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Parton densities for LHC
Elisabetta Gallo (INFN Firenze)IFAE Bologna 28/3/2008
• Introduction
•MRSW,CTEQ, HERA pdfs and data
• Some issues (uncertainties,u/d, s, HQ)
• Some LHC processes
(Diffractive PDFs, LHCb not covered)
E.Gallo IFAE 2008 2
Cross sections at LHC
• Any search for new physics needs a precise understanding of the SM and therefore QCD
• Parton densities, MCs, NLO-NNLO calculations, UE, are all important ingredients
2XD
4XD
6XD
SM
Example: search for Large Extra Dimensions in 2 jets. Main uncertainty is gluon density at high-x, of the same order as the difference between XDs
E.Gallo IFAE 2008 3
Cross sections at LHC
Other processes, like Higgs or Z’ discovery potential not really affected by PDFs
E.Gallo IFAE 2008 4
A bit of history of PDFs
Since then a lot of developments:
• MRST/MSTW group
• CTEQ group
• HERA pdfs (H1 and ZEUS on own data)
• unintegrated, small x
• heavy quark effects
• NNLO
• hessian or offset method?
First F2 from HERA 1993
E.Gallo IFAE 2008 5
Factorization property in hard scattering
Non-perturbative, parton densities, universal, from fit to exps. data
Perturbative process, calculable in pQCD
i.e. at LHC
E.Gallo IFAE 2008 6
How does a parton density look like?
• Determine xu,xd,xS,xg from fits at a certain Q02 and
then evolve in Q2 with the DGLAP evolution equations
• splitting functions calculated recently at NNLO
E.Gallo IFAE 2008 7
How does a parton density look like?
• u,d-valence, dominate at high x
• xS, sea, it is driven by the gluon, dominates at low x
• gluon, steep rise at low x
• evolution with Q2, example with a ZEUS QCD fit
E.Gallo IFAE 2008 8
Data for parton densities
LHC
HERA Fixed target
Tevatron jets
Data PDFsF2→q,qbar q,qbar low x
dF2/dlnQ2 g at low x
Fixed targ. u,d,s
TeV jets q,g high-x
TeV W u/d large-x
TeV prom γ g
pN DrellYan ubar-dbar
x1,2=(M/√s)exp(±yrap)~10-4-10-2 at LHC
E.Gallo IFAE 2008 9
Global fits
• CTEQ and MRST groups use DIS+hard scattering data, H1 and ZEUS their data only
• In principle 11 parton distributions (u,ubar,d,dbar,s,sbar,c,cbar,b,bbar,g)
• Charm and beauty from BGF process (g→b bar, c cbar, with b=bbar, c=cbar)
• s~sbar~0.2(ubar+dbar) at Q2=1 GeV2
• xf(x,Q20)=A(1-x)βxα(1+ε√x+γx)
• 10-11 parameters to fit, momentum sum rule to fix normalizations. Recently up to 20 parameters in MSTW.
E.Gallo IFAE 2008 10
• include NNLO. Uncertainties in NLO and NNLO are similar but SMALLER than individual uncertainties
• Improved treatment of charm (General Mass Variable Number Scheme at NNLO)
MRST/MSTW group (Martin, Stirling, Thorne et al., Durham UK)
Roberts retired from project in 2006, G. Watt joined (MSTW). More recent ones MSTW2007, MSTW2008
E.Gallo IFAE 2008 11
MSTW2008 datasets
E.Gallo IFAE 2008 12
MSTW2008
Differences to MRST2001 sometimes larger than uncertainties
E.Gallo IFAE 2008 13
CTEQ (Wu-Ki Tung and collaborators in USA)
• Global fit to HERA and colliders data
• Latest is CTEQ6.6 (arXiv:0802.007)
• Improves on CTEQ6.5 • Correlations for W,Z,ttbar
production studied• s(x)≠sbar(x) • New charm scheme in
CTEQ6.6/6.5 (GMVFNS) gives a different u,d at x~10-3 and Q~Mz
W,Z correlated
W,top anticorrelated
E.Gallo IFAE 2008 14
CTEQ6.6/5 vs CTEQ6.1
• Less c, more u,d →The different u,d densities cause a 8% difference in the W production x-section at LHC
CTEQ6.6
CTEQ6.1
E.Gallo IFAE 2008 15
H1, ZEUS
• latest ZEUS-JETS, H1 PDF 2000
•Fit their own data (no nuclear effects, errors under control)
• valence from NC/CC at high Q2
• gluon and sea from F2 data at low x
• middle-x gluon from jets (latest ZEUS-JETS)
E.Gallo IFAE 2008 16
Comparisons
E.Gallo IFAE 2008 17
HERA F2
E.Gallo IFAE 2008 18
Combined H1-ZEUS F2
Grows at low-x, precision ZEUS or H1 2-3%, <2% combined
DGLAP works, can extract PDFs from fit
Decrease at large x, 10% precision due to statistics
Errors reduced in combination, each experiment ‘calibrates’ the other
Fits on these combined data awaited
E.Gallo IFAE 2008 19
HERA charged current
CC(e-p)~xuv
CC(e+p)~(1-y)2dv
Allows to separate the two flavors at high x and Q2
E.Gallo IFAE 2008 20
HERA neutral current/jets
gluon from F2from F2+jets
HERA I HERA II
E.Gallo IFAE 2008 21
Uncertainties
• Hessian method (MRST,CTEQ,H1, allow data point to move according to correlated error, fit determines optimal setting of correlated errors)
• Offset method (ZEUS, shift for each systematics and refit)
• Experiments: distinguish between correlated and uncorrelated errors in tables of x-sections,
• i.e. ZEUS, H1: - normalization, overall shift up-and-down - correlated, affect many points together, like the
energy scale - uncorrelated, like efficiencies etc.. - statistical, only relevant at high x,Q2
E.Gallo IFAE 2008 22
Uncertainties
Experiments have learnt to provide correlated and uncorrelated systematics for every useful cross-section in order to make fits
Ex. ZEUS 2002 gluon
E.Gallo IFAE 2008 23
Uncertainties
• Note that band of uncertainties are smaller than differences of PDFs.
