev, LANL

  12. X P xaP xbP’ P’ TheBasic pQCD Process J.Collins, D.Soper, G.Sterman, Nucl.Phys.B223 (1983) Extended to include power corrections J.W.Qiu, I.V., hep-ph/0405068 One way of implementing radiative energy loss: Pd Pd / zd Pc / zc X • Single inclusive hadron production Pc • Double inclusive hadron production (most of what will be discussed) Ivan Vitev, LANL

  13. 600 MeV The E-loss Connection S.Pal, S.Pratt, Phys.Lett.B574 (2003) The plasmon frequency forces radiation in fewer semi-hard gluons 25-40% increase in the multiplicity Factor of 2 in mult. Poisson approximation • Increase in the jet multiplicity • In the approximations used the • medium induced multiplicity • scales as • One can hopefully establish the • subsequent rescattering and • thermalization of the gluons 2 GeV Ivan Vitev, LANL

  14. SPS relative to D.d’Enterria, nucl-ex/0403055 S.S.Adler, et al., Phys.Rev.Lett.91 (2003) Jet Quenching and Jet Tomography • Attenuation of the inclusive hadron spectra • Extraction of the soft underlying parton • density (bulk matter) • In jet algorithms – a need for hard pT cut I.V., nucl-th/0404052 I.V., M.Gyulassy, Phys.Rev.Lett. 89 (2002) Ivan Vitev, LANL

  15. peripheral Centrality Dependence ofJet Quenching central G.G.Barnafoldi et al., hep-ph/0311343 X.N.Wang, nucl-th/0305010 Ivan Vitev, LANL

  16. Modification of the Jet-like Correlations In triggering on the near side all effects are taken by the away side correlation function • The attenuation of the double inclusive • hadron production is between the two • naïve limits , • Attenuation (disappearance) of the away-side • correlation function • Dependence relative to the reaction plane Jet 1 Jet 2 Ivan Vitev, LANL

  17. Conclusions • Jet tomographic and jet quenching studies in heavy ion collisions have rapidly developed as one of the most exciting and successful directions in RHIC and LHC physics Relate to:Spectra, jets and di-hadron correlations • The propagation of jets through cold and hot and dense nuclear matter results in calculable modifications to the pQCD factorization approach • A multitude of novel observable effects are predicted and observed at RHIC and expected at the LHC: - Strong suppression of the simple and double inclusive hadron cross sections (4-5 times for single), (5-7 times double) - Broadening and disappearance jet-jet correlations. Dependence on centrality and orientation relative to the reaction plane - Redistribution of the lost energy into the system - Increase of the jet multiplicities by 30% to 100% - Broadening of the jet cone (small) Ivan Vitev,LANL

  18. A. Predictive Power of pQCD J.Collins, D.Soper, G.Sterman, Nucl.Phys.B223 (1983) • Factorization theorem: Scale of hadron wave function: Scale of hard partonic collision: Factorization: Process-dependent: Process-independent: • Predictive power:Universality of Infrared safety of • Systematically addresses the deviations: Power corrections Radiative energy loss (dynamical nuclear shadowing) (jet quenching) Ivan Vitev, LANL

  19. k’ k  xP P … X X P xaP xbP’ P’ X Basic pQCD Processes (I) J.Collins, D.Soper, G.Sterman, Nucl.Phys.B223 (1983) All orders • DIS: • Drell-Yan: Eikonal line. Disappears in A+ = 0 Extended to corrections in e()+A J.W.Qiu, I.V., hep-ph/0309094 All orders G.Bodwin, Phys.Rev. D31 (1985)  Ivan Vitev, LANL

  20. X P xaP xbP’ P’ X Basic pQCD Processes (II) Factorization:at leading power and leading power corrections Pd • Hadron production in N+N: Pd / zd J.Collins, D.Soper, G.Sterman, Adv.Ser.Dir. 5 (1988) J.W.Qiu, G.Sterman, Nucl.Phys.B353 (1991) Pc / zc Extended to in p+A corrections J.W.Qiu, I.V., hep-ph/0405068 • Single inclusive hadron production Pc • Double inclusive hadron production (most of what will be discussed) Ivan Vitev, LANL

