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Structure, Function, and Measurements of PDFs and Strong Coupling Constant

This paper discusses the structure, function, and measurements of Parton Distribution Functions (PDFs) and the strong coupling constant. It covers topics such as deep inelastic scattering, scaling violations, cross-sections, kinematic plane coverage, theoretical predictions, PDF fits, and the determination of the strong coupling constant.

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Structure, Function, and Measurements of PDFs and Strong Coupling Constant

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  1. Structure function measurements and what they tell us about PDFs and the strong coupling constant Tomáš Laštovička (H1 collaboration) DESY Zeuthen, Charles University Prague at LLWI2003, Lake Louise, Canada H1 and ZEUS Structure functions at HERA αs and PDFs Summary/Outlook

  2. H1 and ZEUS at HERA • HERA at DESY, Hamburg • ep accelerator ring, 27.5 x 920 GeV • circumference: 6.3km • 4 experiment halls ZEUS H1 Tomas Lastovicka, LLWI 2003

  3. H1 and ZEUS experiments • nearly aparatus • delivering data since early 90ies 2 • recently both experiments upgraded Tomas Lastovicka, LLWI 2003

  4. Deep Inelastic Scattering Four-momentum transfer squared: Bjorken scaling variable: Inelasticity scaling variable: Centre of mass energy squared: Tomas Lastovicka, LLWI 2003

  5. Dominant contribution Sizeable only at high y (y>~0.6) Contribution only important at high Q2 CC Reduced cross section: Cross-sections and Structure Functions NC Cross Section: NC Reduced cross section: CC Cross Section: Tomas Lastovicka, LLWI 2003

  6. DIS slang reminder low Q2- transition domain from non-perturbative domain to deep inelastic domain strong coupling is large, limits of pQCD high Q2- strong coupling is relatively small pQCD calculations reliable xF3 and CCenter the game at large Q2 low x (high y)- driven by gluons sea (confinement) region longitudinal str. function FL unique acceptance by H1 high x (low y)- driven by quarks valence quark region fixed target experiments Tomas Lastovicka, LLWI 2003

  7. Kinematic plane coverage • covered almost to the limits of phase space • compared to fixed target experiments, measurements extend to high Q2 and high y by more than 2 orders of magnitude Tomas Lastovicka, LLWI 2003

  8. The Structure Function F2 • F2 is not calculable from the first principles • Various theoretical predictions a decade ago • during its running HERA made an impressive progress • - directly related to quark densities 1993 2000 Tomas Lastovicka, LLWI 2003

  9. The Structure Function F2 Tomas Lastovicka, LLWI 2003

  10. Scaling violations of F2 • at low x driven by gluons • described by QCD: DGLAP evolution equations • many open questions: • does F2 saturate? when gluon density is large -> gluon fusion • low Q2 region • QCD analysis digests quarks and gluon densities from fits to F2 (parametrised at an initial scale, then DGLAP evolution takes over) e.g. Tomas Lastovicka, LLWI 2003

  11. CC and NC measurements • Standard model describes both NC and CC very well over a large range of Q2 • Electroweak unification at about MZ2 scale • e+ and e- cross sections different due to different quark contribution and helicity structure of EW interactions Tomas Lastovicka, LLWI 2003

  12. xF3 and FL measurements • xF3 errors dominated by stat. errors, higher luminosity needed • FL not measured directly, runs at different beam energies needed Tomas Lastovicka, LLWI 2003

  13. PDF fits and the strong coupling • Choice of data sets used • Treatment of experimental systematic uncertainties • Q02 starting scale • Q2min of data included in fit • Renormalisation / factorisation scales • Choice of densities to parameterise • Allowed functional form of PDF parameterisation • Cuts to limit analysis to perturbative phase space • Treatment of heavy quarks • etc... QCD analyses require many choices to be made Should be reflected in PDF uncertainty: Tomas Lastovicka, LLWI 2003