• Blows up at high x, increases at low x
MRST04CTEQ6.1M
E.Gallo IFAE 2008 24
d/u ratio at large-x
• For x>0.4 NuTeV F2 data higher then CCFR, different magnetic field calibration and therefore muon momentum
• tension in global fits between NuTeV (ν-Fe) data and other data, especially for d/u ratio
Ex. CTEQ6 fits
E.Gallo IFAE 2008 25
W-asymmetry at Tevatron
Sensitive to the u,d, in practice measure the lepton asymmetry
CDF,D0 II data have some influence especially on the d-valence density (compared to fixed-target)
E.Gallo IFAE 2008 26
Z production at Tevatron
New precise data show some tension with MRSW and fits to W-asymmetry.
Doing better at NNLO
CTEQ NLO in good agreement
Higher rapidities → smaller x, closer to LHC x-range
E.Gallo IFAE 2008 27
Tevatron jet dataConstrain high-x gluon
(Note MRSW also uses now HERA jet data to constrain middle-x gluon)
CDFII prefers a smaller high-x gluon compared to Run I data in MRST
E.Gallo IFAE 2008 28
strange
• Release assumption • Asymmetry not zero• Fit strange ‘directly’:
in MSTW find reduced factor compared to usual r=½ of strange to u,d
Determine strange from CCFR/NuTeV dimuon data
E.Gallo IFAE 2008 29
strangeAsymmetry comes out compatible with zero.
At Q2=10 GeV2 asymmetry is 0.0017 ± 0.0020
Why bother?
• Leaving strange free in these fits increases uncertainties in ubar, dbar from 1.5% to 2-2.5%
• c+sbar→ H+ at LHC
E.Gallo IFAE 2008 30
Charm,beauty
•For Q2~m2c the
charm does not act as a parton, BGF process, massive scheme (FFNS)
For Q2>m2c the
charm behaves has a massless parton (ZM-VFNS)
Variable number scheme in between (GM-VFNS)
Different schemes, quite different predictions, data increasing precision
FFNS
VFNS
E.Gallo IFAE 2008 31
LHC “standard candles” W,Z
Flavour decomposition in W,Z production and as determined in structure function data
Note the high contribution bb→ Z
E.Gallo IFAE 2008 32
LHC “standard candles” W,Z
• calculated at NNLO, accuracy at 1%
• can be measured with high exp. accuracy
• can be used as luminosity monitor, what about the pdf uncertainty?
E.Gallo IFAE 2008 33
LHC “standard candles” W ,Z
Total cross sections known with an accuracy of <5% (driven by the sea-gluon)
Note also small uncertainty of 2% claimed by MRST01, but difference to CTEQ6.1 (or CTEQ6.5) is bigger
E.Gallo IFAE 2008 34
LHC “standard candles” W,Z
• correlations between W and Z cross-sections (not so at Tevatron). Ratio Z/W quite independent of PDFs, can be used as SM benchmark
• CTEQ6.6 (GMVFN) a bit away from ZEUS-MSTW06 predictions
• different HQ mass schemes in ZEUS make smaller difference, so CTEQ6.6 is away not only due to charm
E.Gallo IFAE 2008 35
Parton luminosities at LHC
Uncertainties grow at high-x and rapidities
E.Gallo IFAE 2008 36
Extraction of PDFs from LHC• W asymmetry, Z rapidity → valence at smaller x~0.005 (gluon cancel in ratio in W-asymmetry)
• Z+jets, γ+jet, prompt photons→ gluon
• jet cross sections (jet energy scale has to be controlled)
CMS
E.Gallo IFAE 2008 37
Conclusions
• Precise prediction of SM essential for discovery of new signals
• PDF uncertainties and effects to be considered;
- pdfs known only down to x~10-4 , where DGLAP works (no need for saturation or BFKL effects)
- uncertainties around 5% for W production
• Heavy quark effects need to be watched out (CTEQ6.6 higher 8% W cross-section compared to CTEQ6.1)
• LHAPDF accord, PDF4LHC workshop, DIS08 Workshop and HERA-LHC WS in May at CERN, fruitful discussion going on.