Parton Distributions Functions and Electroweak Physics
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Parton Distributions Functions and Electroweak Physics
James Stirling
IPPP, University of Durham
• Precision predictions for (W), (Z) at hadron colliders
• QED-improved parton distributions
• Isospin violation and the NuTeV sin2W “anomaly”
(with Alan Martin, Dick Roberts and Robert Thorne)
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ICHEP04 2
the QCD factorization theorem for hard-scattering (short-distance) inclusive processes:
where X=W, Z, H, high-ET jets, SUSY sparticles, … and Q is the ‘hard scale’ (e.g. = MX), usually F = R = Q, and is known to some fixed order in pQCD and pEW (or to all orders in some LL approximation)
^
precision QCD at hadron colliders
what limits the precision?
• the order of the perturbative expansion
• the uncertainty in the input parton distribution functions
example σ(Z) @ LHC
σpdf ±3%, σpt ± 2%
→ σtheory ± 4%whereas for gg→H :
σpdf << σpt
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ICHEP04 3
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
100
101
102
103
104
105
106
107
108
109
fixedtarget
HERA
x1,2
= (M/1.96 TeV) exp(y)Q = M
Tevatron parton kinematics
M = 10 GeV
M = 100 GeV
M = 1 TeV
422 04y =
Q2
(GeV
2 )
x10
-710
-610
-510
-410
-310
-210
-110
010
0
101
102
103
104
105
106
107
108
109
fixedtarget
HERA
x1,2
= (M/14 TeV) exp(y)Q = M
LHC parton kinematics
M = 10 GeV
M = 100 GeV
M = 1 TeV
M = 10 TeV
66y = 40 224
Q2
(GeV
2 )
x
longer Q2
extrapolation
smaller x
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ICHEP04 4
-6 -4 -2 0 2 4 60
1
2
3
4
5
x1 = 0.0003x2 = 0.12
x1 = 0.12x2 = 0.0003
x1 = 0.006x2 = 0.006
yW
MRST2002-NLO LHC
dW
/dy W
. B
l
(nb)
forward W, Z, dijet… production at LHC samples small and high x
but no acceptance, no triggers?!
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ICHEP04 5
examples of ‘precision’ phenomenology
W, Z productionjet production
NNLO QCDNLO QCD
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ICHEP04 6
σ(W) and σ(Z) : precision predictions and measurements at the Tevatron and LHC
• the pQCD series appears to be under control
• the EW corrections are known and can in principle be included (see below)
• with sufficient theoretical precision, these ‘standard candle’ processes can be used to measure machine luminosity
4% total error(MRST 2002)
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ICHEP04 7
LHC σNLO(W) (nb)
MRST2002 204 ± 6 (expt)
CTEQ6 205 ± 8 (expt)
Alekhin02 215 ± 6 (tot)
similar partons different Δχ2
different partons
the rapidity distributions dσ/dy are also known to NNLO matching to experimental acceptance
however…
Anastasiou et al. hep-ph/0306192hep-ph/0312266
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ICHEP04 8
Djouadi & Ferrag, hep-ph/0310209the differences between pdf sets needs to be better understood!
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ICHEP04 9
why do ‘best fit’ pdfs and errors differ?
• different data sets in fit– different subselection of data
– different treatment of exp. sys. errors
• different choice of
– tolerance to define fi (CTEQ: Δχ2=100, Alekhin: Δχ2=1)
– factorisation/renormalisation scheme/scale
– Q02
– parametric form Axa(1-x)b[..] etc
– αS
– treatment of heavy flavours
– theoretical assumptions about x→0,1 behaviour
– theoretical assumptions about sea flavour symmetry
– evolution and cross section codes (removable differences!) → see ongoing HERA-LHC Workshop PDF Working Group
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ICHEP04 10
• small MRST and CTEQ differences largely understood, see hep-ph/0211080
mainly: CTEQ gluon at Q02 required to be positive at
small x means gCTEQ > gMRST there, also 2 = 50 (MRST), 100 (CTEQ)
• ALEKHIN gluon smaller at high x (no Tevatron jet data in fit) and different content of sea at small x from different assumptions about ubar-dbar as x 0 and (ii) ratio of strange to non-strange pdfs. Also 2 = 1 allowed by use of smaller overall data set.
