Resummed QCD Power Corrections to F2

1
PQCD Approach to Parton Propagation in
Matter
Ivan Vitev
Hard Probes 2006, Pacific Grove, CA
2
Outline of the Talk
Acknowledgement thanks to the organizers for the
invitation to give this talk
Acknowledgement thanks to my collaborators,
P.Huovinen, T.Goldman,
M.Gyulassy, M.B.Johnson, P.Levai,
J.W.Qiu, X.N.Wang

• Initial state interactions
• ? Transverse momentum diffusion
  and Cronin effect
• ? Energy loss in cold nuclear
  matter and forward rapidity

• Final state interactions in cold nuclear
  matter
• ? Coherent power corrections and
  nuclear shadowing
• ? Open charm production and
  modification in pA reactions

• Final state interactions in the QGP
• ? Radiative energy loss, universal
  features of jet quenching
• ? Modifications of di-jets, large
  angle correlations and flow

3
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
• 
  

pT (E) GeV
4
In-Medium Modification of the PQCD Cross Sections

• The way to understand medium effects on hadron
  cross sections in the framework of PQCD
• is to follow the history of a parton from the IS
  nucleon wave function (PDF) to the FS hadron
• wave function (FF)

a) Initial state interactions Elastic
scattering and Cronin effect
d) Final state interactions in the QGP Jet
quenching
b) Initial state interactions Energy loss
and forward Y suppression
e) Final state interactions in the QGP Large
angle correlations, Di-Jet suppression,
Deflection of jets by flow
c) Final state interactions Dynamical
shadowing, Generalization to heavy quarks
Cold nuclear matter effects are present at times

• Jet interactions in the medium result in
  kinematic modifications to the hard scattering
  cross
• section that are process dependent

5
Initial State Elastic Scatterings
a) Initial state elastic scattering
Unitarization of multiple scattering

Reaction Operator all possible on-shell
cuts through a new Double Born interaction
with the propagating system
Initial condition
Mean number of scatterings
Solution
The approximate solution is that of a 2D diffusion

Elastic scattering cross section
Implemented in the PQCD approach as
broadening of the initial state partons
6
Cronin Effect
Good description at mid rapidity
Default
Wrong sign at forward rapidity
Cronin effect enhancement of cross sections at
intermediate transverse momenta relative to the
binary scaled pp
I.V., Phys.Lett.B526 (2003)
A.Accardi, CERN yellow report, references therein
Data
7
Cold Nuclear Matter Energy Loss
b) Initial state inelastic scattering
I.V., T.Goldman, M.B.Johnson, J.W.Qiu,
hep-ph/0605200
B.Kopeliovich, et al., Phys.Rev.C72 (2005)

• Shadowing parameterizations (not)

20 GeV (SPS)

• Dynamical calculations of high twist
• shadowing (not)

• Energy loss in combination with HTS
• (yes)

T.Alber et al., E.Phys.J.C 2 (1998)
Initial state E-loss
J.Gunion and G.Bertsch, Phys.Rev.D25 (1982)
200 GeV (RHIC)
To investigate
S.S.Adler et al., nucl-ex/0603017
8
High Twist Shadowing in DIS
c) Final state coherent scattering

• Dynamical parton mass (QED analogy)

x energy mass
J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004)
9
Heavy Quarks in pp and pA
New possibility hadron composition of heavy
quark triggered jets
FFs Braaten et al., Phys.Rev.D51 (1995)
PDFs CTEQ 6.1 LO, J.Pumplin et al., JHEP 207
(2002)

• Anti-correlation between K and the
• hardness of fragmentation r
• Non-trivial hadron composition of c and b
• triggered jets

10
HTS for Light Hadrons and Open Charm
Single inclusive particles
Away-side correlations

• Very similar dynamical shadowing
• for light hadrons and heavy quarks
• Insufficient to explain the forward
• rapidity data
• Single and double inclusive cross
• sections are similarly suppressed

I.V., T.Goldman, M.B.Johnson, J.W.Qiu,
hep-ph/0605200
J.W.Qiu, I.V., Phys.Lett.B632 (2006)
11
Energy Loss and High Twist Shadowing
Single inclusive particles
Double inclusive yields (away-side)
I.V., T.Goldman, M.B.Johnson, J.W.Qiu,
hep-ph/0605200

• Main difference is much more pT independent
  suppression as compared to high twist
• shadowing

• Very similar e-loss effects for light hadron
  and heavy quark spectra
• Single and double inclusive cross sections are
  similarly suppressed

Same
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Process Dependence of Power Corrections
Suppression ( )
(For example forward rapidity)

• The function F(xb) contains the small xb
  dependence

(For example DY)
Enhancement ( )

• Power corrections are process dependent and not
  separable in PDFs and FFs

S.Brodsky et al, Phys.Rev.D65 (2002)

• Similar process dependence in single spin
  asymmetries

S.Brodsky et al, Phys.Lett.B530 (2002)

• Shadowing is dynamically generated in the
  hadronic collision

13
Radiative Energy Loss in the QGP
d) Final state radiative energy loss
Find a full solution to all orders in the
correlation between multiple scattering centers
M.Gyulassy,P.Levai,I.V., Nucl.Phys.B 594 (2001)
Different problems require different solutions
Uncertainty relation
M.Gyulassy, I.V., X.N.Wang , Phys.Rev.Lett.86
(2001)
J.D.Bjorken, Phys.Rev.D 27 (1983)
14
Approximately universal behavior
Baseline
Prediction
Scalings
Natural variables
Fractional energy loss
Suppression
I.V., Phys.Lett.B in press, hep-ph/0603010
15
0-10, 20-30 and 60-80 AuAu, CuCu and
central PbPb
M.Gyulassy, P.Levai, I.V., Phys.Lett.B (2002)

