xlist recontres de moriond, qcd and hadronic interactions la thuile, march 18 th – 25 th , 2006

N. Raicevic Moriond QCD 2006

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Structure Functions and Extraction of PDFs at HERA

Nataša RaičeviċUniversity of Montenegro

On behalf of the H1 and ZEUS Collaborations

XLIst Recontres de Moriond, QCD and Hadronic Interactions

La thuile, March 18th – 25th, 2006

Outline:

HERA accelerator and luminosity

DIS physics

Main input from HERA-I data for PDF extraction

Highlights from HERA-II

Results from QCD fits - PDFs and αs

Combined QCD and electro-weak fit from HERA-I Improvements of PDFs expected from HERA-II

Summary and outlook


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In 2000-2002 HERA-I upgraded to HERA-II

• Increased luminosity

• Polarised leptons - new feature of HERA

HERA will run until summer 2007

HERA beams

HERA-ILuminosity

(pb-1)

HERA-II luminosity

(pb-1)

e-p ≈ 15 > 150

e+p ≈ 100 > 40

HERALuminosity per experiment, roughly


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Charged Current (CC) ZEUS CC event display

Neutral Current (NC) H1 NC event display

qpQ

x

2

2

kpqp

y

222 )'( kkqQ

Virtuality of exchanged boson:

Fraction of proton momentum carried by struck quark

Fraction of energytransferred from incoming lepton at proton rest frame

Inclusive Deep Inelastic Scattering (DIS)


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Cross Sections and Structure Functions

2Z

Z2

e2

e2

2γZ

Ze22 FK)a(vFK)(vFF~

3Z

Z2

ee3γZ

Ze3 FxKa2vFxKaF~x

FL = (Q2/4πα)σL

-dominant contribution

- important only at high Q2

- sizable contribution for high y

)qxqx(]av,v2e,[e]F,F,F[ q2q2qqq2

2Z

2γZ

2

)qxqx](av,a[e2]Fx,Fx[ qqqq3Z

3γZ

),(~ 2QxNC - NC reduced cross-section

γ-exchange γZ-interference Z-exchange

W2

W22

Z

2 2

2

Z

θcosθsin4

1)MQ(

QK

Generalised

Structure Functions

(SF)

Neutral current cross section

y)(11Y2

][ F~

xYY

F~

Yy

F~Y

Qx2

Qdxd)pe(d

3L

2

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2

2NC

2

In the Quark Partom Model (QPM): FL = 0

SFs


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Charged current cross section (LO)

)]()1()([)(2

2222

42

2

2

sdxycuxMQx

MG

dxdQ

d

W

WF

pe

CC

)]()1()([)(2

2222

42

2

2

sdxycuxMQx

MG

dxdQ

d

W

WF

pe

CC

),(~ 2QxCC - CC reduced cross-section

Sensitivity to the flavor of the valence distributions at high x

uv at high x

dv at high x

Quark PDFs - from NC (F2) and CC DIS

Gluon – from scaling violation - dF2/dlnQ2

SF can also constrain PDFs and quark couplings to the Z boson (vq, aq)

FL ~ αs · xg(x,Q2)In pQCD:

))) 222 ,(,,(,,( QQQ xxgxqxxxq - Parton Density Functions - PDFs


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Main Inputs from HERA-I Data for the PDF Extraction

F2em(x,Q2) ~ Σq eq

2(q + q)

δF2/F2 ~ 30%Q2 / GeV2

δF2/F2 ~ 2-3%

_


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Measurements of CC Cross Sections from HERA-II with Longitudinally Polarised Beams

SM:

Linear dependence of CC cross section on Pe

±(Pe) = (1±Pe)±(Pe=0)

ZEUS and H1 measurements in agreement with SM

no right handed charged currents

LHRH

LHRHe NN

NNP

Textbook measurements

H1 Collaboration , Phys. Lett. B 634 (2006), ZEUS Collaboration , DESY-06-015 (February 2006) - submitted to Physics Letters B


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Measurements of NC Cross Sections with HERA-II with Longitudinally Polarised Beams

• For NC, em. contribution which dominates at low Q2 does not depend on polarisation

