Kinematic Map in x,Q for CTEQ4

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

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

LHC Parton Kinematics

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

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

F2 vs Q2: global fit NMC BCDMS SLAC H1

Sources of information on the gluon distribution

Gluon Distribution

Gluon Distribution

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

Run 1b inclusive jet cross section Comparisons to MRST series

Uncertainties in the W cross section

Cross Section Scaling to LHC

Conclusions Most of this information is in a note: http://www.pa.msu.edu/~huston/lhc/ 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 http://lappc-th8.in2p3.fr/houches99/intro.html QCDWB workshop for Run 2 at the Tevatron

Photon cross sections at the LHC

Uncertainties in pQCD predictions

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: ----------------------------------------------------------- flv x x*f(x) % diff (x-sp) % diff (n-sp) ------------------------------------------------------------ 0 1.00E-05 9.6665E+01 6.9671E-04 -1.3539E-02 0 1.00E-04 4.7091E+01 2.3216E-03 -1.3763E-02 0 1.00E-03 2.0801E+01 3.4665E-03 -1.1222E-02 0 1.00E-02 7.5998E+00 1.1328E-03 -7.0850E-03 0 1.00E-01 1.4260E+00 1.5117E-03 9.1547E-03 0 3.00E-01 1.9173E-01 -1.7180E-04 2.2003E-02 0 7.00E-01 1.1276E-03 1.0452E-03 3.9966E-02 --------------------------------------- 1 1.00E-05 9.2793E-03 2.3031E-04 -1.3757E-02 1 1.00E-04 2.8777E-02 4.8777E-04 -1.2111E-02 1 1.00E-03 8.7208E-02 5.2582E-04 -9.4132E-03 1 1.00E-02 2.4598E-01 1.8347E-04 -4.8735E-03 1 1.00E-01 4.7450E-01 1.1173E-04 3.9625E-03 1 3.00E-01 3.1152E-01 -3.4775E-04 1.1143E-02 1 7.00E-01 2.5048E-02 -9.1626E-04 2.4232E-02 2 1.00E-05 5.2115E-03 2.1625E-04 -1.3657E-02 2 1.00E-04 1.6134E-02 4.9783E-04 -1.1874E-02 2 1.00E-03 4.8678E-02 5.1533E-04 -9.0122E-03 2 1.00E-02 1.3494E-01 1.7696E-04 -4.1771E-03 2 1.00E-01 2.3215E-01 1.1466E-04 5.2241E-03 2 3.00E-01 1.1662E-01 -3.8570E-04 1.2727E-02 2 7.00E-01 3.9486E-03 -7.1739E-04 2.6768E-02 3 1.00E-05 2.6670E+01 1.3487E-03 -7.5694E-02 3 1.00E-04 1.3862E+01 2.7529E-03 -5.7936E-02 3 1.00E-03 6.7508E+00 3.5341E-03 -3.9274E-02 3 1.00E-02 2.8562E+00 1.0767E-03 -2.1667E-02 3 1.00E-01 5.7924E-01 1.1110E-03 1.8720E-03 3 3.00E-01 5.7780E-02 -1.5780E-04 1.6789E-02 3 7.00E-01 8.0219E-05 3.7475E-02 9.3112E-02 4 1.00E-05 2.5433E+00 1.7350E-03 -9.7596E-02 4 1.00E-04 1.2347E+00 3.1819E-03 -8.0931E-02 4 1.00E-03 5.3315E-01 4.0872E-03 -6.3619E-02 4 1.00E-02 1.7881E-01 1.3315E-03 -4.7211E-02 4 1.00E-01 2.3248E-02 9.2037E-04 -1.8624E-02 4 3.00E-01 1.7634E-03 -1.4854E-03 1.2059E-02 4 7.00E-01 2.0055E-06 1.7935E-01 3.5141E-01