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High P T and QGP. Ivan Vitev Iowa State University, Ames, IA 50011. AGS-RHIC Annual Users’ Meeting May 10 – May 14, 2004 Brookhaven National Lab, Upton NY. Ivan Vitev, ISU. If no “effects”: R AA < 1 in regime of soft physics R AA = 1 at high-p T where hard
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High PT and QGP Ivan Vitev Iowa State University, Ames, IA 50011 AGS-RHIC Annual Users’ Meeting May 10 – May 14, 2004 Brookhaven National Lab, Upton NY Ivan Vitev, ISU Ivan Vitev, ISU
If no “effects”: RAA < 1 in regime of soft physics RAA = 1 at high-pT where hard scattering dominates Suppression: RAA < 1 at high-pT Motivation: Address this Deviations from the Hard Scattering Regime Main focus: 62 GeV Au+Au Will also mention: 200 GeV d+Au p+A collisions are ideal since the deviations from the QCD factorization can be systematically computed nucleon-nucleon cross section <Nbinary>/sinelp+p AA AA Rapidity dependence, centrality dependence Ivan Vitev, ISU Ivan Vitev, ISU
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 • Address the deviations: power corrections radiative energy loss (dynamical nuclear shadowing) (jet quenching) Ivan Vitev, ISU Ivan Vitev, ISU
Results for A- and Bjorken x- Dependence Generated by the multiple final state scattering of the struck quark Scale of higher twist Q2dependence, Longitudinal structure function J.W.Qiu and I.V., hep-ph/0309094 Ivan Vitev, ISU Ivan Vitev, ISU
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 Ivan Vitev, ISU
Starting Point: LO pQCD Resum the multiple final state scattering of the parton “d” with the remnants of the nucleus A p Isolate all the xb dependence of the integrand: The results look like LO pQCD with the substitution: J.W.Qiu, I.V., hep-ph/0405068 Cd = 1 for quarks, 9/4 for gluons Ivan Vitev, ISU Ivan Vitev, ISU
single and double inclusive • shift in ~ 2 /t Numerical Results for the Power Corrections • Similar power corrections • modification to single and double • inclusive hadron production - increases with rapidity - increases with centrality • disappears at high pTin accord with • the QCD factorization theorems • Dominated by dynamical gluon • shadowing Small at midrapidity C.M. energy 200 GeV Even smaller at midrapidity C.M. energy 62 GeV J.W.Qiu, I.V., hep-ph/0405068 Ivan Vitev, ISU Ivan Vitev, ISU
+ + Medium Induced Non-Abelian Energy Loss Reaction opeartor Iterative solution 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 Inverse formation times • Incorporatesfinite • kinematics and small • number of scatterings Color current propagators • Applicable for realistic • systems Ivan Vitev, ISU Ivan Vitev, ISU
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 Ivan Vitev, ISU
17 GeV 62 GeV 200 GeV Calculated Gluon Spectra Estimate: Isospin symmetry Parton-hadron duality B.Back et al., Phys.Rev.Lett. 88 (2002) • Already large fractional energy • loss • Important: • The radiative quanta may be • experimentally observable • Difference in the manifestation • of large e-loss in the probabilistic • interpretation Kinematic modification I.V., nucl-th/0404052 Ivan Vitev, ISU Ivan Vitev, ISU
Jet Quenching at C.M. Energy of 62 GeV • At SPSCronin • effect dominates. Even with energy • loss may exhibit enhancement • Cronin effect, shadowing and • jet quenching conspire to give flat • suppression pattern out to the • highest pT at RHIC • At RHIC and no • e-loss: Strong • cancellationbetweenCronin effect • and energy loss. Net quenching. • Weak • dependence I.V., nucl-th/0404052 SPS relative to D.d’Enterria, nucl-ex/0403055 S.S.Adler, et al., Phys.Rev.Lett.91 (2003) Baryons and the charged hadrons:expected to be different Ivan Vitev, ISU Ivan Vitev, ISU
Possible most interesting outcome • Strong deviation from the perturbative • prediction • Strong nonlinearity of in dNg/dy In a Polyakov loop model A.Dumitru, R.Pisarski, Phys.Lett.B 525 (2002) Discussion of Jet Quenchingat Intermediate RHIC Energies • The result, if confirmed, would not be • unexpected • Follow from energy loss jet quenching • calculations • Naturally interpolatebetween the SPS • and the top RHIC energies • X.N.Wang, Phys.Lett.B579 (2004) • RAA=0.5 at pT=4 GeV The nuclear modification ratio • Sensitively depends on the underlying • partonic spectrum • 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 Ivan Vitev, ISU Ivan Vitev, ISU
Conclusions • 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 GeVneutral 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 Ivan Vitev, ISU