• Polarisation dependence occures via interference between γ and Z boson exchanges Measurements well

described by the SM

ZEUS Collaboration , DESY-06-015 (February 2006) - submitted to Physics Letters B


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HERA PDFs for the LHC

• Proton structure described by precise PDFs needed for making accurate predictions for any process involving protons

• DGLAP QCD evolution provides Q2

dependence of the PDFs x dependence must come from data:

HERA covers the most important

region for the LHC


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Additional Constrains on Gluon Density from JETS

Sensitive to αs and quark/gluon density

Break the strong correlation between αs and the gluon PDF from DGLAP

αs can be free parameter simultaneously with all the PDFs (ZEUS-JETS fit)

Events with distinct jets in the final state

Jet data constrain g(x) at medium and high-x (0.01-0.4)


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Fits from HERA-I

H1 PDF 1997

Eur. Phys. J C21 (2001)

H1 PDF 2000Eur. Phys. J C30 (2003)

ZEUS-SPhys. Rev. D67 (2003)

ZEUS-JETSEur. Phys. J C42 (2005)

Data from other exp

BCDMS (μp) ---- BCDMS,NMC,E665,CCFR (μp, μd, νFe)

----

Fitted distributions

ep valence and sea terms

cu,sd

s,dc,ug,

udS,,d,ug, vv

Advantage of using data from one experiment:

Systematic uncertainties understood

Pure proton target no uncertainties of heavy target corrections no need for strong isospin assumptions

Q02 starting scale for parameterization, cuts for perturbative phase space (Q2

min) , choice of PDFs to parameterize, treatment of heavy quarks, allowed functional form of parameterization,

treatment of exp. uncertainties, renormalisation / factorisation scales …. Should be reflected in PDF uncertainty

QCD analysis requires many choices to be made:

QCD Fits from HERA-I

In global fits main contributions from HERA data from low-x sea and gluon

Purpose αs, g(x) pdfs pdfs, αs pdfs, αs

udS,,d,ug, vv


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• Results broadly consistent within uncertainties (also consistent with global fitters)

Extracted PDFs

• Still large uncertainties on gluon density and on d density at large x

)( cux

)( sdx

)( cux

)( sdx


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Strong Coupling Constant - αs

Inclusion of jet data significantly improves αs

Δαs(th.) = ± 0.005 mainly due to the uncertainty of the renormalisation scale NNLO QCD analysis

NNLO calculations available (hep-ph/0403192, 0404111)


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H1 Combined QCD and EW fit

Determination of light quark axial (au, ad) and vector (vu, vd) couplings to Z-boson for the first time at HERA (all HERA-I data)

Combined fit of au, vu, ad, vd and PDFs (H1 PDF 2000 scheme)

HERA-II will bring improvement with statistics and polarisation

H1 measurement determine sign of precise measurements from LEP

Standard Model:

aq = Iq3

au = +1/2, ad = -1/2

Vq = Iq3 – 2eqsin2θW

H1 Collaboration, Phys. Lett. B632 (2006) 35-42

)qxqx(ae2Fx qq3γZ

More sensitivity to au

then to vu

_


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Improvements on PDFs expected with HERA-II should come from:

Higher precision measurements of F2 and CC cross section

Precise measurement of xF3

Direct measurement of FL

Jet data – new results are still coming from HERA-I (see talk of C. Wissing)

Higher precision of heavy flavor contribution – new results are still coming from HERA-I (see talk of B. List)

SF – xF3

When enough statistics possible consistency check of valence contribution

_

xF3 ~ σ-NC – σ+

NC

xF3 = -aeKzxF3γZ + Z-exchange

xF3γZ ~ 2x Σqeqaq( q – q ) ~ qv

~

~

x


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Gluon distributions obtained in global NLO analysis

Direct measurement of FL require runs with lower proton beam energy:

For the same (Q2,x) σr to be measured from different beam energies (i.e. y)

Perform straight line fit of σr vs f(y) to extract F2 and FL

Longitudinal SF - FL

Longitudinal SF - FL

From pQCD

Much more precise input for low-x gluon distribution is necessary via precise measurement of FL

xg(x) ~FL (at very low x)

x

σr

f(y)0 1

F2F2-FL

σr = F2(x,Q2) – f(y) •FL(x,Q2)

