1. High Q 2 Structure Functions and Parton Distributions Ringberg Workshop 2003 : New Trends in HERA physics Benjamin Portheault LAL Orsay On behalf of the Zeus and H1 Collaborations

2. I. Introduction The legacy of HERAI : What do we learn ? II. Structure Function Results State of the art of Zeus and H1 inclusive measurements III. Extraction of parton distributions H1 and Zeus schemes Motivation and necessity for a common fit IV. Overview of present (and future) possibilities Towards a H1+Zeus Fit A brief look at Mw

3. Deep Inelastic Scattering At leading order in the EW interaction : The QCD factorization theorem allows to express the structure functions as convolutions of universal parton density functions (p.d.fs) and perturbatively computable kernels dominant high y high Q 2

4. Through the measurement of high Q 2 inclusive Cross Section : We can measure/extract structure functions Test the structure of the EW interaction (and look for new physics) Use fits to test the pQCD evolution and Measure the universal p.d.fs An HERA QCD analysis can also be used to Extract p.d.fs and the EW parameters (,…) For  s and the gluon measurements and prospects see talk by V. Shekelian

5. low Q 2 high Q 2 (F 2 ) (xF 3 ) The HERA EW plot Charged Current parton distributions helicity factor

6. The HERA QCD plot beautiful Scaling Violations HERA data Far from fixed target precision at high x (stat. lim.) Important for QCD evolution BCDMS  F2/F2~7% HERA typical  F2/F2 ~2-3%  F2/F2~30% Interesting Region for exotic searches

7. xF3 contribution changes sign between e+/e- (by definition) Extraction done by subtraction

8. suppressed (<3% contribution to xF 3 ) access to valence p.d.fs evolved to the same Q 2 ~30% error, dominated by e - statistics xF 3  Z

9. Direct constraint on d at high x Typical systematic errors are ~6%

10. Direct constraint on u at high x Both e + and e - Cross sections Are necessary For flavor separation in QCD fits

11. extraction with from fitmeasured extend CCFR measurement uncertainty from e - statistics

12. H1 & Zeus QCD Fits Zeus Fits : ZEUS-Standard Use Zeus NC 96/97 e + BCDMS, NMC, E665 proton data NMC,E665 deuterium data, CCFR xF 3 iron data For high x constraint and better flavor separation ZEUS-Only Use only Zeus data NC and CC e + and e - up to 99 The number of d.o.f. is reduced by fixing parameters Both use TR Variable Flavour Scheme H1PDF2000 and H1+BCDMS Use only H1 data (all HERAI NC and CC high Q 2 +low Q 2 96/97) Massless Flavour Scheme

13. Too much freedom to constrain all these parton densities with H1 alone or Zeus alone Need for additional assumptions or data Fixes parameters robust scheme Use internal constraints Between parameters Not constrained by HERA data Assumptions are needed (parameters fixed/constrained) Zeus H1

14. Error determination Both fits handle (differently) correlated systematic errors in parameter determination and error estimate H1 : Pascaud-Zomer method Zeus : offset method (uses external data sets) Only a proper treatment of the these correlated Systematic error allow the application Of a error estimate See talk by J. Pumplin

15. The Art of parameterization At the (low) scale Q 0 2 parton distributions are Parameterized with It is not trivial to have P(x) such that the fit is flexible enough and stable Errors (and distributions) depend on the parametric form chosen One also has to be kind enough with MINUIT as the fit is non-linear (dependency upon the starting parameters …) Any choice is arbitrary (nature do not choose a parametric form) low xhigh x

16. Results on parton distributions u type quark distribution precision is 1% for x=0.001 and 7% for x=0.65 (H1PDF2000) d type quark distribution precision is 2% for x=0.001 and 30% for x=0.65 (H1PDF2000) Sea distribution precision is 5% between x=10 -4 and 10 -1 (ZEUS-S) Good achievement but the fits are at the edge of the fitting possibilities Use all HERA data to gain in flexibility

17. Reasonable agreement between the fits given the different Data and fitting schemes

18. HERA data and global fits The HERA data are highly valuable for global analysis of Parton distributions : Crucial low x constraint on quarks and antiquarks, gluon High y data also constraining gluons The knowledge and understanding of the correlated systematic errors of HERA data made then central in any of parton distributions analysis Reliable error determination The CTEQ and MRST will benefit from including the 99/00 Zeus and H1 data in their fits

19. Towards HERA fits Now (nearly) all Zeus and H1 data sets are available The Zeus and H1 data are in very good agreement (in the sense of global parton distribution analysis) Test of the Zeus data with H1PDF2000 : Data set NC e+ low Q2 104/75 NC e+ highQ2 210/162 CC e+ 19/29 NC e- 53/92 CC e- 23/26 /ndata 96/97 98/99 NB : Zeus systematics fitted

20. Potential of an HERA fit Fit procedure using less technical assumptions Combination could help a lot on technical fit aspects (we can also run into new problems) And a meaningful for error determination Extensive studies must be made e.g. for the choice of parametric forms (and settle if the HERA gluon is ‘H1 like’ or ‘Zeus like’, see talk by V. Shekelian) As a proof of principle : Prospects using a case study fit of Zeus+H1 data (except Zeus 99/00 data) The Mw mass measurement

21. To confront the SM with experimental data one needs to specify several parameters: The On Mass Shell (OMS) scheme uses masses as an input: Whereas the Modified OMS uses: Electroweak reminder The couplings of leptons to the Z 0 and its propagator normalisation also depend on the scheme

22. Several strategies are possible : It is possible to fit Mw to the CC cross section As a ‘propagator mass’ with fixed Structure Functions (used by Zeus and H1) Or fit Mw together with the p.d.fs OMS scheme, Mw as propagator mass and normalisation ( error estimate, similar to  s ) HERA fit (no Zeus 99/00,  r fixed) H1PDF2000 scheme Fitting strategies for

23. Results and expected sensitivity experimental error only (central value consistent with world average) Significant improvement Still far from world average (not so far from NuTeV alone or D0 alone ~80 MeV uncertainty) HERA fit

24. Results and expected sensitivity Major improvements in sensitivity Could be better using Zeus 99/00 Unfortunately a significant theoretical error may be present even with better data But still far from world average : HERA is not an electroweak facility QCD (EW) common fits should start now to prepare the strong physics message of HERAI+II on p.d.fs and SM parameters

25. Conclusion Many cornerstone results in DIS have been achieved by HERAI. DIS NC and CC differential cross sections are measured with reasonable precision. High statistics (and polarization) would bring more accuracy Has already been turned into many physics results through QCD Fits The potential for the results still unexploited: Zeus-H1 common fit is absent and needed to settle important physics issues (pdfs,  s, gluon, …)