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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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slide1

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

If

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

If

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

slide6

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

contributions

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

slide10

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

slide11

+

  • 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

corrections

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

p

A

“d”

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

slide19

Conclusions

  • 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

correlations

Jianwei Qiu, ISU