1. ZEUS PDF analysis 2004 A.M Cooper-Sarkar, Oxford Low-x 2004 New Analysis of ZEUS data alone using inclusive cross-sections from all of ZEUS data from HERA-I – 112pb -1 Proton target data –no heavy target or deuterium corrections Information on d-valence at high-x Analysis within one experiment – well understood systematic errors New analysis of ZEUS data alone including jet data from inclusive jet production in DIS and dijet production from photoproduction Extraction of α s and PDFs simultaneously ICHEP04 Paper 5-0294, hep-ph/0407309 (DIS2004)

2. Now, after the HERA I phase (1994-2000) of data-taking, the full set of e + and e - inclusive Neutral Current (NC) and Charged Current (CC) cross sections are available for QCD analysis Q 2 = -(k-k’) 2 xpxp Deep Inelastic Scattering x = momentum fraction of proton carried by quark (HERA: 10 -6 ~ 1) Q 2 = “resolving power” of probe

3. C HERA data covers a large region in (x,Q 2 )  Also in relevant x-region for LHC physics

4. The HERA contribution- at low-x F 2 dominates cross section  direct information on quarks  Information on gluon and sea through QCD radiation (scaling violations) at low-x But higher-Q2 data have been accumulating→high-x And this matters for PDF fits→ Consequences for low-x BCDMS:  F 2 /F 2 ~7% HERA:  F 2 /F 2 ~30% Typically 2-3% precision

5. HERA at high Q 2  Z 0 and W +/- exchanges become important for NC processes F 2 = 3 i A i (Q 2 ) [xq i (x,Q 2 ) + xq i (x,Q 2 )] xF 3 = 3 i B i (Q 2 ) [xq i (x,Q 2 ) - xq i (x,Q 2 )] A i (Q 2 ) = e i 2 – 2 e i v i v e P Z + (v e 2 +a e 2 )(v i 2 +a i 2 ) P Z 2 B i (Q 2 ) = – 2 e i a i a e P Z + 4a i a e v i v e P Z 2 P Z 2 = Q 2 /(Q 2 + M 2 Z ) 1/sin 2  W  Z exchange gives a new valence structure function xF 3 measurable from low to high x- on a pure proton target

6. At High Q2 there are also significant cross-sections for CC processes which give flavour information d 2  (e - p) = G F 2 M 4 W [x (u+c) + (1-y) 2 x (d+s)] dxdy 2  x(Q 2 +M 2 W ) 2 d 2  (e + p) = G F 2 M 4 W [x (u+c) + (1-y) 2 x (d+s)] dxdy 2  x(Q 2 +M 2 W ) 2 u v at high x d v at high x Measurement of high x, d-valence on a pure proton target. NC processes dominantly measure u- valence. Fixed target measurement of d-valence is from Fe/Deuterium target – needs corrections even for Deuterium Typical systematic uncertainties are ~ 6%

7. ANALYSES FROM HERA ONLY …  Systematics well understood  measurements from our own experiments !!!  No complications from heavy target Fe or D corrections GlobalHERA Only ValencePredominantly fixed target data ( -Fe and  D/  p) High Q 2 NC/CC e  cross sections SeaLow-x from NC DIS High-x from fixed target Flavour from fixed target Low-x from NC DIS High-x less precise Flavour ?(need assumptions GluonLow-x from HERA dF 2 /dlnQ 2 High-x from momentum sum Both ZEUS (2004) and H1 (2003) now make PDF fits to their own data MRST, CTEQ (and ZEUS 2002) make global fits to HERA data, fixed target DIS data etc. Where does the information come from in a global fit compared to a HERA only fit ? Tevatron jet data?ZEUS jet data? Mostly uv some dv

8. 96/97 e+p NC 30 pb -1 2.7 < Q2 < 30000 GeV 2 Eur.Phys.J. C21(2001)443 94-97 e+p CC 33 pb -1 280. < Q2 < 30000 GeV 2 Eur Phys J C12(2000)411 98/99 e-p NC 16 pb -1 200 < Q2 < 30000 GeV 2 Eur Phys J C28 (2003)175 98/99 e-p CC 16 pb -1 200 < Q2 < 30000 GeV 2 Phys Lett B539(2002)197 99/00 e+p NC 63 pb -1 200 < Q2 < 30000 GeV 2 hep-ex/0401003- Phys.Rev.D 99/00 e+p CC 61 pb -1 200 < Q2 < 30000 GeV 2 Eur Phys J C32(2003)16 χ2 = Σ i [ F i NLOQCD (p) + Σ λ s λ Δ iλ sys – F i (meas)]2 + Σ λ s λ 2 ( σ i 2 stat + σ i 2 unc ) χ2 must account for correlated systematic errors AND normalizations Total of 33 sources of point to point correlated errors and 4 normalizations Applied conservatively by OFFSET method see J.Phys.G 28(2002) 2717 Now use ALL inclusive cross-section data from HERA-I 112 pb -1

