1. Kinematic Map in x,Q for CTEQ4

2. Global pdf analyses
Lepton-lepton, lepton-hadron and hadron-hadron collisions probe complementary aspects of pQCD
Lepton-lepton provides as(Q2) and fragmentation functions
Lepton-hadron (DIS; F2, F3) along with hadron-hadron (DY) provide info on quark distributions
At leading order, g(x,Q) enters directly in hadron-hadron production of photons and jets
Modern global analyses are carried out to NLO which allows as(Q2), q(x,Q) and g(x,Q) to all mix and contribute for all processes
Nevertheless, the broad picture still holds to some degree in global pdf analyses

3. as in global fits and the gluon
Gluon distribution is always accompanied by a factor of as, in both cross sections and evolution equations
Determination of as and g(x,Q) is a strongly coupled problem
as can be determined separately from e+e- or as and g(x,Q) can be determined jointly in global pdf analysis
Coupling may not lead to a unique solution to either (see discussion in CTEQ4 paper)
World average for as(MZ) is 0.119; DIS expts prefer 0.116
Solution both CTEQ and MRS adopt is to use world average for as

4. LHC Parton Kinematics

5. Parameterizations and Schemes
Global pdf analysis carried out at NLO needs to be performed in specific renormalization and factorization scheme
Msbar
DIS
leading order
Preferable for use with leading order matrix element calculations like Herwig (but differences from NLO pdf’s are of NLO)
several schemes that differ on treatment of heavy quark masses (fixed flavor, zero-mass-charm, massive charm)
All global analyses use a generic form for the paramterization of both the quark and gluon distributions at some reference value Qo(few GeV)
F(x,Qo)=AoxA1(1-x)A2 P(x;A3,…)
A1 associated with small-x Regge behavior
In some fits, A1gluon tied to A1seaquark (but not in recent fits like CTEQ4/5, MRST)
A2 associated with large x quark counting rules
PMRS(x;A3,A4) = 1 + A3 sqrt(x) + A4x
PCTEQ3 = 1 + A3x
PCTEQ2,4,5 = 1 + A3xA4->flexibility in CTEQ4HJ

6. Uncertainties on pdf’s
Comparing 2 pdf’s to determine uncertainties is not reliable
Most groups use similar assumptions/data
Ideal technique would be to perform full error analysis and provide error correlation matrix for pdf’s, but...
only subset of experiments provide correlation information
no established way of quantifying theoretical uncertainties

7. F2 vs Q2: global fit
NMC BCDMS SLAC H1

8. Sources of information on the gluon distribution

9. Gluon Distribution

10. Gluon Distribution

11. Run 1b inclusive jet cross section
Comparisons to CTEQ4M, CTEQ4HJ, MRST pdf’s

12. Run 1b inclusive jet cross section
Comparisons to MRST series

13. Uncertainties in the W cross section

14. Cross Section Scaling to LHC

15. Conclusions Most of this information is in a note:
lhc_pdfnote.ps
Great deal of information that can still be useful for pdf fits (see figs)
Still important questions to be answered:
kT smearing/resummation->gluon dist at high x
d/u ratio at high x
Work will continue on trying to quantify our knowledge of parton distributions at HERA, the LHC and Tevatron and the effect on physics cross sections
Standard Model workshop at CERN
Workshop on Physics at TeV Colliders
Les Houches France June 8-18
QCDWB workshop for Run 2 at the Tevatron

16. Photon cross sections at the LHC

17. Uncertainties in pQCD predictions

18. Precision of evolution
CTEQ evolution program has recently been improved (main factor is making a subtraction to improve the accuracy of an integral near x=1)
Results are well within 1% when compared to DESY ‘standard’ table using both ‘x-space’ and ‘n-space’ techniques
Improvement leads to very small differences
c2 improves by 1-2 out of 1300
All theory vs expt plots look the same
New pdf’s look like old
PDF's evolved from a set of standard input at Q^2=4 GeV^2:
Compare output at Q^2=100 GeV^2:
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