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PDF Structure and Functions at HERA: Insights and Outlook

Learn about the structure and functions of PDFs at HERA, including DIS physics, QCD fits, and PDF extraction. Explore the contributions of HERA-I and HERA-II data, improvements in PDFs, and the combined QCD and electro-weak fit. Discover the impacts on LHC predictions and gluon density constraints from JETS events.

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PDF Structure and Functions at HERA: Insights and Outlook

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  1. Structure Functions and Extraction of PDFs at HERANataša RaičeviċUniversity of MontenegroOn behalf of the H1 and ZEUS Collaborations • 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 XLIst Recontres de Moriond, QCD and Hadronic Interactions La thuile, March 18th – 25th, 2006 Moriond QCD 2006

  2. HERA Luminosity per experiment, roughly In 2000-2002 HERA-I upgraded to HERA-II • Increased luminosity • Polarised leptons - new feature of HERA • HERA will run until summer 2007 Moriond QCD 2006

  3. Inclusive Deep Inelastic Scattering (DIS) Neutral Current (NC) H1 NC event display Virtuality of exchanged boson: Fraction of proton momentum carried by struck quark Charged Current (CC) ZEUS CC event display Fraction of energy transferred from incoming lepton at proton rest frame Moriond QCD 2006

  4. Cross Sections and Structure Functions Neutral current cross section • NC reduced cross-section Z-exchange γ-exchange γZ-interference • dominant contribution Generalised Structure Functions (SF) - importantonly at high Q2 FL = (Q2/4πα)σL • sizable contribution for high y FL = 0 In the Quark Partom Model (QPM): SFs Moriond QCD 2006

  5. FL ~ αs ·xg(x,Q2) In pQCD: - Parton Density Functions - PDFs dvat high x Charged current cross section (LO) Sensitivity to the flavor of the valence distributions at high x uvat high x - CC reduced cross-section • 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) Moriond QCD 2006

  6. Main Inputs from HERA-I Data for the PDF Extraction _ F2em(x,Q2) ~ Σq eq2(q + q) δF2/F2 ~ 2-3% Q2 / GeV2 Moriond QCD 2006 δF2/F2 ~ 30%

  7. Measurements of CC Cross Sections from HERA-II with Longitudinally Polarised Beams H1 Collaboration , Phys. Lett. B 634 (2006), ZEUS Collaboration , DESY-06-015 (February 2006) - submitted to Physics Letters B • SM: • Linear dependence of CC cross section on Pe • s±(Pe) = (1±Pe)s±(Pe=0) • ZEUS and H1 measurements in agreement with SM •  no right handed charged currents Textbook measurements Moriond QCD 2006

  8. Measurements of NC Cross Sections with HERA-II with Longitudinally Polarised Beams ZEUS Collaboration , DESY-06-015 (February 2006) - submitted to Physics Letters B • 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 Moriond QCD 2006

  9. 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 Moriond QCD 2006

  10. Additional Constrains on Gluon Density from JETS Events with distinct jets in the final state Sensitive to αs and quark/gluondensity • 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) • Jet data constrain g(x) at medium and high-x (0.01-0.4) Moriond QCD 2006

  11. QCD Fits from HERA-I • In global fits main contributions from HERA data from low-x sea and gluon 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 QCD analysis requires many choices to be made: Q02 starting scale for parameterization, cuts for perturbative phase space (Q2min) , 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 Moriond QCD 2006

  12. Extracted PDFs • Still large uncertainties on gluon • density and on d density at large x • Results broadly consistent within • uncertainties (also consistent with • global fitters) Moriond QCD 2006

  13. 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) Moriond QCD 2006

  14. H1 Combined QCD and EW fit H1 Collaboration, Phys. Lett. B632 (2006) 35-42 • Determination of light quark axial (au, ad) and vector (vu, vd) couplings to Z-bosonfor the first time at HERA (all HERA-I data) • Combined fit of au, vu, ad, vd and PDFs (H1 PDF 2000 scheme) Standard Model: aq = Iq3 au = +1/2, ad = -1/2 Vq = Iq3 – 2eqsin2θW _ More sensitivity to au then to vu  H1 measurement determine sign of precise measurements from LEP  HERA-II will bring improvement with statistics and polarisation Moriond QCD 2006

  15. SF – xF3 Improvements on PDFs expected with HERA-II shouldcome from: ~ xF3 ~ σ-NC – σ+NC xF3 = -aeKzxF3γZ + Z-exchange xF3γZ ~ 2x Σqeqaq( q – q ) ~ qv ~ • 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) _ x When enough statistics  possible consistency check of valence contribution Moriond QCD 2006

  16. Longitudinal SF - FL  Gluon distributions obtained in global NLO analysis • Much more precise input for low-x gluon distribution is necessary  via precise measurement of FL xg(x) ~FL (at very low x) • FrompQCD • High precision measurement of FL can be • only achieved by measuring it directly x σr = F2(x,Q2) – f(y) •FL(x,Q2) • Direct measurement of FLrequire • runs with lower protonbeam 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 σr · · · F2 F2-FL 0 1 f(y) Moriond QCD 2006

  17. 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 Moriond QCD 2006

  18. extras Moriond QCD 2006

  19. 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 Moriond QCD 2006

  20. H1 QCD Analysis • Data: 8·10-5 < x < 0.65, 1.5 < Q2 < 30000 GeV2 • Q20 = 4 GeV2, Q2min = 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 Moriond QCD 2006

  21. H1 QCD Analysis, g(x) and αs • 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 Moriond QCD 2006

  22. 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, Q2min = 2.5 GeV2 • Parameterisation of: xuv, xdv, xg, Sea, xΔ = x(d – u) • - fix AΔconsistent 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) Moriond QCD 2006

  23. ZEUS-JETS QCD Analysis DIS jets: 125 < Q2 < 30000 GeV2, EBT,jet > 8 GeV, -2 < ηBjet < 1.8 γp dijets: ETjet1,(2) > 14 (11) GeV, -1 < ηjet1,2 < 2.4, xγobs > 0.75, 134 < W2γp < 277 GeV2 Direct-process enriched region • A complete NLO calculation for jet cross sections for each iteration of the χ2 • minimisation is extremely slow. • Method: • 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: Χ2/ndf = 0.81 Grid cross section reproduce real NLO predictions to better than 0.5% Now, direct information on gluon available  gluon parameters free Moriond QCD 2006

  24. Extracted PDFs Moriond QCD 2006

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