Probing small x gluon with low mass DrellYan dilepton

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Factorization and Resummation in QCD
Perturbation Theory Lecture 5
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 Five

• QCD at a new level of accuracy

• Processes with double logarithms

• CSS b-space resummation formalism

• Small-x effect and predictive power

• W/Z, and Higgs production

• Upsilon production

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QCD at a new level of accuracy

• Fermilab Run II and the LHC
• new testing ground for precision test of
  QCD

• Heavy boson transverse momentum distribution are
• important for light Higgs search and new
  physics

• Resummation of double logarithms is a very
  important
• part of QCD test and background control for
  potential
• signals of new physics

• Collins, Soper and Stermans b-space resummation
• has been very successful, but, it has some
  drawbacks

• difficulties in extracting predictions from
  parameter fitting
• due to the needed nonperturbative input

• Lack of consistency between data at collider
  energies and
• fixed target energies e.g., an overall
  normalization, as small
• as 0.8, is needed to fit the E288 data

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Recent developments

• QCD predictive power of CSS formalism has a
  strong
• dependence on collision energy small-x
  effect

• At collider energies, heavy boson
  QT-distributions
• are not sensitive to the nonperturbative input

• Calculated W and Z QT-distributions are
  consistent
• with all existing data without any free
  fitting parameter

• Predict that Higgs QT-distribution has a very
  small
• dependence on nonperturbative input

• For the first time, we can quantitatively
  understand
• Tevatron data on Upsilon production

• Many new applications in B-physics

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QT-distribution of W production
Showing the different theoretical regions in
momentum space
Drell-Yan type subprocess
Photon can replaced by W, Z, Higgs, etc.
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QT-distribution in fixed order pQCD
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Resummation of double logarithms
LO Differential QT-distribution as QT?0
Integrated QT-distribution
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Resummed QT-distribution

• Differentiate the integrated QT-distribution

• compare to the explicit LO calculation

• We just resummed (exponentiated) an infinite
  series of
• soft gluon emissions double logarithms

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Still a wrong QT-distribution

• Experimental fact

Resummation of uncorrelated soft gluon emission
leads to too strong suppression at QT0

• Why?
• Particle can receive many finite kT kicks
• via soft gluon radiation yet still have QT0

• Solution
• impose 4-momentum conservation
• at each step of soft gluon resummation

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CSS b-space resummation formalism

• Leading order KT-factorized cross section

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Role of each term in CSS formalism
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The b-space resummation
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CSS model for the large b-region

• Introduce a non-perturbative Sudakov form factor
• SNP for the large b-region

bmax 0.5

• Potential problems

• Uncertainties in choosing the non-perturbative
  function SNP

• Introduce non-perturbative dependence to small-b
  region

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What is the predictive power of the resummation
formalism?
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Two typical sets of fitting parameters
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Predictive power of the formalism
? The QT-distribution is completely
determined by the b-space function
bWAB(b,Q)
bsp
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Location of the saddle point
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vS-dependence of QCD predictions
Since gluon has a larger anomalous dimension than
quark
Gluon initiated subprocesses should lead to
smaller bsp
Better prediction for Higgs production!
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Understand the large b-region
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A new approach to the large b-region

• solution of the CSS evolution equation in
  small-b region
• preserve the perturbative small b-region
  unchanged
• solution of the modified CSS evolution equation,
  including
• leading power corrections, in large b-region

Leading twist
Intrinsic power corrections
Dynamical power corrections

• g1 and a are fixed by the continuity of W(b,Q)
  at bmax
• vS is built in the value of g1 and a

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Power correction is very small, excellent
prediction!
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No free fitting parameter!
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Hadronic Upsilon production

• Process

• Similarities and differences from W/Z, or Higgs

• Events are dominated by low QT region
• Gluon shower should play an important role in
• determine the QT distribution

• M? ltlt MW , or Q is now small
• Heavy b-quark pair is not necessary color
  singlet
• Additional nonperturbative physics from b-quark
  to
• Upsilon

• Key approximation

Neglect gluon radiation from heavy quarks
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The b-space distribution
Gluon-gluon dominate the production Dominated by
perturbative contribution even M?10 GeV
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Upsilon production at Tevatron
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Higgs production at the LHC
Uncertainties from the power corrections are less
than 1
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Resummation in perturbative QCD

• Re-organize the perturbation series

• Leading twist