N. RaicevicMoriond QCD Structure Functions and Extraction of PDFs at HERA Nataša Raičeviċ University of Montenegro On behalf of the H1 and ZEUS Collaborations XLIst Recontres de Moriond, QCD and Hadronic Interactions La thuile, March 18 th – 25 th, 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 α s  Combined QCD and electro-weak fit from HERA-I  Improvements of PDFs expected from HERA-II  Summary and outlook

N. RaicevicMoriond QCD In HERA-I upgraded to HERA-II Increased luminosity Polarised leptons - new feature of HERA HERA will run until summer 2007 HERA beams HERA-I Luminosity (pb -1 ) HERA-II luminosity (pb -1 ) e-p≈ 15> 150 e+p≈ 100> 40 HERA Luminosity per experiment, roughly

N. RaicevicMoriond QCD Charged Current (CC) ZEUS CC event display Neutral Current (NC) H1 NC event display Virtuality of exchanged boson: Fraction of proton momentum carried by struck quark Fraction of energy transferred from incoming lepton at proton rest frame Inclusive Deep Inelastic Scattering (DIS)

N. RaicevicMoriond QCD Cross Sections and Structure Functions F L = (Q 2 /4πα)σ L -dominant contribution - important only at high Q 2 - sizable contribution for high y - NC reduced cross-section γ-exchangeγZ-interference Z-exchange Generalised Structure Functions (SF) Neutral current cross section In the Quark Partom Model (QPM): F L = 0 SFs

N. RaicevicMoriond QCD Charged current cross section (LO) - CC reduced cross-section Sensitivity to the flavor of the valence distributions at high x u v at high x d v at high x  Quark PDFs - from NC (F 2 ) and CC DIS  Gluon – from scaling violation - dF 2 /dlnQ2  SF can also constrain PDFs and quark couplings to the Z boson (v q, a q ) F L ~ α s · xg(x,Q 2 ) In pQCD: - Parton Density Functions - PDFs

N. RaicevicMoriond QCD Main Inputs from HERA-I Data for the PDF Extraction F 2 em (x,Q 2 ) ~ Σ q e q 2 (q + q) δF 2 /F 2 ~ 30% Q 2 / GeV 2 δF 2 /F 2 ~ 2-3% _

N. RaicevicMoriond QCD Measurements of CC Cross Sections from HERA-II with Longitudinally Polarised Beams SM: Linear dependence of CC cross section on P e  ± (P e ) = (1±P e )  ± (P e =0)  ZEUS and H1 measurements in agreement with SM  no right handed charged currents Textbook measurements H1 Collaboration, Phys. Lett. B 634 (2006), ZEUS Collaboration, DESY (February 2006) - submitted to Physics Letters B

N. RaicevicMoriond QCD Measurements of NC Cross Sections with HERA-II with Longitudinally Polarised Beams For NC, em. contribution which dominates at low Q 2 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 (February 2006) - submitted to Physics Letters B

N. RaicevicMoriond QCD 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 Q 2 dependence of the PDFs  x dependence must come from data: HERA covers the most important region for the LHC

N. RaicevicMoriond QCD Additional Constrains on Gluon Density from JETS Sensitive to α s and quark/gluon density  Break the strong correlation between α s and the gluon PDF from DGLAP  α s 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 ( )

N. RaicevicMoriond QCD Fits from HERA-I H1 PDF 1997 Eur. Phys. J C21 (2001) H1 PDF 2000 Eur. Phys. J C30 (2003) ZEUS-S Phys. Rev. D67 (2003) ZEUS-JETS Eur. Phys. J C42 (2005) Data from other exp BCDMS (μp)----BCDMS,NMC,E665, CCFR (μp, μd, νFe) ---- Fitted distributions ep valence and sea terms 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 Q 0 2 starting scale for parameterization, cuts for perturbative phase space (Q 2 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 α s, g(x) pdfspdfs, α s

