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

2. Tomas Lastovicka, LLWI 2003 2/22 H1 and ZEUS at HERA HERA at DESY, Hamburg ep accelerator ring, 27.5 x 920 GeV circumference: 6.3km 4 experiment halls H1 ZEUS

3. Tomas Lastovicka, LLWI 2003 3/22 H1 and ZEUS experiments nearly aparatus delivering data since early 90ies recently both experiments upgraded 2

4. Tomas Lastovicka, LLWI 2003 4/22 Deep Inelastic Scattering Bjorken scaling variable: Centre of mass energy squared: Inelasticity scaling variable: Four-momentum transfer squared:

5. Tomas Lastovicka, LLWI 2003 5/22 Dominant contribution Sizeable only at high y (y>~0.6) Contribution only important at high Q 2 Cross-sections and Structure Functions NC Cross Section: CC Cross Section: CC Reduced cross section: NC Reduced cross section:

6. Tomas Lastovicka, LLWI 2003 6/22 DIS slang reminder low Q 2 - transition domain from non-perturbative domain to deep inelastic domain strong coupling is large, limits of pQCD low x (high y) - driven by gluons sea (confinement) region longitudinal str. function F L unique acceptance by H1 high x (low y) - driven by quarks valence quark region fixed target experiments high Q 2 - strong coupling is relatively small pQCD calculations reliable xF 3 and CC enter the game at large Q 2

7. Tomas Lastovicka, LLWI 2003 7/22 Kinematic plane coverage   covered almost to the limits of phase space   compared to fixed target experiments, measurements extend to high Q 2 and high y by more than 2 orders of magnitude

8. Tomas Lastovicka, LLWI 2003 8/22  F 2 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 The Structure Function F 2 1993 2000

9. Tomas Lastovicka, LLWI 2003 9/22 The Structure Function F 2

10. Tomas Lastovicka, LLWI 2003 10/22 Scaling violations of F 2   at low x driven by gluons   described by QCD: DGLAP evolution equations   many open questions:   does F 2 saturate? when gluon density is large -> gluon fusion   low Q 2 region   QCD analysis digests quarks and gluon densities from fits to F 2 (parametrised at an initial scale, then DGLAP evolution takes over) e.g.

11. Tomas Lastovicka, LLWI 2003 11/22 CC and NC measurements  Standard model describes both NC and CC very well over a large range of Q 2  Electroweak unification at about M Z 2 scale  e + and e - cross sections different due to different quark contribution and helicity structure of EW interactions

12. Tomas Lastovicka, LLWI 2003 12/22 xF 3 and F L measurements xF 3 errors dominated by stat. errors, higher luminosity needed F L not measured directly, runs at different beam energies needed

13. Tomas Lastovicka, LLWI 2003 13/22 PDF fits and the strong coupling  Choice of data sets used  Treatment of experimental systematic uncertainties  Q 0 2 starting scale  Q 2 min 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:

14. Tomas Lastovicka, LLWI 2003 14/22 Results on the strong coupling constant EPJ C21(01)33 H1 0.1150 +- 0.0017(exp) + 0.0009 - 0.0007(model) 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) large chi 2 variations if Q 2  (¼.. 4) Q 2 renormalisation scale:+-0.005 (H1)  (½.. 2) : +- 0.004 (ZEUS) not included in error 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 GeV 2, W2>20GeV 2, 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)

15. Tomas Lastovicka, LLWI 2003 15/22 Parton distribution functions from NLO QCD fits (ZEUS)   xg and Sea distributions determined by low x / Q 2 HERA F 2 data   xu v determined from high x NC data   xd v determined from high x CC e + data dvdv uvuv Sea, g

16. Tomas Lastovicka, LLWI 2003 16/22 CC and NC cross sections are sensitive only to U, antiU, D,antiD (F2N has c-s admixture) H1+BCDMS H1 only u v, d v, sea are replaced by the observables ! possible to determine PDFs with H1 data alone (with assumption on sea symmetry) Parton distribution functions from NLO QCD fits (H1) H1 ICHEP02

17. Tomas Lastovicka, LLWI 2003 17/22 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%

18. Tomas Lastovicka, LLWI 2003 18/22 NLO gluon momentum density H1 EPJ C21(01)33 fixed flavour number scheme Laenen, Riemersma, Smith, vanNeerven needs precision data at low Q 2, all x! needs precision F L measurement!

19. Tomas Lastovicka, LLWI 2003 19/22 New low Q 2 measurements low Q 2 1999 dedicated run Transition region between perturbative and non-perturbative kinematic range shifted vertex 2000 run low Q 2 x-section and F 2 determination at low x

20. Tomas Lastovicka, LLWI 2003 20/22 New measurements at low Q 2, small x Extended phase space: Data fill the gap in pre- cision measurements around Q 2 ~1GeV 2 and extend phase space to higher y at all Q 2 (till 12 GeV 2 )  r changes behavior at high y (small x)  F L signature (even at very low Q 2 ) Data with Q 2  0: Valuable for studying underlying dynamics of DIS → γp

21. Tomas Lastovicka, LLWI 2003 21/22 Rise of F 2 towards low x   H1 / ZEUS / NMC data used to fit Q 2 dependencies for x<0.01 :   Behaviour is changing at around 1 GeV 2   Theory expects λ to reach value of ~0.08 for Q 2 → 0   No sign of saturation at small x observed (yet)

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