Parton distribution uncertainty

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Parton distribution uncertainty and W and Z
production at hadron colliders
Dan Stump Department of Physics and
Astronomy Michigan State University
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PDF uncertainty and inclusive jet production
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PDF uncertainty and the cross section for
inclusive jet production at the Tevatron. Run
1 CTEQ6.1, central fit and 40 Eigenvector Basis
Sets
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Comparing the CDF data (Run 1) and the NLO
calculation with CTEQ6.1 Green 1 40
alternative sets Red full uncertainty range
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The master equation for the Hessian method
asymmetric errors, or one could use the
Sullivan-Nadolsky formula
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Inclusive jet cross section for Run 2, in 5
rapidity bins, predicted by CTEQ6.1.
Red central prediction Blue full uncertainty
range
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Inclusive jet cross section for the
LHC, predicted by CTEQ6.1.
central prediction 40 alternatives
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PDF uncertainty the method
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Uncertainties of Parton Distribution Functions a
major challenge for global analysis
The total cross sections for W and Z production
were among the first examples to which we applied
the new methods of uncertainty analysis. sW and
sZ were good test cases.
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Estimate the uncertainty on the predicted cross
section for ppbar ? WX at the Tevatron collider.
global c2
local c2s
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Each experiment defines a prediction and a
range. This figure shows the Dc2 1 ranges.
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This figure shows broader ranges for each
experiment based on the 90 confidence level
(cumulative distribution function of the rescaled
c2).
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The final result is an uncertainty range for the
prediction of sW.
Survey of sw?Bln predictions (by R. Thorne, 2002)
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Each experiment defines a prediction and a
range. This figure shows the Dc2 1 ranges for
the value of aS.
Particle data group (shaded strip) is 0.117?0.002.
The fluctuations are larger than expected for
normal statistics. The vertical lines have
Dc2global100 as(MZ)0.1165?0.0065.
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How well can we determine the value of aS( MZ )
from Global Analysis?
For each value of aS, find the best global fit.
Then look at the c2 value for each experiment as
a function of aS.
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PDF uncertainty for W/Z production
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Inclusive Z production at the Tevatron, Run 2 (K
factor for NNLO/NLO 1.045 has been applied)
Red 1 40 alternatives Blue full uncertainty
range 0.258 ? 0.008 nb Green Latest CDF value
Purple Latest D0 value 0.2539?0.0033?0.0046?0.
0152 nb 0.2649?0.0039?0.0099?0.0172 nb
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Inclusive W production at the Tevatron, Run 2 (K
factor for NNLO/NLO 1.037 has been applied)
Red 1 40 e.v. basis sets Blue full
uncertainty range 2.63 ? 0.09 nb Orange MRST
prediction 2.69?0.11 nb Green Latest CDF value
2.780?0.014?0.060?0.167 nb Purple Latest D0
value 2.865?0.008?0.075?0.186 nb
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The error ellipse for W and Z production at the
Tevatron, Run 2
Red 1 40 e.v. basis sets Purple Full
uncertainty range (error ellipse) Blue
Uncorrelated ranges, roughly ?3 each
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Are the up and down displacements along the
eigenvector directions symmetric?
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Z production at the LHC
Red 1 40 e.v. basis sets Blue Full
uncertainty range 1.95 ? 0.07 nb
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W production at the LHC
Red 1 40 e.v. basis sets Blue Full
uncertainty range 19.5 ? 0.8 nb Orange MRST
prediction 20.0?0.8 nb
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Error ellipse for W and Z production at the LHC
Red 1 40 e.v. basis sets Blue uncorrelated
ranges Purple Full uncertainty range (error
ellipse)
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The PDF uncertainty in the ratio sZ/sW is very
small ? possible test for new physics.
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Why calculations dont agree
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W production at the Tevatron MRST calculations
from their paper on Theoretical Errors
CTEQ 2.63?0.09 nb
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W production at the LHC MRST calculations from
their paper on Theoretical Errors
CTEQ 19.5?0.8 nb
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• Other theoretical uncertainties
• Branching ratio
• Treatment of W width (off shell W)
• EW parameter values, e.g., CKM matrix
• Treatment of heavy quark mass effects
• may lead to differences of order 1

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A survey of results from different
programs (Pavel Nadolsky, C P Yuan)
?s 1.96 TeV
?s 14 TeV
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PT dependence of vector boson production
Collins, Soper and Sterman (CSS) formalism for pT
resummation, schematically,
BLNY parametrization
(Brock, Landry, Nadolsky, Yuan)
i.e., 4 N.P. parameters (g1,g2,g3,bmax)
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The BLNY fit to E288, E605, CDF Z, and D0 Z data
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Standard Dc2 1 parameter errors
but are such small uncertainties realistic?
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Reassess the parameter uncertainties, using the
methods that we have used for PDF uncertainties.
The most interesting parameter, and which should
have the largest uncertainty, is g2.

• Method
• Scan the BLNY fit versus g2 values.
• For a range of g2 values, construct the best fit
  to g1 and g3.
• Then look how c2 varies with g2.

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A c2 parabola for each experiment
implies an allowed range for the value of g2
for each experiment.
bmax 0.5 GeV-1
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A c2 parabola for each experiment
implies an allowed range for the value of g2
for each experiment.
bmax 1.12 GeV-1
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Comparison of CDF Z and D0 Z data (Run 1) to
resummation calculation with BLNY parametrization
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More work needs to be done to obtain a final
uncertainty range for g2.
Our larger goal is to include pT cross sections
in the global analysis i.e., simultaneously to
fit PDF parameters and resummation parameters,
for both W and Z production.