Probing small x gluon with low mass DrellYan dilepton

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Factorization and Resummation in QCD
Perturbation Theory Lecture 6
Jianwei Qiu Iowa State University
The Eastern Formosa Summer School - III on
Particles and Fields July 5 - 12, 2004 National
Dong-Hwa University, Hua-Lien, Taiwan
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Outline of Lecture Six

• Excitements from RHIC

• Important role of coherent multiple scattering

• Small-x and power corrections

• Resummation of power corrections

• Another look of an old problem shadowing

• Suppression of away side jet

• Summary and outlooks

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Single inclusive hadron in AA collision

• Conventional perturbative QCD Factorization

• Soft interactions between the ions does not
  change
• the effective PDFs
• Nuclear A-dependence
• effective nuclear PDFs
• initial-state multiple scattering
• final-state jet quenching strong suppression
  in RAA

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Strong suppression of leading particles
Interpretation
Energy lose when the parton passes through the
medium
Parent partons should be produced locally at a
distance scale lt 0.02 fm for pT10GeV
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Quantitative agreement across experiments
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No suppression in dA collisions
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Excellent calibration in pp collision
NLO pQCD calculation works fine within
the uncertainties of fragmentation functions
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Suppression in away-side correlation
STAR data at QM2004
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Quantum coherence at low x

• 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)

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The low x physics (II)

• IF xltxc, a hard probe can interact coherently
• with more than one low x partons at a same
• impact parameters

• Each additional coherent scattering
• is suppressed by a factor

- Coefficient
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The low x physics (III)

• For a nucleus, if
  , the probe
• cannot tell which nucleon the parton is from

• Each additional coherent scattering
• is suppressed by a factor

- Coefficient is enhanced
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The low x physics (IV)

• Low x partons can also interact coherently
• among themselves if there are more than one
• at a given impact parameter

x

• Interaction among low x partons produces a
• collective feature of whole nucleus

• How many partons are there in a hadron?

• How different coherent interactions contribute
• to a physical cross section?

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Number of partons in a hadron

• Number of partons depends on the resolution
• of the probe

Momentum exchange of the interaction, x, Q2, etc.

• also depends on the definition of parton
• distributions

Parton distributions might not be positive
definite
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Parton Distribution Functions (PDFs)

• PDF, f(x,µ2), is a number density to find
• a parton of flavor f quark, antiquark,
  gluon
• with a momentum fraction x
• at a factorization scale µ2.

CTEQ6M, CTEQ6D, CTEQ6L, MRST, GRV,
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Parton Distribution Functions (II)

• PDFs depend on how they were extracted!

• the order of perturbative part used to compare
• with data LO PDFs, NLO PDFs,

• momentum scale of the probe Q2
• PDFs Q2 dependence evolution equations

• Beyond LO, PDFs do not have to be positive!

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Negative gluon distribution

• NLO global fitting
• based on leading
• twist DGLAP
• evolution leads to
• negative gluon
• distribution

• MRST PDFs
• have the same
• features

Does it mean that we have no gluon for x lt 10-3
at 1 GeV?
No!
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Coherent power corrections to DGLAP

• Negative gluon distribution is not consistent
  with cross
• sections where gluon enters at LO order

FL at low x and low Q2, Low mass Drell-Yan at
moderate QT, Low PT direct photon, etc.

• Parton recombination slows down the
  µ2-dependence
• of DGLAP evolution

LP
LL
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Recombination prevents negative gluon

• In order to fit new
• HERA data, like
• MRST PDFs, CTEQ6
• gluon has to be much
• smaller than CTEQ5,
• even negative at
• Q 1 GeV

Recombination
CTEQ5

• The power correction
• slows down the Q2-
• dependence, prevents
• PDFs to be negative

CTEQ6

• Low mass DY to give
• direct information on
• gluon

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Nucleon is almost transparent

• Number of gluons between x and x?x

Higher µ2 will not help much, ng grows
logarithmic in µ2 unless x is very small
Large nuclei may increase ng by as much as a
factor of 6

