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Published on November 15, 2007

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Slide1:  Jets in Nuclear Collisions ISMD 2004, July 26 - August 1, 2004 Sonoma County, California, USA Ivan Vitev, LANL Outline of the Talk:  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. Ivan Vitev, LANL 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: Slide3:  Clean Jets in DIS and e+, e- Ivan Vitev, LANL Jets in DIS (Single clean jet) C.C. example Jets in p+p Slide4:  Jets in A+A Reactions Ivan Vitev, LANL Jets in nuclear collisions The complication at the Tevatron (D0) 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 Di-hadron Correlations:  Di-hadron Correlations Ivan Vitev, LANL Relate the widths and the momentum measures Vacuum: intrinsic, NLO corrections, soft gluon resummation Medium: transverse momentm diffusion Hadron 1 Di-hadron correlation function: Hadron 2 Relative to : Fragmentation: not collinear, a jT kick to the hadron G.Altarelli, R.K.Ellis, G.Martinelli, Phys.Lett. 151B (1985) Analytic Multiplicity Results:  Analytic Multiplicity Results Ivan Vitev, LANL Double ordering The probability to emit n gluons: Average gluon number: Z0 mass scale Experimentally 1.54 +/- … See e.g. Field and Feynman, Dokshitzer et al. Slide7:  Angular Distribution Ivan Vitev, LANL The LDLA Definite shortcomings In the limit of small coupling Normalization and mean kT2 The OPAL experiment: Within 4% of the jet axis 17% of g-energy 30% of q-energy pT Diffusion in Nuclei:  pT Diffusion in Nuclei Ivan Vitev, LANL Summary Additional approximation for a Gaussian form L d+Au and Au+Au:  d+Au and Au+Au pp: <z><|kTy|> pp: <|jTy|> 2.5pTtrigg4.0, 1.0pTassoc2.5 J.Rak, hep-ex/0403038 P.Constantin, N.Grau J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068 From: <z> = 0.75, <|kTy|>pp = 1.05 GeV <|kTy|>pA = 1.25 GeV <z><|kTy|>AA = 1.25 - 1.45 GeV p+A A+A Feedback? Ivan Vitev, LANL The vacuum broadening is large Cold nuclear matter – only a small effect Hot nuclear matter – seems insufficient Medium Induced Non-Abelian Energy Loss:  Medium Induced Non-Abelian Energy Loss Explicitly the Landau- Pomeranchuk-Migdal destructive interference effect in QCD Incorporates finite kinematics and small number of scatterings Applicable for realistic systems M.Gyulassy, P.Levai, I.V., Nucl.Phys. B594 (2001); Phys.Rev.Lett.85 (2000) Inverse formation times Color current propagators Iterative solution Ivan Vitev, LANL Interplay of formation times and medium size Also see R. Baier et al., B. Zakharov, U. Wiedemann, X.N. Wang Radiative Spectra:  I.V., nucl-th/0404052 Radiative Spectra Estimate: Isospin symmetry Parton-hadron duality B.Back et al., Phys.Rev.Lett. 88 (2002) Ivan Vitev, LANL Small and finite The basis for jet tomography – the extraction of the density of the medium - transport coefficient - effective gluon rapidity density The Basic pQCD Process:  The Basic pQCD Process Ivan Vitev, LANL Pc Pd Pc / zc Pd / zd Double inclusive hadron production (most of what will be discussed) Single inclusive hadron production J.W.Qiu, I.V., hep-ph/0405068 Extended to include power corrections X One way of implementing radiative energy loss: J.Collins, D.Soper, G.Sterman, Nucl.Phys.B223 (1983) The E-loss Connection:  The E-loss Connection Ivan Vitev, LANL S.Pal, S.Pratt, Phys.Lett.B574 (2003) 2 GeV The plasmon frequency forces radiation in fewer semi-hard gluons 25-40% increase in the multiplicity 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 Factor of 2 in mult. Jet Quenching and Jet Tomography :  Jet Quenching and Jet Tomography I.V., nucl-th/0404052 Ivan Vitev, LANL I.V., M.Gyulassy, Phys.Rev.Lett. 89 (2002) Attenuation of the inclusive hadron spectra Extraction of the soft underlying parton density (bulk matter) In jet algorithms – a need for hard pT cut Centrality Dependence of Jet Quenching:  X.N.Wang, nucl-th/0305010 Ivan Vitev, LANL central G.G.Barnafoldi et al., hep-ph/0311343 Centrality Dependence of Jet Quenching Modification of the Jet-like Correlations:  Modification of the Jet-like Correlations Ivan Vitev, LANL Attenuation (disappearance) of the away-side correlation