• Small probability not to radiate
• Small fractional energy loss at large ET

• Scales in the QGP

Initial parameters
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System Size Dependence of Jet Quenching

• Absolute scale comparisons can and should be
  done at large pT
• Similar pT dependence (flat) in AuAu and CuCu

• In classes with the same we find
• numerically the same suppression

For example central CuCu and mid central AuAu

• Future tests of high energy nuclear
• physics at the LHC

I.V., Phys.Lett.B in press, hep-ph/0603010
17
Energy Loss and Di-Jets

e) QGP effects on di-jet production
One way of incorporating energy loss

• Standard quenching of leading
• hadrons

• Redistribution of the lost energy
• in soft hadrons

Satisfies the momentum sum rule
AA
Single inclusive particles
Away-side yields
RHIC
LHC
I.V., Phys.Lett.B630 (2005)
18
Radiation Distribution and Flow Effects
q0
Gluon number distribution without or with q0 1
GeV

• Mechanical analogy, Theoretical derivation

Problem
Result same energy loss and shifted reference
frame
Solution expand about
Show that vanishes

• We cannot confirm the prescription

N.Armesto et al., Phys.Rev.C (2005)

• Important for deflected jets, to be seen in
• experiment

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Conclusions

• In-medim interactions can be understood
• following the history of a jet in a hard
  scatter

• Initial state interactions
• ? Transvevrse momentum diffusion and
  Cronin effect
• ? Energy loss and rapidity
  asymmetry in pA

• Coherent final state interactions
• ? Shadowing is dynamically generated
  and arises from the final state
• ? Shadowing for D mesons and light
  pions is similar

• Radiative energy loss in the QGP
• ? Predicted suppession for CuCu
  vesus centrality and pT
• ? QGP suppression is consistent
  with perturbative interaction of jets
• in the medium

• Modification of di-jets
• ? Gluon feedback is important for
  di-hadrons at large angle
• ? Flow leads to deflection of the
  jetgluons, so be exp. determined

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II. Coherent Power Corrections
Deviation from A-scaling
What remains for theory power corrections in
DIS - suppression
Data from NMC
FSI are always present
S.Brodsky et al.
Ivan Vitev, LANL
21
Medium-Induced Bremsstrahlung

• Calculating the multiple scatterings in the
  plasma

p
2
p
Example of hard scattering
Medium
M.Gyulassy, P.Levai, I.V., Nucl.Phys.B594 (2001)
Reaction operator (Cross section level
)
Potential
Advantage applicable for elastic, inelastic and
coherent scattering
controlled approach to
coherent radiation (LPM)
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Transport Coefficients in Thermalized QGP

• Theoretical Gluon dominated plasma

• Experimental Bjorken expansion

• Energy density

• Transport coefficients (not a good measure for
  expanding medium)

• Define the average for Bjorken

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• Strong coupling used as a parameter
• Find T 370 MeV (OK)

S.Turbide et al., Phs.Rev.C. (2005)

• Find (NOT OK)

G.Paic et al., Euro Phys.J C (2005) K.Eskola et
al., Phys.Rev.D (2005)

• Find dNg/dy 1200 (OK)

I.V., M.Gyulassy, Phys.Rev.Lett. (2002) I.V.
Phys.Lett.B in press
B.Cole, QM 2005 proceedings

• These are not equivalent descriptions the
  medium properties differ by more than
• an order of magnitude (sometimes close to two)

• How do you build from T 400 MeV

LHC from T 1 GeV
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The Source of the Problem
C.A.Salgado, U.Wiedeman, Phys.Rev.D (2003)
A useful table
Problem
Realistic
Typical gluon energy
GLV

• Note that the region of PT at RHIC is
• 10-20 GeV and at the LHC 100-200 GeV

Negative gluon number and jet enhancement from
energy loss
Problem
Problem
Negative probability density

• Symptomatic of problems in the underlying model
  of energy loss

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Analytic Limits of Delta E

• Controlled approach to coherence GLV

• Average implementations in the large
• number of scatterings limit

BDMPS, AMY
Includes the fluctuations of the gluon momentum
and energy

• Calculate differential spectra in

• Calculate the energy loss

Different dynamics REQUIRES different solutions
M.Gyulassy, I.V., X.N.Wang , Phys.Rev.Lett.86
(2001)
- transport coefficient - effective gluon
rapidity density
Static
BJ expansion BJ2D
26
Energy Loss and High Twist Shadowing
Double inclusive yields (away-side)
Single inclusive particles
I.V., T.Goldman, M.B.Johnson, J.W.Qiu,
hep-ph/0605200

• Main difference is much more pT independent
  suppression as compared to high twist
• shadowing

• Very similar e-loss effects for light hadron
  and heavy quark spectra
• Single and double inclusive cross sections are
  similarly suppressed

Same
27
Future Directions of Jet Interaction Studies

• Self consistency of the description of
  interactions in cold nuclear matter

Cronin effect
What is the energy loss for such momentum
transfer from the medium?

• Regimes of initial state energy loss

Is there a full Reaction Operator (GLV-like)
expression via a formal solution to recurrence
relations?
I.V., in preparation