• Saturation

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Coherent dynamical power corrections
When the probe size is larger than a Lorentz
contracted large nucleus, the probe could
interact coherently with any number of partons of
the nucleus

• If the probe interacts with only one parton,

Nuclear dependence can only from the modified
evolution equation and the input distributions
needed to solve for the equation
Probe the shadowed nPDFs (possibly, saturated
nPDFs) ?Leading twist shadowing process
independent
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Coherent dynamical power corrections (II)

• If the probe interacts with many partons,

Each additional coherent scattering is
suppressed by a factor

• Resummation to connect
• partonic hard to high
• density soft physics

All power resummation
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Resummation in perturbative QCD

• Re-organize the perturbation series

• Leading twist

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Resummation in perturbative QCD (II)

• Power corrections

Lower x ? larger power corrections
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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
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Resummed A1/3-Enhanced Power Corrections

• Results

• One parameter scale of power
• corrections

U-quark, CTEQ5 LO
Upper limit of the saturation scale
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Scale for cold matter power corrections
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Power Corrections in Neutrino-Nucleus DIS

• Coherent power corrections are process dependent

• Power of factorization

Same nonperturbative ?2
Predict high twist shadowing In neutrino-nucleus
structure Functions
Qiu and Vitev, Phys.Lett.B 587 (2004)
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The Gross-Llewellyn Smith Sum Rules
Fully coherent final-state power corrections to
the sum rule almost cancel due to the unitarity
Qiu and Vitev, Phys.Lett.B 587 (2004)
Prediction is compatible with the trend in the
current data
Process-dependent power corrections are important!
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Power Corrections in pA Collisions

• Hadronic factorization fails for power
  corrections of
• the order of 1/Q4 and beyond

• Medium size enhanced dynamical power corrections
• in pA could be factorized

to make predictions for pA 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
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A-enhanced power corrections in pA

• A-enhanced power corrections, A1/3/Q2, are
  factorizable

• But, power corrections are process-dependent,
  and
• they are different from DIS

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Single hadron inclusive production

• Resum the coherent final state multiple
  scattering of
• the parton of momentum l with the remnants of
  the
• nucleus

• Other interactions are less
• coherent (elastic) and
• suppressed at forward
• rapidity by a large scale
• 1/u, or 1/s

Qiu and Vitev, hep-ph/0405068
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Dihadron Correlation Broadening and Attenuation
J.Adams et al., Phys.Rev.Lett. 91 (2003)
Midrapidity and moderate pT
Forward rapidity and small pT
J.W.Qiu, I.V., Phys.Lett.B 570 (2003)
hep-ph/0405068
Ivan Vitev, ISU
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Summary and outlooks

• 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

• Low x partons can not only interact among
  themselves,
• but also interact coherently with the probe

• Leading medium size enhanced power corrections
• are Infrared safe and can be systematically
  resummed
• into a translation operator acting on
  partons
• momentum fraction, which leads to a shift in
  partons
• momentum fraction without changing the
  leading
• twist factorized formula

• Maximum characteristic scale of the dynamical
  power
• corrections ?20.1 GeV2 (9/4 for gluon) ltlt
  GeV2

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Challenges and open questions

• b-quarks at Tevatron

We cannot really measure b-quark momentum
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b-mesons at Tevatron
Peterson fragmentation functions
Better fragmentation function Cacciari, Nason,
PRL 89 (2002)
Resummation to heavy quark fragmentation
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NRQCD model vs CDF data on polarization
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Direct photon production
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And many more questions

• Many questions are unanswered for data from RHIC
• often, we do not even know how to ask a right
  
• question Is there the state of Quark-Gluon
  plasma?

• Small-x parton saturation or color glass
  phenomena
• Could the phenomenon exist? Or have we seen
  it?

• Where can we find the phenomena of color
• superconductivity?
• We think that it could be there.
• Will we be able to see it?

• etc.

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