N. RaicevicMoriond QCD 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

N. RaicevicMoriond QCD Strong Coupling Constant - α s  Inclusion of jet data significantly improves α s  Δα s (th.) = ± mainly due to the uncertainty of the renormalisation scale  NNLO QCD analysis  NNLO calculations available (hep-ph/ , )

N. RaicevicMoriond QCD H1 Combined QCD and EW fit  Determination of light quark axial ( a u, a d ) and vector (v u, v d ) couplings to Z-boson for the first time at HERA (all HERA-I data)  Combined fit of a u, v u, a d, v d 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: a q = I q 3 a u = +1/2, a d = -1/2 V q = I q 3 – 2e q sin 2 θ W H1 Collaboration, Phys. Lett. B632 (2006) More sensitivity to a u then to v u _

N. RaicevicMoriond QCD Improvements on PDFs expected with HERA-II should come from :  Higher precision measurements of F 2 and CC cross section  Precise measurement of xF 3  Direct measurement of F L  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 – xF 3 When enough statistics  possible consistency check of valence contribution _ xF 3 ~ σ - NC – σ + NC xF 3 = -a e K z xF 3 γZ + Z-exchange xF 3 γZ ~ 2x Σ q e q a q ( q – q ) ~ q v ~ ~ x

N. RaicevicMoriond QCD  Gluon distributions obtained in global NLO analysis Direct measurement of F L require runs with lower proton beam energy:  For the same (Q 2,x) σ r to be measured from different beam energies (i.e. y)  Perform straight line fit of σ r vs f(y) to extract F 2 and F L Longitudinal SF - F L  From pQCD  Much more precise input for low-x gluon distribution is necessary  via precise measurement of F L xg(x) ~F L (at very low x) x σrσr f(y) 01 F2F2 F 2 -F L σ r = F 2 (x,Q 2 ) – f(y) F L (x,Q 2 )  High precision measurement of F L can be only achieved by measuring it directly · · ·

N. RaicevicMoriond QCD 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

N. RaicevicMoriond QCD extras

N. RaicevicMoriond QCD General Fitting Procedure for PDF extraction  Parametrisation of PDFs at starting scale Q 0 2 Some parameters constrained by the number and momentum sum rules  Evolve in Q 2 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

N. RaicevicMoriond QCD H1 QCD Analysis  Data: 8·10 -5 < x < 0.65, 1.5 < Q 2 < GeV 2  Q 2 0 = 4 GeV 2, Q 2 min = 3.5 GeV 2  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 χ 2 saturation  Fit performed in ZERO MASS scheme (appropriate for high Q 2 )  Use H1+BCDMS p and D data as a cross check __ _ Bellow bottom threshold ___ Χ 2 /ndf = 0.88 __

N. RaicevicMoriond QCD 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 = 9/4u v + 3/2d v xA = u + ¼(u v + 2 d v ) F 2 = 1/3xV + 11/9xA  Use massive 3-flavour number scheme H1 QCD Analysis, g(x) and α s

N. RaicevicMoriond QCD ZEUS Only QCD Analysis  Data: 6.3· GeV 2 (W 2 > 20 GeV 2 – removes higher twists)  Q 2 0 = 7 GeV 2, Q 2 min = 2.5 GeV 2  Parameterisation of: xu v, xd v, xg, Sea, xΔ = x(d – u) - fix A Δ 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 (c s and c g ) __

N. RaicevicMoriond QCD ZEUS-JETS QCD Analysis A complete NLO calculation for jet cross sections for each iteration of the χ 2 minimisation is extremely slow. Method: 1.Use NLO QCD program initially to produce grid of weights (x,μ F 2 ), 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: GeV, -2 < η B jet < 1.8 γp dijets: E T jet1,(2) > 14 (11) GeV, , 134 < W 2 γp < 277 GeV 2 Now, direct information on gluon available  gluon parameters free Χ 2 /ndf = 0.81 Direct-process enriched region

N. RaicevicMoriond QCD Extracted PDFs