High precision measurement of FL can be only achieved by measuring it directly

· ··


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Summary and Outlook

HERA has provided crucial input for understanding proton structure

PDFs have been extracted using HERA data only with the high precision

First results from HERA-II about CC and NC cross section from polarised beams published H1 and ZEUS measurements in agreement with Standard Model expectations

Combined QCD+EW fit from HERA-I data a first measurement at HERA of the light quark weak couplings to the Z-boson

Still, results from HERA-I are coming and can be used as inputs for the PDFs extraction (see also talks of C. Wissing and B. List)

HERA-II is running and additional data are coming with significantly improved statistics improvement of PDF uncertainties


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extras


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General Fitting Procedure for PDF extraction

Parametrisation of PDFs at starting scale Q02

Some parameters constrained by the number and momentum sum rules

Evolve in Q2 using DGLAP pQCD evolution in NLO

Convolute PDFs with coefficient functions to give structure functions and cross sections Make fit to data iteratively changing starting parameters until best fit is found


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H1 QCD Analysis

Data: 8·10-5 < x < 0.65, 1.5 < Q2 < 30000 GeV2

Q20 = 4 GeV2, Q2

min = 3.5 GeV2

Parameterisation of: xU, xD, xU, xD, xg

xU = x(u + c)

xD = x(d + s)

xU = x(u + c)

xD = x(d + s)

Parameterisation of each PDF by searching χ2 saturation

Fit performed in ZERO MASS scheme (appropriate for high Q2)

Use H1+BCDMS p and D data as a cross check

_ __ Bellow bottom threshold_ _ _

Χ2/ndf = 0.88

_ _


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Performed dedicated QCD analysis to determine gluon density and αs:

Use precise H1 and BCDMS-p F2 data to constrain valence region (proton target only no nuclear corrections required)

Parametrisation of: xg, xV, xA

xV = 9/4uv + 3/2dv

xA = u + ¼(uv + 2 dv)

F2 = 1/3xV + 11/9xA

Use massive 3-flavour number scheme

H1 QCD Analysis, g(x) and αs


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ZEUS Only QCD Analysis

Data: 6.3·10-5 < x < 0.65, 2.7 < Q2 < 30000 GeV2, W2 > 20 GeV2

(W2 > 20 GeV2 – removes higher twists)

Q20 = 7 GeV2, Q2

min = 2.5 GeV2

Parameterisation of: xuv, xdv, xg, Sea, xΔ = x(d – u)

- fix AΔ consistent with Gottfried sum rule (no sensit. from HERA)

Experimental systematic uncertainties are propagated onto final PDF uncertainty

Use Thorne/Roberts Variable Flavour Number scheme Compared to global fits, information lost on high-x sea and gluon:

Use ZEUS global fit to constrain high-x sea and gluon (cs and cg)

__


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ZEUS-JETS QCD Analysis

A complete NLO calculation for jet cross sections for each iteration of the χ2

minimisation is extremely slow.

Method:

1. Use NLO QCD program initially to produce grid of weights (x,μF2), giving

perturbatively calculable part of cross section

2. Convolute with PDFs to produce fast prediction for cross section:

Grid cross section reproduce real NLO predictions to better than 0.5%

DIS jets: 125 < Q2 < 30000 GeV2, EBT,jet > 8 GeV, -2 < ηB

jet < 1.8

γp dijets: ETjet1,(2) > 14 (11) GeV, -1 < ηjet1,2 < 2.4, xγ

obs > 0.75, 134 < W2

γp < 277 GeV2

Now, direct information on gluon available gluon parameters free

Χ2/ndf = 0.81

Direct-process enriched region


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Extracted PDFs

xlist recontres de moriond, qcd and hadronic interactions la thuile, march 18 th – 25 th , 2006

Documents

hera pdfs

qcd fits pdfs

hera accelerator

scombined qcd

sfsmoriond qcd

outlookmoriond qcd

lhc moriond qcd

extraction of pdfs