function Dependence relative to the reaction plane 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 , Jet 1 Jet 2 Slide17:  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 A. Predictive Power of pQCD:  A. Predictive Power of pQCD 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 J.Collins, D.Soper, G.Sterman, Nucl.Phys.B223 (1983) Ivan Vitev, LANL (dynamical nuclear shadowing) (jet quenching) Basic pQCD Processes (I):  Basic pQCD Processes (I) DIS: Drell-Yan: Ivan Vitev, LANL  Eikonal line. Disappears in A+ = 0 J.Collins, D.Soper, G.Sterman, Nucl.Phys.B223 (1983) All orders All orders G.Bodwin, Phys.Rev. D31 (1985) Extended to corrections in e()+A J.W.Qiu, I.V., hep-ph/0309094 Basic pQCD Processes (II):  Basic pQCD Processes (II) Hadron production in N+N: Ivan Vitev, LANL Pc Pd Pc / zc Pd / zd Double inclusive hadron production (most of what will be discussed) Single inclusive hadron production Factorization: at leading power and leading power corrections J.Collins, D.Soper, G.Sterman, Adv.Ser.Dir. 5 (1988) J.W.Qiu, G.Sterman, Nucl.Phys.B353 (1991) J.W.Qiu, I.V., hep-ph/0405068 Extended to in p+A corrections Slide21:  Ivan Vitev, LANL Particle Production Fragmentation: natural near-side and away-side correlations Relativistic hydrodynamics: Cooper-Frye formula From an uncorrelated evolved fluid Coalescence models: After solving 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 Slide22:  Ivan Vitev, LANL 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 Slide23:  Ivan Vitev, LANL LO pQCD Example Calculated as in: J.W.Qiu, I.V., hep-ph/0405068 Perturbative unbiased calculation Clear anti-correlation between pT assoc and 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 B. Motivation: Deviations from Hard Scaling :  AA nucleon-nucleon cross section B. Motivation: Deviations from Hard Scaling Rapidity dependence, centrality dependence Examples: 200, 62 GeV Au+Au; 200 GeV d+Au Ivan Vitev, LANL <Nbinary>/sinelp+p Quenching Shadowing Acoplanarity Acoplanarity:  Acoplanarity Consider di-hadron correlations associated with hard (approximately) back-to-back scattering If Ivan Vitev, LANL Relate the widths and the momentum measures Di-hadron correlation function Vacuum: intrinsic, NLO corrections, soft gluon resummation Medium: transverse momentm diffusion Experimental Results:  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?) DIS Coherence :  DIS Coherence Lightcone gauge: Breit frame: 2D lightcone dynamics Pole – on-shell, long distance No pole – contact, short distance J.W.Qiu, Phys.Rev. D42 (1990) First coherent calculation Factorization approach: separate the short sistance computable dynamics from the long distance matrix emenets. Final state effect Ivan Vitev, LANL Resummed Power Corrections:  Resummed Power Corrections Simple analytic formula: QM shift operator Scale of power corrections (geometric and vertex factors, two gluon correlation function) Ivan Vitev, LANL Dynamical generation of a parton’s mass in the final state Numerical Results:  Numerical Results J.W.Qiu and I.V., hep-ph/0309094 Q2 dependence, Longitudinal SF Generated by the multiple final state scattering of the struck quark Compares well to the EKS98 scale- dependent shadowing parameterization. Ivan Vitev, LANL +A Reactions and Mass Corrections :  Equations of motion - nuclear enhanced power corrections and mass corrections commute +A Reactions and Mass Corrections Special propagator structure: - Axial and vector part (weak current) - Similarly for the neutral current Helps us understand charm and bottom in heavy ion collisions Ivan Vitev, LANL F2(x,Q2) and xF3(x,Q2) QCD Sum Rules:  F2(x,Q2) and xF3(x,Q2) QCD Sum Rules J.W.Qiu, I.V., Phys.Lett.B 587 (2004) Valance quark shadowing and QCD sum rules: examples where dipole models will fail Ivan Vitev, LANL J.W.Qiu, I.V., Phys.Lett.B 587 (2004) D.J.Gross and C.H Llewellyn Smith , Nucl.Phys. B 14 (1969) p+A Collisions:  p+A Collisions Isolate all the xb dependence of the integrand: Resum the multiple final state scattering of the parton “d” with the remnants of the nucleus p A 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 Ivan Vitev, LANL Numerical