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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

motivation address this deviations from the hard scattering regime

If no “effects”:

RAA < 1 in regime of soft physics

RAA = 1 at high-pT where hard

scattering dominates


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


cross section




Rapidity dependence, centrality dependence

Ivan Vitev, ISU

Ivan Vitev, ISU

predictive power of pqcd
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:




  • 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
Results for A- and Bjorken x- Dependence

Generated by the

multiple final

state scattering

of the struck quark

Scale of higher twist


Longitudinal structure function

J.W.Qiu and I.V., hep-ph/0309094

Ivan Vitev, ISU

Ivan Vitev, ISU

the single inclusive spectra revisited

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



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
Starting Point: LO pQCD

Resum the multiple final state scattering

of the parton “d” with the remnants of

the nucleus



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

numerical results for the power corrections

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



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


  • Incorporatesfinite
  • kinematics and small
  • number of scatterings

Color current


  • Applicable for realistic
  • systems

Ivan Vitev, ISU

Ivan Vitev, ISU

analytic limits for energy loss

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



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)

Ivan Vitev, ISU

Ivan Vitev, ISU

calculated gluon spectra

17 GeV

62 GeV

200 GeV

Calculated Gluon Spectra


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
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

discussion of jet quenching at intermediate rhic energies

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



  • 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