Review of Parton Distributions and Implications for the Tevatron and LHC (Partons in Collision at Physics in Collision)

1. Review of Parton Distributions and Implications for the Tevatron and LHC(Partons in Collision at Physics in Collision) J. Huston Michigan State University thanks to James Stirling, Lenny Apanasevich and Michael Botje, Heidi Schellman and Ursula Bassler for figures See also http://www.pa.msu.edu/~huston/lhc/ lhc_pdfnote.ps

2. Determination ofparton distribution functions (pdf’s) • Calculation of production cross sections at the Tevatron and LHC relies upon knowledge of pdf’s in relevant kinematic range • pdf’s are determined by global analyses of data from DIS, DY and jet and direct g production • Two major groups that provide semi-regular updates to parton distributions when new data/theory becomes available • CTEQ->CTEQ4(5) • MRS->MRST98 • GRV(not really global analysis; concentrate on x) • Giele-Keller-Kosower (no pdf’s yet; error analysis)

3. “Evolution” (in time) of pdf’s • u sea quark distribution; influence of • HERA data clearly seen • u valence quark distribution HERA data included

4. Evolution (in Q2) is the great equalizer

5. Gluon Distribution-log x

6. Gluon Distribution-linear x

7. Comparison of LO and NLO pdf’s • LO fits conducted separate from NLO fits; many processes have large K-factors (NLO/LO); resulting LO pdf’s reflect this

8. Comparison of LO and NLO pdf’s

9. Comparison of LO pdf’s • Many LHC comparisons have used CTEQ2L (default in PYTHIA), a pdf that is “several generations old” …again differences are smaller at high Q2 light Higgs region

10. Comparison of LO pdf’s

11. Comparison of gluons-linear

12. In the last few years, improved and new experimental data have become available in many processes; these data have been incorporated into the new CTEQ and MRST analyses DIS: NMC and CCFR have published final analyses; H1 and ZEUS have published more extensive and precise data on F2 Lepton-pair production (p/d)asymmetry: E866 has measured ratio of lepton-pair production in pp and pd collisions over the x range of (0.03-0.35) Lepton charge asymmetry in W production: CDF has improved accuracy and extended the y range Inclusive large pT jet production: CDF and D0 have recently finished final analyses of Run 1b inclusive jet cross section, including full information on correlated systematic errors; provides crucial constraints on gluon distribution in CTEQ5 analysis Impact of new data

13. CTEQ5M: main pdf set; performed in MSbar scheme CTEQ5D: fit performed in DIS scheme CTEQ5L: fit performed using leading order matrix elements CTEQ5HJ: in MSbar scheme but with increased emphasis on high ET jet points CTEQ5HQ: uses systematic generalization of MSbar scheme to include heavy-quark partons CTEQ5F3: uses a fixed 3-flavor scheme where charm and bottom quarks are treated as heavy particles and not partons MRST1: main pdf set performed in MSbar scheme with nominal as(MZ) and kT smearing values MRST2: smaller kT corrections MRST3: larger kT smearing corrections MRST4: as in MRST1 but with a lower value of as(MZ) MRST5: as in MRST1 but with a higher value of as(MZ) MRSTDIS(1-5): DIS versions of MRST(1-5) MRSTLO(1-5): LO versions of MRST(1-5) MRSTHT(1-5): HT versions of MRST(1-5) The latest in pdf’s

14. Evolution and the uncertainty in as • pdf’s determined at a given x and Q2 “feed down” to lower x values at higher Q2 • accuracy of extrapolation depends both on accuracy of original measurement and uncertainty on as • @ large x, DGLAP equation for F2 can be approximated as∂F2/∂logQ2 ~as(Q2)PqqXF2 • Effect on evolution of error on as for F2 shown on right • Extrapolation uncertainty of ±5% in F2 at high Q2 from uncertainty in as

15. Higher orders in evolution • There is a relatively large effect going from LO to NLO. • Should be smaller going from NLO to NNLO. • Necessary for LHC?