Results:  Numerical Results J.W.Qiu, I.V., hep-ph/0405068 Similar power corrections modification to single and double inclusive hadron production - increases with rapidity and centrality disappears at high pT in accord with the QCD factorization theorems Ivan Vitev, LANL Slide34:  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 The Single Inclusive Spectra Revisited:  The Single Inclusive Spectra Revisited Ivan Vitev, ISU I. Arsene et al., nucl-ex/0403050 GCG GCG ~ 0.4 – 0.5 Looks like 0.5! Power corrections It makes no sense to try and fit the charded hadrons at low pT and these rapidities The Technology of Power Corrections:  The Technology of Power Corrections Ivan Vitev, ISU The small-x limit of the leading twist gluon distribution function Only one contributing uniquely defined sequence: Lowest Order Contributions to:  Lowest Order Contributions to Ivan Vitev, ISU (Twist 4) Short distance, not A1/3-enhanced G.Altarelli and G.Martinelli, Phys.Lett. B76 (1978) M.Gluck and E.Reya, Nucl.Phys. 145 (1978) Bremsstrahlung diagram Box diagram Genuinely new higher twist contribution The old and known Leading Twist contribution Color Glass Inspired Calculations:  Color Glass Inspired Calculations Ivan Vitev, ISU Kharzeev, Kovchegov, Tuchin, High pT workshop at RHIC Evolves very quickly Forward d-A Y=2,3,4 J.Jalilian-Marian, nucl-th/0402080 RdAu = 0.5 RdAu = 0.3-0.5 Violate factorization! R.Baier et al., Phys.Rev.D 68 (2003) The effect never disappears RdAu = 0.4 Discuss problems Motivation: pQCD in Nuclear Collisions:  Motivation: pQCD in Nuclear Collisions Universal nuclear dependence: from nuclear wave functions Process-dependent nuclear effects: ● Initial-state: ● Final-state: Nuclear PDF’s versus medium-induced nuclear effect Data from: NMC K.Eskola,V.Kolhinen and C.Salgado, Eur.Phys.J. C9 (1999) M.Hirari,S.Kumano and M.Miyama, Phys.Rev. D64 (2001) Shadowing (Will be discussed) Ivan Vitev, LANL Power Correction Contributions to LO pQCD:  Power Correction Contributions to LO pQCD Ivan Vitev, ISU J.W.Qiu, I.V., hep-ph/0405068 The results look like LO pQCD with the substitution: Cd = 1 for quarks, CA/CF = 9/4 for gluons c d Driven by the Mandelstam invariant (-t) the resulting suppression will be sensitive to pT and rapidity y. 1. Recall that the two gluon ladder generates the scale of higher twist - 2. For a fixed number of interactions (2N) we take all possible cuts 3. Sum over all possible N I.B.P New contributions to the cross section Observing the Acoplanarity and the Power Corrections:  Observing the Acoplanarity and the Power Corrections Ivan Vitev, ISU Before the hard scatter After the hard scatter Consider di-hadron correlations associated with hard (approximately) back-to-back scattering If Dijet Acoplanarity in d+Au and Au+Au:  Dijet Acoplanarity in d+Au and Au+Au Ivan Vitev, ISU pp: <z><|kTy|> pp: <|jTy|> (2.5pTtrigg4.0)(1.0pTassoc2.5) J.Rak, hep-ex/0403038 P.Constantin, N.Grau J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068 Estimate from: From: <z> = 0.75, <|kTy|>pp = 1.05 GeV <|kTy|>pA = 1.25 GeV <z><|kTy|>AA = 1.25 - 1.45 GeV p+A A+A Very interesting! Feedback? Nuclear Effects in Inclusive Deeply Inelastic Lepton-Nucleus Scattering :  Nuclear Effects in Inclusive Deeply Inelastic Lepton-Nucleus Scattering Ivan Vitev, ISU - the DIS structure functions Used to determine the parton distribution functions (PDFs) Convenient to calculate in a basis of polarization stares of  Slide44:  The Reaction Operator Approach to Multiple Elastic and Inelastic Scatterings Reaction Operator = all possible on-shell cuts through a new Double Born interaction with the propagating system For the elastic scattering case illustrated here by iteration: Mandelstam s,t,u kT kick that helps Ivan Vitev, ISU Dihadron Correlation Broadening and Attenuation:  Dihadron Correlation Broadening and Attenuation Ivan Vitev, ISU J.W.Qiu, I.V., Phys.Lett.B 570 (2003); hep-ph/0405068 Midrapidity and moderate pT Forward rapidity and small pT J.Adams et al., Phys.Rev.Lett. 91 (2003) Trigger bias can also affect: The Gross-Llewellyn Smith and Adler Sum Rules:  The Gross-Llewellyn Smith and Adler Sum Rules To one loop in