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)

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

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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

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

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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


MSTW2008 datasets


MSTW2008

Differences to MRST2001 sometimes larger than uncertainties


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


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


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)


Comparisons


HERA F2


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


HERA charged current

CC(e-p)~xuv

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

Allows to separate the two flavors at high x and Q2


HERA neutral current/jets

gluon from F2from F2+jets

HERA I HERA II


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


Uncertainties

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

Ex. ZEUS 2002 gluon


Uncertainties

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

• Blows up at high x, increases at low x

MRST04CTEQ6.1M


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


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)


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


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


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


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


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


LHC “standard candles” W,Z

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

Note the high contribution bb→ 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?


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



• 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


Parton luminosities at LHC

Uncertainties grow at high-x and rapidities


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


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.

Parton densities for LHC

Documents

low x gluon

low x middlex gluon

low x evolution

high x xs

zeus latest zeusjets

f2 data

data unintegrated

precision zeus