Physics in Collision J. Huston June 1999 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 lhc_pdfnote.ps

Physics in Collision J. Huston June 1999 Determination of parton 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  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)

Physics in Collision J. Huston June 1999 “Evolution” (in time) of pdf’s u valence quark distribution u sea quark distribution; influence of HERA data clearly seen HERA data included

Physics in Collision J. Huston June 1999 Evolution (in Q 2 ) is the great equalizer

Physics in Collision J. Huston June 1999 Gluon Distribution-log x

Physics in Collision J. Huston June 1999 Gluon Distribution-linear x

Physics in Collision J. Huston June 1999 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

Physics in Collision J. Huston June 1999 Comparison of LO and NLO pdf’s

Physics in Collision J. Huston June 1999 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 Q 2 light Higgs region

Physics in Collision J. Huston June 1999 Comparison of LO pdf’s

Physics in Collision J. Huston June 1999 Comparison of gluons-linear

Physics in Collision J. Huston June 1999 Impact of new data 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 F 2 Lepton-pair production (p/d)asymmetry: E866 has measured ratio of lepton-pair production in pp and pd collisions over the x range of ( ) Lepton charge asymmetry in W production: CDF has improved accuracy and extended the y range Inclusive large p T 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

Physics in Collision J. Huston June 1999 The latest in pdf’s 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  s (M Z ) and k T smearing values MRST2: smaller k T corrections MRST3: larger k T smearing corrections MRST4: as in MRST1 but with a lower value of  s (M Z ) MRST5: as in MRST1 but with a higher value of  s (M Z ) 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)

Physics in Collision J. Huston June 1999 Evolution and the uncertainty in  s pdf’s determined at a given x and Q 2 “feed down” to lower x values at higher Q 2 accuracy of extrapolation depends both on accuracy of original measurement and uncertainty on  large x, DGLAP equation for F 2 can be approximated as ∂F 2 /∂logQ 2 ~  s (Q 2 )P qq XF 2 Effect on evolution of error on  s for F 2 shown on right  Extrapolation uncertainty of ±5% in F 2 at high Q 2 from uncertainty in  s

Physics in Collision J. Huston June 1999 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?

Physics in Collision J. Huston June 1999 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=m c to Q>>m c. 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  2 by 600

Physics in Collision J. Huston June 1999 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.

Physics in Collision J. Huston June 1999 Uncertainties on pdf’s  of quark distributions (q + qbar) is well-determined over wide range of x and Q 2  Quark distributions primarily determined from DIS and DY data sets which have large statistics and systematic errors in few percent range (±3% for <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 H 2 and D 2 targets  Note dbar≠ubar strange quark sea determined from dimuon production in DIS (CCFR) d/u at large x comes from FT DY production on H 2 and D 2 and lepton asymmetry in W production Bodek and Yang have argued that D 2 data need to be corrected for nuclear binding effects which would lead to larger d/u ratio at large x

Physics in Collision J. Huston June 1999 Nuclear corrections to D 2 and the d/u ratio Bodek and Yang: if nuclear corrections are applied to D 2, then d/u->0.2 (rather than 0) as x->1. Result is d quark distribution increases. Impact on high x CC at HERA Impact on jet production at Tevatron

Physics in Collision J. Huston June 1999 NMC and W asymmetry NMC data and CDF W asymmetry can be well-fit without using nuclear corrections for D 2 data No model of nuclear corrections is used in the CTEQ5 fits (i.e. D 2 cross section is treated as incoherent sum of p and n ones.

Physics in Collision J. Huston June 1999 d/u uncertainty M. Bottje study; hep-ph/ With present data, can’t say one way or another. Higher statistics should provide definitive answer.

Physics in Collision J. Huston June 1999 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.