Nuclear-enhanced power corrections are very important Ivan Vitev, ISU D.J.Gross and C.H Llewellyn Smith , Nucl.Phys. B 14 (1969) Compatible with the trend in the current data S.Adler , Phys.Rev. 143 (1964) Can set a limit on the 4-point parton correlation function Leading twist shadowing does not contribute to GLS Modifications to the Structure Functions in Scattering:  Modifications to the Structure Functions in Scattering Ivan Vitev, ISU Similarly for the neutral current The NuTeV experiment claims: Based on: Beware: Monte Carlo with many effects taken on average Motivation Axial and vector part (weak current) Recall the tensorial decomposition Power Corrections at Forward Rapidity:  Statistical errors only 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 35<Ep<45GeV Ivan Vitev, ISU Power Corrections at Forward Rapidity Preliminary: L.Bland, [STAR Colaboration] CGC logic Analytic Limits For Energy Loss:  Ivan Vitev, ISU Analytic Limits For Energy Loss a) Static medium: b) Bjorken expanding medium: M.Gyulassy, I.V., X.N.Wang, Phys.Rev.Lett. 86 (2001) R.Baier et al., JHEP (2001) M.Gyulassy, P.Levai, I.V., Phys.Lett.B538 (2002) transport coefficient 0 400 Npart New Contribution to :  Ivan Vitev, ISU On-shell paricle (M) New Contribution to 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) |V| - the CKM matrix elements xi Along the way we will develop techniques that may be useful in the discussion of charm production at RHIC (Cuts fix kinematics) Discussion of Jet Quenching at Intermediate RHIC Energies :  Discussion of Jet Quenching at Intermediate RHIC Energies Ivan Vitev, ISU The result, if confirmed, would not be unexpected Follow from energy loss jet quenching calculations Naturally interpolate between the SPS and the top RHIC energies X.N.Wang, Phys.Lett.B579 (2004) RAA=0.5 at pT=4 GeV In their power law behavior the 62 GeV spectra are much closer to the 130 GeV and the 200 GeV cross sections than to the 17 GeV ones The nuclear modification ratio Sensitively depends on the underlying partonic spectrum Experimental Results at 62 GeV:  Experimental Results at 62 GeV (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) Experimental Results (Continued):  Experimental Results (Continued) STAR preliminary PHOBOS (submitted) May have twice as many baryons as pions! Charged behave differently: factor of 50% enhancement in peripheral but suppression develops at high pt, as expected, in central Slide54:  Conclusions (I) Dynamical nuclear shadowing from resummed QCD power corrections. Results consistent with its x-, Q2- and A- dependence. Neutrino-nucleus DIS. Modification of the QCD sum rules. First calculations of dynamical power corrections for hadronic collisions, . Results for the centrality and rapidity dependent suppression of single inclusive spectra and the dihadron correlations. The power corrections disappear at high pT. They are small at 62 GeV and would not affect the extraction of RAA In central Au+Au collisions at C.M. energy of 62 GeV neutral pions were found to be suppressed by a factor of 2-3 by jet quenching. Relatively weak pT dependence of RAA Interpretation of the rapidity density in 1+1D Bjorken expansion: at the energy density - already significantly above the current critical value. Charged hadrons, especially baryons, are expected to be less suppressed and are beyond the reach of the current perturbative techniques Ivan Vitev, ISU Slide55:  Conclusions (II) In d+Au collisions midrapidity and moderate pT the dominant effect is small broadening of the correlations. At very forward rapidity (y=4) and small pT the power corrections give a factor of 2-3 reduction of the area of the away side correlations. If the preliminary STAR results at forward y correlations persist – there isn’t monojettines or high density gluon fusion effects at x=2x10-4 (following saturation logic) in Au. Will be interesting to measure neutral pions at forward y and compare the suppression effect (RAA) to the suppression for charged Given the results of correlation analysis one can go back and rethink their favorite d+Au suppression scenarios Ivan Vitev, ISU

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