Resummed QCD Power Corrections to F2

1
The pQCD Factorization Approach in High
Energy Nuclear Collisions
Hot Quarks 2004, July 19 - July 24, 2004 Taos
Ski Valley, New Mexico, USA
Ivan Vitev, LANL
2
Outline of the Talk

• A review of the collinear pQCD factorization
• approach
• ? DIS, Drell-Yan and hadronic
  collisions. Basic concepts and
• advantages of the factorization
  approach
• ? Hadron production. (The
  fragmentation seesaw mechanism)

• Corrections to the leading twist perturbative
• formalism
• ? Emphasis on reactions involving
  nuclei
• Elastic Transverse momentum
  diffusion. Broadening of the
• away-side
  correlation function
• Inelastic QCD radiative energy
  loss. Jet quenching and the
• new 62 GeV run.
• Coherent Nuclear enhanced power
  corrections. Shadowing in
• F2 and xF3. QCD
  sum rules. pA reactions

• Conclusions

Ivan Vitev, LANL
3
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)
(dynamical nuclear shadowing)
(jet quenching)
Ivan Vitev, LANL
4
Basic pQCD Processes (I)

• DIS
• Drell-Yan

J.Collins, D.Soper, G.Sterman, Nucl.Phys.B223
(1983)
All orders
Eikonal line. Disappears in A 0
Extended to corrections in
e(?)A
J.W.Qiu, I.V., hep-ph/0309094
All orders
G.Bodwin, Phys.Rev. D31 (1985)
??
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Basic pQCD Processes (II)

• Hadron production in NN

Factorization at leading power and leading
power corrections
Pd
Pd / zd
J.Collins, D.Soper, G.Sterman, Adv.Ser.Dir. 5
(1988)
J.W.Qiu, G.Sterman, Nucl.Phys.B353 (1991)
Pc / zc
Extended to in pA corrections
J.W.Qiu, I.V., hep-ph/0405068

• Single inclusive hadron production

Pc

• Double inclusive hadron production (most of what
  will be discussed)

Ivan Vitev, LANL
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Particle Production

• Fragmentation natural near-side and away-side
  correlations

• Relativistic hydrodynamics

Cooper-Frye formula
After solving
P.Kolb,J.Sollfrank,U.Heinz, Phys.Rev.C62, (2002)
From an uncorrelated evolved fluid
Folding the quark Wigner functions and the meson
or baryon wave functions

• Coalescence models

R.J. Fries et al., Phys.Rev.Lett.90, (2003)
Folding two gluon distributions into one gluon
(particle)

• Saturation gluon fusion models

Gribov, Levin, Rischkin, Phys.Rep., (1981)
These mechanisms dont have natural dont have
natural correlations
Ivan Vitev, LANL
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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
Ivan Vitev, LANL
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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

Ivan Vitev, LANL
9
B. Motivation Deviations from Hard Scaling
Examples 200, 62 GeV AuAu 200 GeV dAu
AA
ltNbinarygt/sinelpp
nucleon-nucleon cross section

• Quenching
• Shadowing
• Acoplanarity

NMC collaboration
Rapidity dependence, centrality dependence
Nucl.Phys. B441, (1995)
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Acoplanarity

• Consider di-hadron correlations associated with
  hard
• (approximately) back-to-back scattering

J.Rak, hep-ex/0403038
Di-hadron correlation function
J.W.Qiu, I.V., Phys.Lett.B 570 (2003)
Relate the widths and the momentum measures
If
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pT Diffusion


Incoherent local Glauber.
Elastic application of the GLV approach
M.Gyulassy, P.Levai, and I.V., Phys.Rev. D66,
(2002)
Additional approximation for a Gaussian form
Summary
Ivan Vitev, LANL
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dAu and AuAu
Estimate from
J.W.Qiu, I.V., Phys.Lett.B 570 (2003)
hep-ph/0405068
ltkTygtpA 1.25 GeV ltzgtltkTygtAA 1.25 - 1.45
GeV
pA
From ltzgt 0.75, ltkTygtpp 1.05 GeV

• The vacuum broadening is large
• Cold nuclear matter only a small effect
• Hot nuclear matter seems insufficient

AA
(2.5?pTtrigg?4.0)?(1.0?pTassoc?2.5)
Feedback?
pp ltzgtltkTygt
pp ltjTygt
J.Rak, hep-ex/0403038
Very interesting!
P.Constantin, N.Grau
Ivan Vitev, LANL
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The E-loss Connection
S.Pal, S.Pratt, Phys.Lett.B574 (2003)
- The separation of the v2 and jetty parts - The
feedback form the energy loss - Power law type
scattering
600 MeV
I.V., nucl-th/0403089
2 GeV

