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Coherent Multiple Scattering and Di-hadron Correlation in Heavy Ion Collisions. Jianwei Qiu Iowa State University. (in collaboration with Dr. Ivan Vitev). 32 nd International Conference on High Energy Physics August 16-22, 2004, Beijing, China. K.Filimonov, nucl-ex/0403060.

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Coherent Multiple Scattering

and Di-hadron Correlation

in Heavy Ion Collisions

Jianwei Qiu

Iowa State University

(in collaboration with Dr. Ivan Vitev)

32nd International Conference

on High Energy Physics

August 16-22, 2004, Beijing, China

Jianwei Qiu, ISU

nuclear dependence in d a collisions

K.Filimonov, nucl-ex/0403060

Nuclear dependence in d+A collisions

J.Adams et al., Phys.Rev.Lett. 91 (2003)

  • Small broadening (and/or attenuation) is
  • observed in d+Au
  • Large attenuation is observed in Au+Au
  • (sensitive to the orientation relative to the
  • reaction plane) – clearly a final state effect

J.Rak, hep-ex/0403038

Jianwei Qiu, ISU

coherent vs incoherent scattering


Coherent vs incoherent scattering
  • Consider di-hadron correlations associated with

hard (approximately) back-to-back scattering

  • Incoherent additional scattering does

not change the production probability

– area under the peak

  • Coherentinelastic scattering does change

the total production probability


Jianwei Qiu, ISU

size of the hard probes
Size of the hard probes
  • Size of a hard probe is very localized and much smaller

than a typical hadron at rest

  • But, it might be larger than a Lorentz contracted hadron:
  • low x: uncertainty in locating the parton is much larger

than the size of the boosted hadron (a nucleon)

If the active x is small enough

a hard probe can cover more than

one Lorentz contracted nucleon!

Jianwei Qiu, ISU

coherence for small x partons





  • For a nucleus, if , the probe cannot

tell which nucleon the parton comes from

Coherence for small x partons
  • IF x<xc, a hard probe can interact coherently with more

than one low x partons at a same impact parameters

Jianwei Qiu, ISU


Universal nuclear dependence

  • Scattering involves one active parton from a nucleus
  • Only single hard scattering and single PDF is involved!
  • Nuclear dependence in PDF does not interfere with the

partonic hard collision – universal nuclear dependence

Same factorized formula with nucleon PDF’s

Replaced by effective nuclear PDF’s

Jianwei Qiu, ISU

process dependent power corrections

Leading twist


All power resummation

Process dependent power corrections
  • power corrections are process dependent:
  • nonvanish parton transverse momentum
  • multiple scattering between partons
  • power corrections in collinear factorization:

Jianwei Qiu, ISU

resummation of power corrections

All power resummation needed

Resummation of power corrections
  • Power corrections:

Lower x  larger

power corrections

Jianwei Qiu, ISU

dynamical power corrections in dis
Dynamical power corrections in DIS
  • Dynamical power corrections generated by the

multiple final state scattering of the struck quark

The probe, virtual

photon, interacts

with all nucleons at

a given impact

parameter coherently

  • Coherence:

High twist shadowing

– process dependent

Jianwei Qiu, ISU


After integration over

Leading power corrections in DIS

  • Quark propagator of momentum xip+q :
  • Gluons are transversely polarized in light-cone gauge:
  • Effective scalar interaction:

Jianwei Qiu, ISU



  • Leading power correction:
  • Medium length enhancement:

Jianwei Qiu, ISU

resummed a 1 3 enhanced power corrections
Resummed A1/3-EnhancedPower Corrections
  • Results:
  • One parameter – scale of power


U-quark, CTEQ5 LO

Upper limit of the saturation scale

Jianwei Qiu, ISU

power corrections in p a collisions
Power Corrections in p+A Collisions
  • Hadronic factorization fails for power corrections of

the order of 1/Q4 and beyond

  • Medium size enhanced dynamical power corrections

in p+A could be factorized

to make predictions

for p+A collisions

  • Single hadron inclusive production:

Once we fix the incoming parton momentum from the beam

and outgoing fragmentation parton, we uniquely fix the

momentum exchange, qμ, and the probe size

 coherence along the direction of qμ - pμ

Ivan Vitev, ISU

Jianwei Qiu, 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:
  • Leading power nuclear dependence with the substitution:

Cd = 1for quarks, 9/4 for gluons

Jianwei Qiu, ISU

numerical results for the power corrections
Numerical results for the power corrections
  • Similar power correction

modification to single and double

inclusive hadron production

  • increases with rapidity
  • increases with centrality
  • disappears at high pTin accord with
  • the QCD factorization theorems
  • single and double inclusive
  • shift in ~ 2 /t

Small at mid-rapidity C.M. energy 200 GeV

Even smaller at mid-rapidity C.M. energy 62 GeV

Qiu and Vitev, hep-ph/0405068

Jianwei Qiu, ISU

acoplanarity and power corrections
Acoplanarity and power corrections
  • Consider di-hadron correlations associated with

hard (approximately) back-to-back scattering

  • Coherent scattering reduces:
  • Incoherent scattering broadens:

Jianwei Qiu, ISU

dihadron correlation broadening and attenuation

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

Mid-rapidity and moderate pT

J.Adams et al., Phys.Rev.Lett. 91 (2003)

Forward rapidity and small pT

Trigger bias can also affect:

Qiu and Vitev, Phys.Lett.B 570 (2003); hep-ph/0405068

Jianwei Qiu, ISU



  • Although hard partonic collisions are localized in space-time,

comparing to the rest size of a nucleon, the interaction length

could be larger than a size of a Lorentz contracted nucleon

  • Coherent multiple interactions lead to power corrections to

physical cross sections:

  • Leading medium size enhanced power corrections are Infrared safe

and can be systematically resummed into a translation operator

acting on parton’s momentum fraction, which leads to a shift in

parton’s momentum fraction without changing the leading twist

factorized formula

  • Dynamical power corrections for p+A collisions lead to

the centrality and rapidity dependent suppression of

single inclusive spectra and the dihadron 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


Jianwei Qiu, ISU