  21. Particle Production • Fragmentation: natural near-side and away-side correlations • Relativistic hydrodynamics: Cooper-Frye formula After solving From an uncorrelated evolved fluid • Coalescence models: Folding the quark Wigner functions and the meson or baryon wave functions • Saturation gluon fussion models: Folding two gluon distributions into one gluon (particle) These mechanisms don’t have natural don’t have natural correlations Ivan Vitev, LANL

  22. The Fragmentation Seesaw Analogy Gell-Mann, Slansky, Yanagida SM + right handed neutrino with large Majorana mass A much simpler analog of the interplay between light and heavy, small and large To lowest order and leading twist Provides a new way of testing the fragmentation picture, the factorization approach and the deviations Ivan Vitev, LANL

  23. LO pQCD Example Calculated as in: J.W.Qiu, I.V., hep-ph/0405068 • Perturbative unbiased calculation • Clear anti-correlation between • pT assocand ztrig . (Not the naïve • expectation that triggering fully fixes • the near side.) • Novel way of studying the pQCD • 2 to 2 hadron production mechanism. • Distinguish from the alternatives Ivan Vitev, LANL

  24. B. Motivation: Deviations from Hard Scaling Examples: 200, 62 GeV Au+Au; 200 GeV d+Au AA <Nbinary>/sinelp+p nucleon-nucleon cross section • Quenching • Shadowing • Acoplanarity Rapidity dependence, centrality dependence Ivan Vitev, LANL

  25. Acoplanarity • Consider di-hadron correlations associated with hard • (approximately) back-to-back scattering Vacuum:intrinsic, NLO corrections, soft gluon resummation Medium:transverse momentm diffusion Di-hadron correlation function Relate the widths and the momentum measures If Ivan Vitev, LANL

  26. Experimental Results (Approximate representation of the theoretical calculation in the Figures) • Qualitative and somewhat quantitative agreement • Indicates the need for a possibly stronger • Cronin effect • Systematic error bars should be taken seriously • Beware of baryon/meson ratios (I wouldn’t attempt • to fit baryons below 4-5 GeV) Similar results: (h+,h-) by PHOBOS and STAR. (BRAHMS?)

  27. Hard part Matrix element DIS Coherence Factorization approach:separate the short sistance computable dynamics from the long distance matrix emenets. Final state effect 2D lightcone dynamics • Lightcone gauge: First coherent calculation • Breit frame: Pole – on-shell, long distance No pole – contact, short distance J.W.Qiu, Phys.Rev. D42 (1990) Ivan Vitev, LANL

  28. (pole-separated, long-distance) U-quark, CTEQ5 LO Resummed Power Corrections Dynamical generation of a parton’s mass in the final state Scale of power corrections (geometric and vertex factors, two gluon correlation function) Simple analytic formula: QM shift operator Ivan Vitev, LANL

  29. For we impose . • (discussion of corrections will follow) Numerical Results Generated by the multiple final state scattering of the struck quark Q2dependence, Longitudinal SF • Compares well to the EKS98scale- • dependent shadowing parameterization. J.W.Qiu and I.V., hep-ph/0309094 Ivan Vitev, LANL

  30. +AReactionsand MassCorrections • - Axial and vector part (weak current) • - Similarly for the neutral current • Helps us understand charm and • bottom in heavy ion collisions Special propagator structure: • Equations of motion - nuclear enhanced power corrections and mass corrections • commute Ivan Vitev, LANL

  31. Testable at the Fermilab NuMI facility J. Morfin, J.Phys.G 29, (2003) 1 3 10 20 Q2 F2(x,Q2) and xF3(x,Q2)QCD Sum Rules Valance quark shadowing and QCD sum rules: examples where dipole models will fail J.W.Qiu, I.V., Phys.Lett.B 587 (2004) D.J.Gross and C.H Llewellyn Smith , Nucl.Phys. B 14 (1969) J.W.Qiu, I.V., Phys.Lett.B 587 (2004) Ivan Vitev, LANL