Physics in Collision J. Huston June 1999 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 Q o =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) to % to 0.013% 0.01 to 0.116% 0.1 to 0.210% 0.2 to 0.36% 0.3 to 0.55% 0.5 to 1.01% Momentum shifted to lower x as Q 2 is increased

Physics in Collision J. Huston June 1999 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  A o X A1 (1-x) A2 (1+A 3 x A4 )  Vary A 1,A 2,A 3,A 4 each time refitting other quark, gluon parameters Fairly tight constraints on the gluon distribution except at high x

Physics in Collision J. Huston June 1999 CTEQ gluon study More important to know uncertainties on gluon-quark and gluon-gluon luminosity functions at appropriate kinematic region (in  =x 1 x 2 =s_hat/s  Define:  dL/d  = ∫g(x,Q 2 )q(  /x,Q 2 )dx/x Define:  dL/d  = ∫g(x,Q 2 )g(  /x,Q 2 )dx/x Uncertainties √  range gluon-gluon gluon-quark <0.1 +/-10% +/-10% /-20% +/-10% /-30% +/-15% /-60% +/-20%

Physics in Collision J. Huston June 1999 Giele-Keller-Kosower Study 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,  o |data) that the parton distribution f along with  o (=  s (m Z 2 ) 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 H 2 and CDF W asymmetry data used. ->a lot of information ‘thrown away’ (my phrasing) “…promises an end to the tyranny of the Global Fitters”

Physics in Collision J. Huston June 1999  Z vs  W H1, BCDMS H 2 aloneAdd CDF W asymmetry also CDF error ellipse

Physics in Collision J. Huston June 1999 Direct Photons and k T NLO QCD inadequate to explain size of observed k T in DY, W/Z, and diphoton distributions; full resummation calculations needed May be similar effect in direct  ; no rigorous resummation calculation available for direct  Soft gluon radiation causes deviations from NLO QCD at low E T at Tevatron 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 E T

Physics in Collision J. Huston June 1999 New Photon Result from CDF (1b)

Physics in Collision J. Huston June 1999 Diphoton Measurements at CDF 2 aspects: QCD measurements of  exotic searches with diphotons, e.g. Higgs->  : looser cuts to maximize efficiency Require: E T  1,  2 > 12 GeV/c Isolation energy in cone of 0.4 < 1 GeV/c saturated by MB energy for  N.B. backgrounds come from jets with z  o (=E  o /E jet ) > E  o /(E  o +1) z min ~0.95 for E T  =20 GeV/c fragmentation functions not well determined here, especially not with gluons and especially not in Monte Carlos Note that distributions that are  functions at LO are not well-described at NLO ->need resummed predictions

Physics in Collision J. Huston June 1999 Direct Photons and k T Effects of k T 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 k T )

Physics in Collision J. Huston June 1999 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 k T E706 with the experimentally measured values of k T

Physics in Collision J. Huston June 1999 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).

Physics in Collision J. Huston June 1999 Influence of jet cross section is proportional to  s 2 g(x,Q)g(x’,Q) and  s 2 g(x,Q)q(x’,Q) flexibility in gluon allows for increase in theoretical cross section at high E T 700 GeV/c 1.4 TeV/c 2.1 TeV/c 2.8 assuming x T universality

Physics in Collision J. Huston June 1999 Differential Dijet Production Differential dijet production directly probes larger x and Q 2 range than inclusive cross section

Physics in Collision J. Huston June 1999 Differential Dijet Production

Physics in Collision J. Huston June 1999 Dijet Mass Cross Section

Physics in Collision J. Huston June 1999 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.

Physics in Collision J. Huston June 1999 Jet Production at the LHC Jet production at the LHC has a similar sensitivity to pdf’s as at the Tevatron

Physics in Collision J. Huston June 1999 Diphoton Production at the LHC  cross section at 14 TeV gg

Physics in Collision J. Huston June 1999 W/Z + top cross sections at the LHC

Physics in Collision J. Huston June 1999 W/Z production at the LHC W + /W - /Z rapidity distributions provide information on quark and antiquark distributions

Physics in Collision J. Huston June 1999 CTEQ5M/5HJ and Tevatron Jets

Physics in Collision J. Huston June 1999 CTEQ5/MRST comparison

Physics in Collision J. Huston June 1999  s from inclusive jet production large correlation between  s and gluon distribution makes indepen- dent measurement of  s difficult