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ICHEP04 11
ratio of W– and W+ rapidity distributions
0 1 2 3 4 5 60.0
0.2
0.4
0.6
0.8
1.0
MRST2002NLO ALEKHIN02NLO
d(W
- )/dy
/ d
(W+)/
dy
yW
x1=0.52 x2=0.000064
x1=0.006 x2=0.006ratio close to 1 because u u etc.
(note: MRST error = ±1½%)
–
sensitive to large-x d/u and small x u/d ratios
Q. What is the experimental precision?
––
d(W-) d(x1) u(x2) + u(x1) d(x2) + …
=d(W+) u(x1) d(x2) + d(x1) u(x2) + …
LHC W-/W+
MRST2002 0.75
CTEQ6 0.75
Alekhin02 0.74
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ICHEP04 12
bbZ contribution to Z production @ LHC
Note: much smaller effect at Tevatron
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QED effects in pdfsQED corrections to DIS include:
included in standard radiative correction packages (HECTOR, HERACLES) Note: Cint finite as mq 0
De Rujula, Petronzio, Savoy-Navarro 1979Krifganz, Perlt 1988Bluemlein 1990Spiesberger 1994Roth, Weinzierl 2004
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ICHEP04 14
• above QED corrections are universal and can be absorbed into pdfs, exactly as for QCD singularities, leaving finite (as mq 0) O(α) QED corrections in coefficient functions
• relevant for electroweak correction calculations for processes at Tevatron & LHC, e.g. W, Z, WH, … (see e.g. U. Baur et al, PRD 59 (2003) 013002)
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ICHEP04 15
QED-improved DGLAP equations• at leading order in α and αS
where
• momentum conservation:
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ICHEP04 16
effect on valence quark evolution:
• effect on quark distributions negligible at small x where gluon contribution dominates DGLAP evolution
• at large x, effect only becomes noticeable (order percent) at very large Q2, where it is equivalent to a shift in αS of αS 0.0003
• dynamic generation of photon parton distribution
• isospin violation: up(x) ≠ dn(x)
• first consistent global pdf fit with QED corrections included (MRST 2004)
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proton
neutron
R-iso
valencedifference
MRST 2004
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ICHEP04 18
first measurement of p(x,Q2) ?
e
p
ZEUS: “Observation of high ET photons in deep inelastic scattering”, hep-ex/0402019
s = 318 GeV, Q2 > 35 GeV2, Ee > 10 GeV139.8o < e < 171.8o 5 < ET
< 10 GeV, -0.7 < < 0.9
(ep eX) = 5.64 0.58 (stat.) (syst.) pb
prediction using MRST2004 QEDpdfs:
(ep eX) = 6.2 pb
0.720.47
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ICHEP04 19
sin2W from N
3 difference
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ICHEP04 20
Conclusion: uncertainties in detailed parton structure are substantial on the scale of the precision of the NuTeV data – consistency with the Standard Model does not appear to be ruled out at present
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ICHEP04 21
summary
• more work needed to establish true theoretical error on the predictions for (W), (Z) at LHC: target is < 5%
• pdf sets with O(α) QED effects are now available and allow pEW corrections at hadron colliders to be consistently included
• details of hadron structure can effect NuTeV measurement of sin2W
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extra slides
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23
perturbative generation of s(x) ≠ s(x)
Pus(x) ≠ Pus(x)at O(αS
3)
Quantitative study by de Florian et alhep-ph/0404240
x(s-s)pQCD < 0.0005
cf. from global pdf fit (Olness et al, hep-ph/0312322,3)
0.001 < x(s-s)fit < +0.004
partial explanation of NuTeV sin2W “anomaly”?
note!