  32. +,- p+A Collisions Resum the multiple final state scattering of the parton “d” with the remnants of the nucleus A p Starting point:LO pQCD • Maximum coherent rescattering of the small xb parton in the • nucleus • Other interactions: less coherent (elastic) and sppressed at • forward rapidity by a large scale 1/u, 1/s Isolate all the xb dependence of the integrand: Ivan Vitev, LANL

  33. Numerical Results • Similar power corrections • modification to single and double • inclusive hadron production - increases with rapidity and centrality • disappears at high pTin accord with • the QCD factorization theorems J.W.Qiu, I.V., hep-ph/0405068 Ivan Vitev, LANL

  34. Conclusions (II) • This talk is only an introduction to the morning session – the details will be given by the experts: Jets and di-hadron correlations: • Experimental: K. Filimonov, “Di-hadron correlations at high pT” J. Jia, “Jets in PHENIX” C. Mironov, “Charged kaons correlations” J. Rak, “Measurement of jet properties and their modification in heavy ion collisions at RHIC” Y. Guo, “Correlations of high-pT particles produced in Au+Au collisions at 200 GeV” • Theoretical: J. Jalilian-Marian,“Two particle production in proton (deuteron) nucleus collisions” A. Majumder, “High pT hadron-hadron correlations” Ivan Vitev,LANL

  35. Data is for qualitative • comparison (pions versus baryons) • The power corrections • modify the ratio from low • pT to high pT • (not vice versa) The Single Inclusive Spectra Revisited I. Arsene et al., nucl-ex/0403050 Power corrections ~ 0.4 – 0.5 GCG GCG It makes no sense to try and fit the charded hadrons at low pT and these rapidities Looks like 0.5! Ivan Vitev, ISU

  36. Hard part Matrix element Note: it is that gives The Technology of Power Corrections Only one contributing uniquely defined sequence: The small-x limit of the leading twist gluon distribution function Ivan Vitev, ISU

  37. Lowest Order Contributions to (Twist 4) • Genuinely new higher twist contribution Short distance, notA1/3-enhanced The old and known Leading Twist contribution Box diagram Bremsstrahlung diagram M.Gluck and E.Reya, Nucl.Phys. 145 (1978) G.Altarelli and G.Martinelli, Phys.Lett. B76 (1978) Ivan Vitev, ISU

  38. Color Glass Inspired Calculations RdAu = 0.3-0.5 Y=2,3,4 J.Jalilian-Marian, nucl-th/0402080 RdAu = 0.5 Forward d-A Discuss problems Evolves very quickly Kharzeev, Kovchegov, Tuchin, High pT workshop at RHIC RdAu = 0.4 The effect never disappears R.Baier et al., Phys.Rev.D 68 (2003) Violate factorization! Ivan Vitev, ISU

  39. Motivation: pQCD in Nuclear Collisions K.Eskola,V.Kolhinen and C.Salgado, Eur.Phys.J. C9 (1999) M.Hirari,S.Kumano and M.Miyama, Phys.Rev. D64 (2001) Shadowing Universal nuclear dependence: from nuclear wave functions Process-dependent nuclear effects: ● Initial-state: ● Final-state: Nuclear PDF’s versus medium-induced nuclear effect (Will be discussed) Data from: NMC Ivan Vitev, LANL

  40. Power Correction Contributions to LO pQCD 1. Recall that the two gluon ladder generates the scale of higher twist - c 2. For a fixed number of interactions (2N) we take all possible cuts d New contributions to the cross section 3. Sum over all possible N The results look like LO pQCD with the substitution: I.B.P • Driven by the Mandelstam invariant(-t) the resulting suppression will be • sensitive to pTand rapidity y. Cd = 1 for quarks, CA/CF = 9/4 for gluons J.W.Qiu, I.V., hep-ph/0405068 Ivan Vitev, ISU

  41. Observing the Acoplanarity and the Power Corrections • Consider di-hadron correlations associated with hard • (approximately) back-to-back scattering Before the hard scatter After the hard scatter If Ivan Vitev, ISU