16. Heavy quark pdf’s • In processes where heavy quarks play important role (charm production at HERA), standard schemes using zero-mass heavy quarks partons may be inadequate. Also of interest is b quark pdf’s for Higgs production at LHC. • Thus, CTEQ has produced CTEQ5HQ set using ACOT scheme which gives a more accurate formulation of charm quark physics, valid from Q=mc to Q>>mc. • PDF’s defined in (mass-independent) MS scheme, matched with hard-scattering cross sections using on-mass shell heavy quarks. • In practice, only makes a difference for DIS structure functions. • CTEQ5HQ gives slightly better overall fit than CTEQ5M • Mixing CTEQ5HQ pdf’s and MS cross sections increases c2 by 600

17. CTEQ and MRST heavy flavor pdf’s • MRST uses similar (Thorne-Roberts) scheme for treating massive quarks; again important primarily for DIS • Differences can be explained by: • slightly different choices of charm mass • differences in procedure for treating • charm quark masses in Wilson • coefficients • Phenomenology is the same if appropriate ME’s • are used.

18. Uncertainties on pdf’s • S of quark distributions (q + qbar) is well-determined over wide range of x and Q2 • Quark distributions primarily determined from DIS and DY data sets which have large statistics and systematic errors in few percent range (±3% for 10-4<x<0.75) • Individual quark flavors, though may have uncertainties larger than that on the sum; important, for example, for W asymmetry • information on dbar and ubar comes at small x from HERA and at medium x from fixed target DY production on H2 and D2 targets • Note dbar≠ubar • strange quark sea determined from dimuon production in n DIS (CCFR) • d/u at large x comes from FT DY production on H2 and D2 and lepton asymmetry in W production Bodek and Yang have argued that D2 data need to be corrected for nuclear binding effects which would lead to larger d/u ratio at large x

19. Nuclear corrections to D2 and the d/u ratio Impact on high x CC at HERA Bodek and Yang: if nuclear corrections are applied to D2, then d/u->0.2 (rather than 0) as x->1. Result is d quark distribution increases. Impact on jet production at Tevatron

20. NMC and W asymmetry • NMC data and CDF W asymmetry can be well-fit without using nuclear corrections for D2 data No model of nuclear corrections is used in the CTEQ5 fits (i.e. D2 cross section is treated as incoherent sum of p and n ones.

21. d/u uncertainty M. Bottje study; hep-ph/9905518 With present data, can’t say one way or another. Higher statistics should provide definitive answer.

22. d/u • Previously, driving force for d/u was one data point (from NA51) for both MRS and CTEQ. E866 covers a much wider kinematic range.

23. Gluon Uncertainty • Gluon distribution is least well known (but one of most important for physics processes at the LHC) • Momentum fraction carried by quarks is very well known from DIS data; at Qo=1.6 GeV • momentum fraction carried by quarks is 58%±2% • thus momentum fraction carried by gluons is 42%±2% ->if gluon increases in one range, it must decrease in another X bin Momentum fraction (Q=5 Gev) 10-4 to 10-3 0.6% 10-3 to 0.01 3% 0.01 to 0.1 16% 0.1 to 0.2 10% 0.2 to 0.3 6% 0.3 to 0.5 5% 0.5 to 1.0 1% Momentum shifted to lower x as Q2 is increased

24. CTEQ Study • CTEQ study; vary gluon parameters in a global analysis and then look for incompatibilities with data • Use only DIS and DY data sets where theoretical and experimental systematic errors are under good control • Use standard parameterization for gluon distribution • AoXA1(1-x)A2(1+A3xA4) • Vary A1,A2,A3,A4 each time refitting other quark, gluon parameters • Fairly tight constraints on the gluon distribution except at high x

25. CTEQ gluon study • Define: • tdL/dt = ∫g(x,Q2)g(t/x,Q2)dx/x • More important to know uncertainties on gluon-quark and gluon-gluon luminosity functions at appropriate kinematic region (in t=x1x2=s_hat/s • Define: tdL/dt = ∫g(x,Q2)q(t/x,Q2)dx/x Uncertainties √t range gluon-gluon gluon-quark <0.1 +/-10% +/-10% 0.1-0.2 +/-20% +/-10% 0.2-0.3 +/-30% +/-15% 0.3-0.4 +/-60% +/-20%