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ICHEP04 24
x dependence of fi(x,Q2) determined by ‘global fit’ to deep inelastic scattering (H1, ZEUS, NMC, …) and hadron collider data
F2(x,Q2) = q eq2 x q(x,Q2) etc
DGLAP equations
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ICHEP04 25
pdfs from global fits
FormalismNLO DGLAPMSbar factorisationQ0
2
functional form @ Q02
sea quark (a)symmetryetc.
Who?Alekhin, CTEQ, MRST,GKK, Botje, H1, ZEUS,GRV, BFP, …
http://durpdg.dur.ac.uk/hepdata/pdf.html
DataDIS (SLAC, BCDMS, NMC, E665, CCFR, H1, ZEUS, … )Drell-Yan (E605, E772, E866, …) High ET jets (CDF, D0)W rapidity asymmetry (CDF)N dimuon (CCFR, NuTeV)etc.
fi (x,Q2) fi (x,Q2)
αS(MZ )
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ICHEP04 26
(MRST) parton distributions in the proton
10-3
10-2
10-1
100
0.0
0.2
0.4
0.6
0.8
1.0
1.2
MRST2001
Q2 = 10 GeV
2
up down antiup antidown strange charm gluon
x
f(x,
Q2 )
x Martin, Roberts, S, Thorne
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ICHEP04 27
uncertainty in gluon distribution (CTEQ)
then fg → σgg→X etc.
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ICHEP04 28
solid = LHCdashed = Tevatron
Alekhin 2002
pdf uncertainties encoded in parton-parton luminosity functions:
with = M2/s, so that for ab→X
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ICHEP04 29
Djouadi & Ferrag, hep-ph/0310209
Higgs cross section: dependence on pdfs
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ICHEP04 30
Djouadi & Ferrag, hep-ph/0310209
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ICHEP04 31
• MRST: Q02 = 1 GeV2, Qcut
2 = 2 GeV2
xg = Axa(1–x)b(1+Cx0.5+Dx)
– Exc(1-x)d
• CTEQ6: Q02 = 1.69 GeV2,
Qcut2 = 4 GeV2
xg = Axa(1–x)becx(1+Cx)d
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ICHEP04 32
2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 140.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Experiment B
Experiment A
systematic error
systematic error
measurement #
• with dataset A in fit, Δχ2=1 ; with A and B in fit, Δχ2=? • ‘tensions’ between data sets arise, for example,
– between DIS data sets (e.g. H and N data) – when jet and Drell-Yan data are combined with DIS data
tensions within the global fit?
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ICHEP04 33
CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100
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ICHEP04 34
0.01 0.1 1-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
f(x)
x0.01 0.1 1
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
f(x)
x0.01 0.1 1
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
f(x)
x
extrapolation errors
theoretical insight/guess: f ~ A x as x → 0
theoretical insight/guess: f ~ ± A x–0.5 as x → 0
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ICHEP04 35
differences between the MRST and Alekhin u and d sea quarks near the starting scale
ubar=dbar
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ICHEP04 36
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ICHEP04 37
Note: high-x gluon should become better determined from Run 2 Tevatron dataQ. by how much?