  42. Dijet Acoplanarity in d+Au and Au+Au Estimate from: J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068 <|kTy|>pA = 1.25 GeV <z><|kTy|>AA = 1.25 - 1.45 GeV p+A From: <z> = 0.75, <|kTy|>pp = 1.05 GeV A+A (2.5pTtrigg4.0)(1.0pTassoc2.5) Feedback? pp: <z><|kTy|> pp: <|jTy|> J.Rak, hep-ex/0403038 Very interesting! P.Constantin, N.Grau Ivan Vitev, ISU

  43. k’ k  xP P … X Nuclear Effects in Inclusive DeeplyInelastic Lepton-Nucleus Scattering - the DIS structure functions Used to determine the parton distribution functions (PDFs) Convenient to calculate in a basis of polarization stares of  Ivan Vitev, ISU

  44. + + The Reaction Operator Approach to Multiple Elastic and Inelastic Scatterings For the elastic scattering case illustrated here by iteration: Reaction Operator = all possible on-shell cuts through a new Double Born interaction with the propagating system Mandelstam s,t,u kT kick that helps Ivan Vitev, ISU

  45. Only small broadening • versus centrality • Looks rather similar at • forward rapidity of 2 • The reduction of the area • is rather modest • Apparently broader • distribution • Even at midrapidity a small • reduction of the area • Factor of 2-3reduction of the • area at forward rapidity of 4 Dihadron Correlation Broadening and Attenuation Midrapidity and moderate pT J.Adams et al., Phys.Rev.Lett. 91 (2003) Forward rapidity and small pT Trigger bias can also affect: J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068 Ivan Vitev, ISU

  46. 1 3 10 20 Q2 The Gross-Llewellyn Smith and Adler Sum Rules D.J.Gross and C.H Llewellyn Smith , Nucl.Phys. B 14 (1969) • To one loop in • Nuclear-enhanced power corrections • are very important • Leading twist shadowing does not contribute to GLS Compatible with the trend in the current data • Can set a limit on the 4-point parton • correlation function S.Adler , Phys.Rev. 143 (1964) Ivan Vitev, ISU

  47. deviation from the Standard Model • Asymmetric strange sea and violation of the isospin symmetry G.P.Zeller et al., Phys.Rev.Lett 88 (2002) G.P.Zeller et al., hep-ex/0203004 Modifications to the Structure Functions in Scattering Motivation Based on: The NuTeV experiment claims: Beware: Monte Carlo with many effects taken on average Axial and vector part (weak current) Similarly for the neutral current Recall the tensorial decomposition Ivan Vitev, ISU

  48. At x2 = 2 x 10-4 and • pT = 1.25 GeV hard • scattering is • similar in p+p and p+A • There isn’tmono • jettiness or g-fusion • I think that the p+A • analysis has under and • over estimated the • away-side area X2 = 1.94 x10-4 STAR • There may be room for • some suppression due • to power corrections X2 = 2.51 x10-4 Power Corrections at Forward Rapidity Preliminary: L.Bland, [STAR Colaboration] What the author concluded Are suppressed in d+Au relative to p+p at small <xF> and <pT,p> Spp-SdAu= (9.0 ± 1.5) % Consistent with CGC picture Are consistent in d+Au and p+p at larger <xF> and <pT,p> As expected by HIJING 25<Ep<35GeV CGC logic 35<Ep<45GeV Statistical errors only Ivan Vitev, ISU

  49. Beyond average : need ansatz • Independent Poisson emission • Guaranteed to be violated • By simple kinematics • Usefulness • Allows the system to adjust itself • Minimizes the effect of energy loss Analytic Limits For Energy Loss transport coefficient a) Static medium: b) Bjorken expanding medium: M.Gyulassy, I.V., X.N.Wang, Phys.Rev.Lett. 86 (2001) Npart 0 400 R.Baier et al., JHEP (2001) M.Gyulassy, P.Levai, I.V., Phys.Lett.B538 (2002) Ivan Vitev, ISU

  50. New Contribution to On-shell paricle (M) (Cuts fix kinematics) xi • Even if one neglects mass • effects show up due to the mixing of electroweak • and mass eigenstates J.W.Qiu, I.V., Phys.Lett.B 587 (2004) • Along the way we will develop techniques that • may be useful in the discussion of charm • production at RHIC |V| - the CKM matrix elements Ivan Vitev, ISU

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