26. Goal is “honest error estimates”; as mentioned before, spread of predictions using different pdf sets is not a proper error estimate. Honest error estimate requires evaluation of errors on pdf’s due to measurement errors and method for propagating these errors to observables. Their solution: use functional integration. Construct a probability functional Prob(f,ao|data) that the parton distribution f along with ao(=as(mZ2) provide a description of the data. Data selection: because of worries about nuclear corrections do not use any data on nuclear targets Because of worries about scale dependence, don’t use prompt photon data. Use only data sets that have published correlated systematic errors In fits so far, only H1 ep (ZEUS rejected), BCDMS H2 and CDF W asymmetry data used. ->a lot of information ‘thrown away’ (my phrasing) “…promises an end to the tyranny of the Global Fitters” Giele-Keller-Kosower Study

27. sZ vs sW H1, BCDMS H2 alone Add CDF W asymmetry also CDF error ellipse

28. Direct Photons and kT • NLO QCD inadequate to explain size of observed kT in DY, W/Z, and diphoton distributions; full resummation calculations needed • May be similar effect in direct g; no rigorous resummation calculation available for direct g • Soft gluon radiation causes deviations from • NLO QCD at low ET at Tevatron • <kT> increases as log of s • 1 GeV/c for fixed target • 3-4 GeV/c for Tevatron collider • 6-7 GeV/c for LHC (low mass states) don’t expect photon-jet balancing at low ET

29. New Photon Result from CDF (1b)

30. Diphoton Measurements at CDF • 2 aspects: • QCD measurements of gg • exotic searches with diphotons, • e.g. Higgs->gg: looser cuts to maximize • efficiency • Require: • ET g1,g2 > 12 GeV/c • Isolation energy in cone of 0.4 < 1 GeV/c • saturated by MB energy for gg • N.B. backgrounds come from jets with • zpo (=Epo/Ejet) > Epo/(Epo+1) • zmin~0.95 for ETp=20 GeV/c • fragmentation functions not well • determined here, especially not • with gluons and especially not • in Monte Carlos • Note that distributions that are d functions • at LO are not well-described at NLO • ->need resummed predictions

31. Direct Photons and kT • Effects of kT more severe at fixed target energies • Theoretical uncertainties too large to use direct photons for determination of gluon distribution (->CTEQ conclusion (jets ‘determine the gluon’); MRST uses direct photons with kT)

32. CTEQ5 and direct photons • So, CTEQ5 has no direct photon data in the fit..but • ...both WA70 and E706 are well-fit with CTEQ5 pdf’s WA70 with no kT E706 with the experimentally measured values of kT

33. CTEQ5 and MRST gluons • Difference in approach to direct photon cross sections (and the gluon distribution) leads to the most striking differences between CTEQ5 and MRST pdf’s (most striking difference in any contemporary pair of CTEQ/MRS pdf sets).

34. Influence of Jets • @LO, jet cross section is proportional to as2g(x,Q)g(x’,Q) and as2g(x,Q)q(x’,Q) • flexibility in gluon allows for increase in • theoretical cross section at high ET 700 GeV/c 1.4 TeV/c 2.1 TeV/c 2.8 TeV/c @LHC assuming xT universality

35. Differential Dijet Production • Differential dijet production directly probes larger x and Q2 range than inclusive cross section

36. Differential Dijet Production

37. Dijet Mass Cross Section

38. Role of LHC in pdf determination • ATLAS/CMS measurements of DY (including W/Z), direct photon, jet, top production,etc will be useful in determining pdf’s relevant for LHC • can try to extract parton-parton luminosities directly from cross sections (Dittmar et al) • can input data into global fitting analyses • DY production will provide information on quark (and anti-quark) distributions while direct photon, jet and top production will provide, in addition, information on the gluon distribution For example, direct photon production.

39. Jet Production at the LHC • Jet production at the LHC has a similar sensitivity to pdf’s as at the Tevatron

40. Diphoton Production at the LHC gg cross section at 14 TeV gg

41. W/Z + top cross sectionsat the LHC

42. W/Z production at the LHC W+/W-/Z rapidity distributions provide information on quark and antiquark distributions

43. CTEQ5M/5HJ and Tevatron Jets

44. CTEQ5/MRST comparison

45. as from inclusive jet production large correlation between as and gluon distribution makes indepen- dent measurement of as difficult