physics in collision j. huston june 1999 review of parton distributions and implications for the...

Physics in CollisionJ. 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 Universitythanks 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


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)

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“Evolution” (in time) of pdf’s

u valence quark distribution •u sea quark distribution; influence of HERA data clearly seen

HERAdataincluded


Evolution (in Q2) is the great equalizer


Gluon Distribution-log x


Gluon Distribution-linear x


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


Comparison of LO and NLO pdf’s


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 highQ2

light Higgs region


Comparison of LO pdf’s


Comparison of gluons-linear


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 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


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(MZ) and kT smearing values

MRST2: smaller kT corrections

MRST3: larger kT smearing corrections

MRST4: as in MRST1 but with a lower value of s(MZ)

MRST5: as in MRST1 but with a higher value of s(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)


Evolution and the uncertainty in s

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 s

@ large x, DGLAP equation for F2

can be approximated as ∂F2/∂logQ2 ~s(Q2)PqqXF2

Effect on evolution of error on s for F2 shown on right

Extrapolation uncertainty of ±5% in F2 at high Q2 from uncertainty in s


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?

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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 2 by 600

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CTEQ and MRST heavy flavor pdf’s

MRST uses similar (Thorne-Roberts) scheme for treating massive quarks; again important primarily for DIS

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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’sare used.


Uncertainties on pdf’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 DIS (CCFR)

d/u at large x comes from FT DY production on H2 and D2 and lepton asymmetry in W production

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Bodek and Yang have argued that D2 dataneed to be corrected for nuclear binding effects

which would lead to larger d/u ratio at large x


Nuclear corrections to D2 and the d/u ratio

Bodek and Yang: if nuclear corrections areapplied to D2, 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


NMC and W asymmetry

NMC data and CDF W asymmetry can be well-fit without using nuclear corrections for D2 data

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No model of nuclear corrections is used inthe CTEQ5 fits (i.e. D2 cross section istreated as incoherent sum of p and n ones.


d/u uncertainty

M. Bottje study; hep-ph/9905518

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With present data, can’t say one way oranother. Higher statistics should provide definitive answer.


d/u

Previously, driving force for d/u was one data point (from NA51) for both MRS and CTEQ.

E866 covers a much wider kinematicrange.

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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


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


CTEQ gluon study More important to know uncertainties

on gluon-quark and gluon-gluon luminosity functions at appropriate kinematic region (in =x1x2=s_hat/s

Define:

dL/d = ∫g(x,Q2)q(/x,Q2)dx/x

Define: dL/d = ∫g(x,Q2)g(/x,Q2)dx/x

Uncertainties√ 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%


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(mZ

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 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”


Z vs W

H1, BCDMS H2 alone Add CDF W asymmetry also

CDF error ellipse


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 ; no rigorous resummation calculation available for direct

•Soft gluon radiation causes deviations fromNLO 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 expectphoton-jet balancingat low ET


New Photon Result from CDF (1b)


Diphoton Measurements at CDF

2 aspects:•QCD measurements of •exotic searches with diphotons,e.g. Higgs->: looser cuts to maximizeefficiency

Require:•ET

1,2 > 12 GeV/c•Isolation energy in cone of 0.4 < 1 GeV/c

saturated by MB energy forN.B. backgrounds come from jets withzo (=Eo/Ejet) > Eo/(Eo+1)

•zmin~0.95 for ET=20 GeV/c

•fragmentation functions not welldetermined here, especially notwith gluons and especially notin Monte Carlos

Note that distributions that are functionsat LO are not well-described at NLO

->need resummed predictions


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)


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

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E706 with the experimentally measured values of kT


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).

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Influence of Jets @LO, jet cross section is proportional

to s2g(x,Q)g(x’,Q) and

s2g(x,Q)q(x’,Q)

• flexibility in gluon allows for increase in

theoretical cross section at high ET

700 GeV/c

1.4TeV/c

2.1 TeV/c

2.8TeV/c

@LHC assuming xT universality


Differential Dijet Production Differential dijet production

directly probes larger x and Q2 range than inclusive cross section


Differential Dijet Production


Dijet Mass Cross Section


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.


Jet Production at the LHC Jet production at the LHC has a

similar sensitivity to pdf’s as at the Tevatron


Diphoton Production at the LHC

cross section at 14 TeV

gg


W/Z + top cross sections at the LHC


W/Z production at the LHC

W+/W-/Z rapidity distributions provideinformation on quark and antiquark distributions


CTEQ5M/5HJ and Tevatron Jets

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CTEQ5/MRST comparison

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s from inclusive jet production large correlation between s and

gluon distribution makes indepen-

dent measurement of s difficult

physics in collision j. huston june 1999 review of parton distributions and implications for the...

Documents

linear slide

nlo pdfs

knowledge of pdfs

pdfs cteq5m

cteq5 analysis slide

error analysis slide

gluon distributionlog

great equalizer slide