Note: CTEQ gluon ‘more or less’ consistent with MRST gluon
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ICHEP04 38
comparison with existing approximate NNLO fits? (MRST, Alekhin)
• exact NNLO splitting functions are very close to approximate splitting functions (van Neerven, Vogt) based on moments & known small- and large-x behaviours…
• … and therefore the corresponding pdfs are almost identical
• Note:– the full NNLO pdf fit awaits calculation of the inclusive high ET jet
cross section at NNLO– including NNLO (splitting & coefficient functions) gives a slight
improvement in overall fit quality, and reduction in αS(MZ) from 0.119 to 0.116
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ICHEP04 39
ratio of MRST2001 NLO and ‘NNLO’ parton distributions
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ICHEP04 40
summary of NNLO collider calculations• p + p → jet + X *; in progress• p + p → γ + X; in principle, subset of the jet calculation
but issues regarding photon fragmentation, isolation etc• p + p → QQbar + X; requires extension of above to non-
zero fermion masses• p + p → (γ*, W, Z) + X *; van Neerven et al, Harlander and
Kilgore corrected (2002)
• p + p → (γ*, W, Z) + X differential rapidity distribution *; Anastasiou, Dixon, Melnikov (2003)
• p + p → H + X; Harlander and Kilgore, Anastasiou and Melnikov (2002-3)
Note: knowledge of processes * needed for a full NNLO global parton distribution fit
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ICHEP04 41
pdfs from global fits
FormalismLO, NLO, NNLO DGLAPMSbar factorisationQ0
2
functional form @ Q02
sea quark (a)symmetryetc.
Who?Alekhin, CTEQ, MRST,GGK, Botje, H1, ZEUS,GRV, BFP, …
http://durpdg.dur.ac.uk/hepdata/pdf.html
DataDIS (SLAC, BCDMS, NMC, E665, CCFR, H1, ZEUS, … )Drell-Yan (E605, E772, E866, …) High ET jets (CDF, D0)W rapidity asymmetry (CDF)N dimuon (CCFR, NuTeV)etc.
fi (x,Q2) fi (x,Q2)
αS(MZ )
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ICHEP04 42
summary of DIS data
+ neutrino FT DIS data Note: must impose cuts on
DIS data to ensure validity of leading-twist DGLAP formalism in the global analysis, typically:
Q2 > 2 - 4 GeV2
W2 = (1-x)/x Q2 > 10 - 15 GeV2
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ICHEP04 43
typical data ingredients of a global pdf fit
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ICHEP04 44
recent global fit work• H1, ZEUS: ongoing fits for pdfs + uncertainties from HERA and other DIS data
• Martin, Roberts, WJS, Thorne (MRST): updated `MRST2001' global fit (hep-ph/0110215); LO/NLO/‘NNLO’ comparison (hep-ph/0201127); pdf uncertainties: from experiment (hep-ph/0211080) and theory (hep-ph/0308087)
• Pumplin et al. (CTEQ): updated ‘CTEQ6’ global fit (hep-ph/0201195), including uncertainties on pdfs; dedicated study of high ET jet cross sections for the Tevatron (hep-ph/0303013); strangeness asymmetry from neutrino dimuon production (hep-ph/0312323)
• Giele, Keller, Kosower (GKK): restricted global fit, focusing on data-driven pdf uncertainties (hep-ph/0104052)
• Alekhin: restricted global fit (DIS data only), focusing on effect of both theoretical
and experimental uncertainties on pdfs and higher-twist contributions (hep-ph/0011002); updated and including ‘NNLO’ fit (hep-ph/0211096)
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ICHEP04 45
HEPDATA pdf server
Comprehensive repository of past and present polarised and unpolarised pdf codes (with online plotting facility) can be found at the HEPDATA pdf server web site:
http://durpdg.dur.ac.uk/hepdata/
pdf.html
… this is also the home of the LHAPDF project
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ICHEP04 46
pdfs with errors….
CTEQ gluon distribution uncertainty using Hessian Method
output = best fit set + 2Np error sets
“best fit” parameters
Hessian Matrix
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ICHEP04 47
Djouadi & Ferrag, hep-ph/0310209
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ICHEP04 48
Djouadi & Ferrag, hep-ph/0310209
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ICHEP04 49
• MRST: Q02 = 1 GeV2, Qcut
2 = 2 GeV2
xg = Axa(1–x)b(1+Cx0.5+Dx)
– Exc(1-x)d
• CTEQ6: Q02 = 1.69 GeV2,
Qcut2 = 4 GeV2
xg = Axa(1–x)becx(1+Cx)d
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ICHEP04 50
2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 140.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Experiment B
Experiment A
systematic error
systematic error
measurement #
• with dataset A in fit, Δχ2=1 ; with A and B in fit, Δχ2=? • ‘tensions’ between data sets arise, for example,
– between DIS data sets (e.g. H and N data) – when jet and Drell-Yan data are combined with DIS data
tensions within the global fit?
