parton densities for lhc

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)

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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

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Cross sections at LHC

Other processes, like Higgs or Z’ discovery potential not really affected by PDFs

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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

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Factorization property in hard scattering

Non-perturbative, parton densities, universal, from fit to exps. data

Perturbative process, calculable in pQCD

i.e. at LHC

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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

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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

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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

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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.

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• 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

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MSTW2008 datasets

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MSTW2008

Differences to MRST2001 sometimes larger than uncertainties

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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

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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

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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)

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Comparisons

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HERA F2

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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

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HERA charged current

CC(e-p)~xuv

CC(e+p)~(1-y)2dv

Allows to separate the two flavors at high x and Q2

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HERA neutral current/jets

gluon from F2from F2+jets

HERA I HERA II

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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

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Uncertainties

Experiments have learnt to provide correlated and uncorrelated systematics for every useful cross-section in order to make fits

Ex. ZEUS 2002 gluon

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Uncertainties

• Note that band of uncertainties are smaller than differences of PDFs.

• Blows up at high x, increases at low x

MRST04CTEQ6.1M

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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

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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)

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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

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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

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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

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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

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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

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LHC “standard candles” W,Z

Flavour decomposition in W,Z production and as determined in structure function data

Note the high contribution bb→ Z

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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?

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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

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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

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Parton luminosities at LHC

Uncertainties grow at high-x and rapidities

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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

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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.