The CTEQ6 parton distribution functions and jet production at the Tevatron. Dan Stump Michigan State University

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1 The CTEQ6 parton distribution functions and jet production at the Tevatron Dan Stump Michigan State University. Preliminary results; intended (when finished) for a paper on jet production by a group of CTEQ co-authors (Huston, Kuhlmann, Lai, Owens, Pumplin, Stump, Tung). A

2 The CTEQ6 parton distribution functions fit, simultaneously, DIS DY the inclusive jet cross section 2 d σ dy dp T Tevatron process data set χ 2 e/n e DIS µp BCDMS p 378/339 DIS µd BCDMS d 28/25 DIS ep Ha 99/4 DIS ep Hb 29/26 DIS ep ZEUS 263/229 DIS µp NMC F2p 35/2 DIS µd NMC F2d/p 2/23 p p jet DØ jet 69/9 p p jet CDF jet 49/33 Ref: Pumplin, et al, JHEP7 (22) process data set χ 2 e/n e DIS ν Fe CCFR 5/56 DY pp E65 95/9 DY pd/pp E866 6/5 p p W CDF W / A2

3 Comparison of CTEQ5 and CTEQ6 The quarks have not changed much. The gluon distribution is larger at large x. A3

4 The gluon distribution function on a log scale A4

5 CDF and DØ measurements of jet production. D Jet cross section dσ dp T nb GeV p T GeV A5

6 A closer look at the DØ data the fractional difference between data and theory data theory theory versus p T GeV Η Η Η Η Η A6

7 A closer look at the CDF measurements data theory theory CDF inclusive jet Comparing data and theory for CTEQ6 partons pt GeV shifted data theory theory CDF inclusive jet Comparing data shifted by the optimal systematic errors pt GeV (statistical error bars) A7

8 The gluon uncertainty band The shaded region is the envelope of possible variations of G(x,Q). Curves: CTEQ6, CTEQ5, MRST2 A8

9 PDF uncertainty Our methods χ 2 minimization w/ fitting of systematic errors Diagonalization of the Hessian The tolerance Χ 2 global 2 χ χ 2 +T with T ~ 2 Χ 2 min Χ 2 min Χ2 tolerance Eigenvector Basis Sets Lagrange multiplier method due to propagation of experimental errors B X allowed range X

10 Comparison of CTEQ6 and MRST2 x 5 3 G x.4 xg x.3 MRST2 CTEQ6M. CTEQ6M MRST x x x 5 3 U x MRST2 CTEQ6M These plots show G(x,Q) for Q = GeV x 3 B2

11 Comparison of CTEQ6 and MRST2 x 5 3 G x.4 xg x.3 MRST2 CTEQ6. CTEQ6 MRST x x x 5 3 U x.4 MRST2.3.2 CTEQ6 Q = GeV x 3 B3

12 Comparison of CTEQ6 and Fermi22 x 5 3 G x.4 xg x.3 Fermi22 CTEQ6. CTEQ6 Fermi x x x 5 3 U x.4 Fermi CTEQ6 Q = GeV x 3 B4

13 Comparison of CTEQ6 and M. Botje PDF s x 5 3 G x.4 xg x.3 Botje CTEQ6. CTEQ6 Botje x x x 5 3 U x.4 Botje.3 CTEQ6.2 Q = GeV x 3 B5

14 The hard gluon distribution of CTEQ6 comes from fitting the Tevatron jet cross section. Why? What is the uncertainty? Predictions for Run 2. B6

15 What domain of momentum fraction is relevant to jet production for given y J and p T? x x 2 = = p T e s p T e s y J y J + e y 2 + e y 2.8 y J = y J = x2 x x Solid : p T = 42 GeV Dashed : p T = 2 GeV x Solid : p T = 25 GeV Dashed : p T = GeV C

16 PDF uncertainty of the jet cross section CDF d 2 Σ dydp T dy nb GeV... 6 CDF jet cross section p T GeV The CDF jet cross section for the 4 Eigenvector Basis Sets The 4 sets need some improvement. Simplest use 4 independent alternatives to the standard CTEQ6. D

17 The CDF jet cross section fractional differences compared to the standard CTEQ6 CDF data theory theory pt GeV D2

18 CDF data theory theory Eigenvector 5 The PDF sets cteq6m_29 and cteq6m_3 are the most extreme variations of the gluon pt GeV.8 fractional difference cteq6 special sets 29 and x 3 D3

19 All eigenvectors (ordinate range.4 to.4) D4

20 The total uncertainty band from the Master Formula (Preliminary!) CDF d 2 Σ dydp T dy nb GeV.. CDF jet cross section CDF data theory theory p T GeV pt GeV D5

21 The DØ jet cross section for the 4 Eigenvector Basis Sets D d 2 Σ dydpt dy nb GeV pt GeV D6

22 The DØ jet cross section for the 4 Eigenvector Basis Sets D d 2 Σ dydpt dy nb GeV pt GeV D7

23 The DØ jet cross section fractional differences compared to the standard CTEQ versus p T in GeV for 5 η bins D8

24 Is there room for new physics in the jet data? E

25 CDF jet data versus theory for Steve Kuhlmann s contact interaction, with the sk2 PDF s CDF inclusive jet cross section theory QCD contact interaction fit sk data theory theory CDF inclusive jet data theory QCD contact interaction fit sk pt GeV pt GeV shifted data theory theory CDF inclusive jet data theory QCD contact interaction fit sk pt GeV E2

26 Points: predicted cross section with SK s contact interaction and sk2 PDF s, compared to pure QCD with standard cteq6 PDF s. Curves: the uncertainty band for pure QCD and cteq6..8 fractional diff contact interaction 6 sk2 fit pt GeV E3

27 DØ jet data versus theory for Steve Kuhlmann s contact interaction with the sk2 PDF s Contact interaction 6 fit sk dσ dpt nb GeV pt GeV E4

28 Predictions for Run 2 DØ η bins D d 2 Σ dp T dy dy nb GeV Run 2 prediction D Η bins p T GeV F

29 D d 2 Σ dp T dy dy nb GeV p T GeV Run 2 prediction 4 E.V. sets D Η bins Predictions for Run 2 DØη bins Η Η Η Η Η F2

30 Predictions for Run 2 bounds from the Master Formula (Preliminary!) Run2 for D Η bins Bounds from Master Formula. dσ dp T nb GeV p T GeV F3

31 D d 2 Σ dp T dy dy nb GeV... 8 Run 2 prediction 4 E.V. sets CDF Η bins Predictions for Run 2 CDF η values p T GeV.9.6 Η Η Η Η F4