pictures from W-K Tung
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ICHEP04 51
CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100
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ICHEP04 52
0.01 0.1 1-4
-3
-2
-1
0
1
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8
f(x)
x0.01 0.1 1
-4
-3
-2
-1
0
1
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f(x)
x0.01 0.1 1
-4
-3
-2
-1
0
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f(x)
x
extrapolation errors
theoretical insight/guess: f ~ A x as x → 0
theoretical insight/guess: f ~ ± A x–0.5 as x → 0
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ICHEP04 53
differences between the MRST and Alekhin u and d sea quarks near the starting scale
ubar=dbar
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ICHEP04 54
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ICHEP04 56
contours correspond to ‘ experimental’ pdf errors only; shift of prediction using CTEQ6 pdfs shows effect of ‘theoretical’ pdf errors
±2%
±3%
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ICHEP04 57
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ICHEP04 59
as small x data are systematically removed from the MRST global fit, the quality of the fit improves until stability is reached at around x ~ 0.005 (MRST hep-ph/0308087)
Q. Is fixed–order DGLAP insufficient for small-x DIS data?!
Δ = improvement in χ2 to remaining data / # of data points removed
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ICHEP04 60
the stability of the small-x fit can be recovered by adding to the fit empirical contributions of the form
... with coefficients A, B found to be O(1) (and different for the NLO, NNLO fits); the starting gluon is still very negative at small x however
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ICHEP04 61
the ‘conservative’ pdfs (blue lines) do not describe the very low x DIS data not included in the fit
MRST, hep-ph/0308087
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ICHEP04 62
the change in the NLO and NNLO gluons when DIS data with x < 0.005 are removed from the global fit
MRST, hep-ph/0308087
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ICHEP04 63
comparison of the standard MRST and ‘conservative’ NNLO pdfs
MRST, hep-ph/0308087
no data in fit
no data in fit
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ICHEP04 64
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ICHEP04 65
(LO) W cross sections at the Tevatron and LHC using (NLO) partons from MRST, CTEQ and Alekhin
Tevatron B.σ(W) (nb)
MRST2002 2.14
CTEQ6 2.10
Alekhin02 2.22
LHC B.σ(W+) (nb) B.σ(W) (nb) W+/W–
MRST2002 10.1 7.6 1.33
CTEQ6 10.2 7.6 1.34
Alekhin02 10.7 7.9 1.35
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ICHEP04 66
flavour decomposition of W cross sections at hadron colliders
recall that the only constraint on very small x quarks from inclusive DIS (F2
ep) data is on the combination
4/9 [u+c+ubar+cbar]+ 1/9 [d+s+dbar+sbar]
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ICHEP04 67
differences between the MRST, CTEQ and Alekhin strange quarks near the starting scale
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ICHEP04 68
NNLO precision phenomenology
• predictions calculated (MRST 2002) using ‘old’ approximate two-loop splitting functions
• width of shows uncertainty from P(2) (biggest at small x)
• this uncertainty now removed, NNLO prediction unchanged
14
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partons: MRST2002NNLO evolution: van Neerven, Vogt approximation to Vermaseren et al. momentsNNLO W,Z corrections: van Neerven et al. with Harlander, Kilgore corrections
NLONNLO
LO
LHC Z(x10)
W
. B
l (
nb)
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
NNLONLO
LO
Tevatron (Run 2)
CDF D0(e) D0()
Z(x10)
W
CDF D0(e) D0()
. B
l (
nb)
4% total error(MRST 2002)