  14. Results on the strong coupling constant • H1 0.1150+-0.0017(exp) +0.0009 -0.0007(model) EPJ C21(01)33 H1 + BCDMS precise data if: systematíc errors are not fitted: +0.0005 NMC replaces BCDMS 0.116+-0.003 (exp) 4 light flavours: +0.0003 BCDMS deuteron data added: 0.1158 +- 0.0016 (exp) • ZEUS 0.1166+-0.0008(unc) +-0.0032(corr) +-0.0036(norm) +-0.0018(model) p:BCDMS,NMC,E665 d:NMC,E665 d/p: NMC xF3: CCFR systematíc errors are not allowed to vary in chi2 minimisation Q2>2.5 GeV2, W2>20GeV2, RT-VFNS, b(uv)=1/2, b(dv)=1/2 fit alphas, xg, uv, dv, sea, dbar-ubar (MRST) if fixed flavour scheme is used: +0.0010 Phys.Rev. D67(03) large chi2 variations if Q2 (¼ .. 4) Q2 renormalisation scale:+-0.005 (H1)  (½ .. 2) : +- 0.004 (ZEUS) not included in error Tomas Lastovicka, LLWI 2003

  15. Parton distribution functions from NLO QCD fits (ZEUS) uv dv Sea, g • xg and Sea distributions determined by low x / Q2 HERA F2 data • xuv determined from high x NC data • xdv determined from high x CC e+ data Tomas Lastovicka, LLWI 2003

  16. Parton distribution functions from NLO QCD fits (H1) CC and NC cross sections are sensitive only to U, antiU, D,antiD (F2N has c-s admixture) H1+BCDMS H1 only uv, dv, sea are replaced by the observables !possible to determine PDFs with H1 data alone (with assumption on sea symmetry) H1 ICHEP02 Tomas Lastovicka, LLWI 2003

  17. Parton distribution functions from NLO QCD fits H1 vs ZEUS comparison of PDFs independent fits, different approaches only experimental errors! (matter of choice) ~3% ~10% Tomas Lastovicka, LLWI 2003

  18. NLO gluon momentum density fixed flavour number scheme Laenen, Riemersma, Smith, vanNeerven needs precision data at low Q2, all x! needs precision FL measurement! H1 EPJ C21(01)33 Tomas Lastovicka, LLWI 2003

  19. New low Q2 measurements low Q2 1999 dedicated run low Q2 x-section and F2 determination at low x shifted vertex 2000 run Transition region between perturbative and non-perturbative kinematic range Tomas Lastovicka, LLWI 2003

  20. New measurements at low Q2, small x Extended phase space: Data fill the gap in pre- cision measurements around Q2~1GeV2 and extend phase space to higher y at all Q2 (till 12 GeV2) srchanges behavior at high y (small x) gFL signature (even at very low Q2) Data with Q2g0: Valuable for studying underlying dynamics of DIS → γp Tomas Lastovicka, LLWI 2003

  21. Rise of F2 towards low x • H1 / ZEUS / NMC data used to fit Q2 dependencies for x<0.01 : • Behaviour is changing at around 1 GeV2 • Theory expects λ to reach value of ~0.08 for Q2 → 0 • No sign of saturation at small x observed (yet) Tomas Lastovicka, LLWI 2003

  22. Summary (concluding remarks) • First phase of HERA running delivered many interesting results • Precision of ~2−3 % achieved for F2 • The inclusive DIS data at HERA are confronted with NLO QCDanalysesQCD (the DGLAP equations) is able to describe all the cross section data: e+p, e-p, NC, CC in a wide kinematical range: both Q2 & x covering 5 orders of magnitude • extracted from DIS data is competetive with the worldaverage • Fits allow HERA data to constrain PDFs • HERA 2 (after luminosity upgrade): high precision xF3direct measurement of FL • The next important step: e-d runs (dv/uv at high x),HERA 3?! Tomas Lastovicka, LLWI 2003

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