9. xuv(x) = Au x av (1-x) bu (1 + c u x) xdv(x) = Ad x av (1-x) bd (1 + c d x) xS(x) = As x as (1-x) bs (1 + c s x) xg(x) = Ag x ag (1-x) bg (1 + c g x) xΔ(x) = x(d-u) = AΔ x av (1-x) bs+2 Model choices  Form of parametrization at Q 2 0, value of Q 2 0,, flavour structure of sea, cuts applied, heavy flavour scheme Recap of the method Parametrize parton distribution functions PDFs at Q 2 0 (= 7 Gev 2) Evolve in Q 2 using NLO DGLAP (QCDNUM 16.12) Convolute PDFs with coefficient functions to give structure functions and hence cross-sections Coefficient functions incorporate treatment of Heavy Quarks by Thorne- Roberts Variable Flavour Number Fit to data under the cuts, W 2 > 20 GeV 2 (to remove higher twist), 30,000 > Q 2 > 2.7 GeV 2 x > 6.3 10 -5 ←Use of NLO DGLAP?

10. xuv(x) = Au x av (1-x) bu (1 + c u x) xdv(x) = Ad x av (1-x) bd (1 + c d x) xS(x) = As x as (1-x) bs (1 + c s x) xg(x) = Ag x ag (1-x) bg (1 + c g x) xΔ(x) = AΔ x av (1-x) bs+2 Major source of model dependence is the form of the parametrization at Q 2 0 These parameters control the low-x shape These parameters control the high-x shape These parameters control the middling-x shape No χ2 advantage in more terms in the polynomial No sensitivity to shape of Δ= d – u AΔ fixed consistent with Gottfried sum-rule - shape from E866 Assume s = (d+u)/4 consistent with ν dimuon data Au, Ad, Ag are fixed by the number and momentum sum-rules au=ad=av for low-x valence since there is little information to distinguish → 12 parameters for the PDF fit Now consider the high-x Sea and gluon

11. Consider the uncertainties for uv, dv, Sea and glue in the ZEUS-S 2002 global fit High-x Sea and Gluon are considerably less well determined than high-x valence (note log scales) even in a global fit - this gets worse when fitting ZEUS data alone uvdvSeaGluon uv and dv are now determined by the ZEUS highQ2 data not by fixed target data and precision is comparable- particularly for dv Sea and gluon at low-x are determined by ZEUS data with comparable precision for both fits – but at mid/high-x precision is much worse Compare the uncertainties for uv, dv, Sea and glue in a fit to ZEUS data alone

12. STRATEGY A: Constrain high-x Sea and gluon parameters xf(x) = A x a (1-x) b (1 + c x) The fit is not able to reliably determine both b and c parameters for the Sea and the gluon – these parameters are highly correlated We could either 1.Choose a simpler parametrization: xf(x) = A x a (1-x) b (e.g H1, Alekhin) 2.Fix parameter b to the value from the ZEUS-S global fit, and vary this value between the one σ errors determined in that fit xf(x) = A x a (1-x) b±Δb (1+cx) Choice 1. would not allow structure in the mid x Sea/gluon distributions even in principle (recall the difference in H1 and ZEUS published gluons) Thus choice 2 is made for the central 10 parameter ZEUS – Only fit In practice choice 1. and 2. give very similar results

13. Zeus-Only H1-Only Zeus and H1 gluons are rather different even when these data are used in the same analysis - AMCS

14. Compare valence partons for ZEUS-S global fit and ZEUS ONLY 2004 fit 1.Global fit uncertainty is systematics dominated whereas ZEUS-Only fit is statistics dominated- much improvement expected from HERA-II, particularly if there is lower energy running to access higher-x 2.ZEUS-Only fit uses proton target data only- particularly important for dv ZEUS-S Global 2002ZEUS-Only 2004

15. Blue hatched band represents model uncertainties with contributions from varying: –Starting scale Q 0 2 –Form of parameterisation –Values of c g and c S  Compatible with ZEUS-S global fit low-x information comes from HERA data anyway high-x compatibility by construction Valence-like gluon at low-x Gluon and Sea from ZEUS-Only 2004 fit

16. And compare ZEUS-Only 2004 PDFs to published ZEUS-S 2002 PDFs including error analyses

17. STRATEGY B: Use more data to tie down the high-x gluon What data? Jet cross sections are directly sensitive to gluon through Boson-Gluon-Fusion process  Use published ZEUS Jet production data from 96/97 40 pb -1 Inclusive jet cross-sections vs E T (Breit) for DIS in bins of Q 2 Phys Lett B547(2002)164 Di-jet photproduction cross-sections vs E T (lab) in bins of rapidity for direct photons (x γ > 0.75) Eur Phys J C23(20020615