• Attenuation (disappearance) of the away-side
• correlation function
• Dependence relative to the reaction plane

Ivan Vitev, LANL
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Correlations versus Reaction Plane

• The attenuation of the away side
• correlation function due to energy
• loss is now established

• More differential study of
• correlation functions a direct
• verification of

• Ratios of attenuations

T.Hirano, Y.Nara, Phys.Rev.Lett.91 (2003)
K. Filimonov, QM 2004 presentation
Ivan Vitev, LANL
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Medium Induced Non-Abelian Energy Loss
Iterative solution
M.Gyulassy, P.Levai, I.V., Nucl.Phys. B594
(2001) Phys.Rev.Lett.85 (2000)
Inverse formation times
R.Baier et al., Nucl.Phys.B483 (1997) ibid. 484
(1997). B.Zakharov, JETP Lett. 63
(1996) U.Wiedemann, Nucl.Phys.B588 (2000)
Color current propagators
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Calculated Gluon Spectra
Isospin symmetry Parton-hadron duality
Estimate
B.Back et al., Phys.Rev.Lett. 88 (2002)
One way of implementing radiative energy loss
Small and finite
Kinematic modification of FFs
(Another way is the modification of the partonic
cross section and folding with unmodified FFs)
I.V., nucl-th/0404052
Ivan Vitev, LANL
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Jet Quenching at C.M. Energy of 62 GeV
I.V., nucl-th/0404052
SPS relative to D.dEnterria, nucl-ex/0403055
S.S.Adler, et al., Phys.Rev.Lett.91 (2003)
Baryons and the charged hadrons expected to be
different
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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 wouldnt
  attempt
• to fit baryons below 4-5 GeV)

Similar results (h,h-) by PHOBOS and STAR.
(BRAHMS?)
19
DIS Coherence
Factorization approach separate the short
sistance computable dynamics from the long
distance matrix emenets. Final state effect
2D lightcone dynamics

• Lightcone gauge

First coherent calculation

• Breit frame

Pole on-shell, long distance
No pole contact, short distance
J.W.Qiu, Phys.Rev. D42 (1990)
Ivan Vitev, LANL
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Resummed Power Corrections
Dynamical generation of a partons mass in the
final state
Scale of power corrections (geometric and vertex
factors, two gluon correlation function)
Simple analytic formula
QM shift operator
Ivan Vitev, LANL
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Numerical Results
Generated by the multiple final state
scattering of the struck quark
Q2 dependence, Longitudinal SF

• Compares well to the EKS98 scale-
• dependent shadowing parameterization.

J.W.Qiu and I.V., hep-ph/0309094
Ivan Vitev, LANL
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?A Reactions and Mass Corrections

• - Axial and vector part (weak current)
• - Similarly for the neutral current
• Helps us understand charm and
• bottom in heavy ion collisions

Special propagator structure

• Equations of motion - nuclear enhanced power
  corrections and mass corrections
• commute

Ivan Vitev, LANL
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F2(x,Q2) and xF3(x,Q2)QCD Sum Rules
Valance quark shadowing and QCD sum rules
examples where dipole models will fail
J.W.Qiu, I.V., Phys.Lett.B 587 (2004)
D.J.Gross and C.H Llewellyn Smith , Nucl.Phys. B
14 (1969)
J.W.Qiu, I.V., Phys.Lett.B 587 (2004)
Ivan Vitev, LANL
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pA Collisions
Resum the multiple final state scattering of the
parton d with the remnants of the nucleus
A
p
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

Isolate all the xb dependence of the integrand
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Numerical Results

• 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

J.W.Qiu, I.V., hep-ph/0405068
Ivan Vitev, LANL
26
Conclusions (I)

• The perturbative QCD factorization approach
  represents the basis
• for the systematic understanding of high energy
  reactions involving nuclei
• Fundamental Provides the baseline
  from elementary reactions with
• nucleons
• Self-improving Contains the
  expansions that arise from loop corrections,
• high twist corrections and
  approximations
• Jet and hadron correlation studies - a new area
  that has opened
• at RHIC and will certainly be even more important
  at the LHC
• Novel ways of testing the particle
  production mechaisms. The
• fragmentation seesaw analogy
• Independent source of information
  about the scattering properties of
• the medium opacity, parton number
  density, energy density
• Identify the scattering regime
  elastic, inelastic or coherent and are
• Final state dynamics seems to dominate the
  majority of the observable nuclear effects

Ivan Vitev, LANL