18. How? NLO QCD predictions for jet production: DISENT for DIS jets, FRIXIONE and RIDOLFI for photoproduced di-jets are too slow to be used every iteration of a fit. Use NLO QCD program initially, to produce grid of weights in (x,  F 2 ), giving perturbatively calculable part of cross section Then convolute with PDFs to produce fast prediction for cross section: This is how well the grids reproduce the predictions – to 0.05% Where c a,n = weight ; f a = PDF of parton a The DIS predictions must also be multiplied by hadronization corrections and Z O corrections The calorimeter energy scale and the luminosity are treated as correlated systematic errors μ F = Q for the DIS jets, μ R =Q or ET as a cross-check μ R = μ F = E T /2 for the γ di-jets (E T is summed E T of final state partons), the AFG photon PDF is used but only direct photon events are used to minimize sensitivity

19. Improvement in gluon determination without jets → with jets 11 parameter fits Retain a, b, c all free in gluon param. xg(x) = Ag x ag (1-x) bg (1 + c g x) →11 parameter fit The reduction in the uncertainty of the gluon distribution at moderate to high-x is quite striking- but the gluon shape is not changed Although the jet data mostly affect 0.01<x<0.1 the momentum sum-rule transfers some of this improvement to higher-x The Sea distribution is not significantly improved and we maintain our previous strategy of constraining a high-x sea parameter (choices 1 or 2 are very similar) For a better high-x Sea determination we await HERA-II (and low energy running?)

20. The ZEUS-Only fit including jet data compared to the inclusive cross-section data

21. The ZEUS-Only fit with Jets compared to DIS inclusive jet data

22. The ZEUS-Only fit with jets compared to di-jet photoproduction data Less good NLOQCD description of data at the lowest ET → hence a cross-check removing the lowest ET bin from both DIS and Photoproduction Jet data was made

23. ZEUS-JETS:  2 /ndf = 0.83 CCompatible with other fits given different data and fitting schemes Now compare ZEUS-JETS 2004 to other PDFs ZEUS-Only 2004 ZEUS-S Global 2002 (Phys ReV D67(2003)012007) MRST2001 CTEQ6M

24. Now compare to H1 with error bands – agreement has improved-but gluon shapes still somewhat different

25. Extra information on gluon allows a competitive determination of  s  treat  s as free parameter in fit Then the PDF errors in the α s extraction are qutomatically accounted Compare this to α s (M Z )=0.1166±0.0008(uncorr) ±0.0048(corr.)±0.0018(model) From the previous ZEUS-S 2002 global fit α s (M Z )= 0.1183±0.0007(uncorr)±0.0027(corr)±0.0008(model) NLO scale uncertainties of ~±0.005 remain

26. Of course when αs is free there is a corresponding increase in the gluon uncertainty – but this has decreased in comparison to the global fit ZEUS-S ZEUS-S 2002 gluon ZEUS-JETS 2004 gluon

27. SUMMARY AND CONCLUSION PDF Analysis of ZEUS data alone reduces the uncertainty involved in the combination of correlated systematic errors from many different experiments with possible incompatibilities Using ZEUS data alone also avoids uncertainty due to heavy target corrections for Fe and Deuterium– particularly important for d valence ZEUS data now cover a large range in the x,Q2 kinematic plane → Valence is well measured → low-x Sea/gluon are well measured Adding jet data gives a significant constraint on the mid/higher x gluon →and a competitive α s measurement Future prospects : 1.Add charm differential cross-sections in ET and rapidity 2.Add resolved photon xsecns (if can control the photon PDF uncertainty) 3.Add jet data from 1998/2000 Add HERA-II data for: more accurate valence ( xF3 from NC/ flavours from CC) : more accurate high-x Sea Low energy running at HERA-II → for higher x and for FL → Gluon

28. Extras after here

29. Percentage difference Sea choice 1 + gluon choice 2. to Sea choice 2 + gluon choice 2 Percentage difference Sea choice 1 + gluon choice 1. to Sea choice 2 + gluon choice 2 Model errors: Percentage difference in choice 1 and choice 2 vs uncertainties on central fit

30. Gluon with and without jets STRATEGY-B summary

31. The χ2 includes the contribution of correlated systematic errors χ 2 = 3 i [ F i QCD (p) – 3 8 s  i SYS – F i MEAS ] 2 + 3 s 2 (  i STAT ) 2 Where Δ iλ SYS is the correlated error on point i due to systematic error source λ and s 8 are systematic uncertainty fit parameters of zero mean and unit variance This has modified the fit prediction by each source of systematic uncertainty The statistical errors on the fit parameters, p, are evaluated from Δχ2 = 1, s λ =0 The correlated systematic errors are evaluated by the Offset method –conservative method - s λ =±1 for each source of systematic error For the global fit the Offset method gives total errors which are significantly larger than the Hessian method, in which sλ varies for the central fit. This reflects tensions between many different data sets (no raise of χ2 tolerance is needed) It yields an error band which is large enough to encompass the usual variations of model choice (variation of Q 2 0, form of parametrization, kinematic cuts applied ) Now use ZEUS data alone - minimizes data inconsistency (but must consider model dependence carefully)