Update on fits for 25/3/08 AM Cooper-Sarkar

1. Update on fits for 25/3/08 AM Cooper-Sarkar • Central fit: choice of parametrization • Central fit: choice of error treatment • Quality of fit to data • PDFs plus experimental errors, compare to older fits • Model uncertainties • Model Variations

2. Possible forms of PDF parametrization: H1 style Published H1 PDF2000 New H1-style parametrization optimised for combined data set Optimization means starting without D,E,F parameters and adding parameters until there is no further χ2 advantage PDFs: gluon, U=u+c, Ubar=ubar+cbar, D=d+s+b, Dbar=dbar+sbar+bbar Sea flavour break-up at Q0: s = fs*D, c=fc*U AU=(1-fs)/(1-fc)AD

3. Possible forms of PDF parametrization: ZEUS style ZEUS-JETS published E New ZEUS-JETS optimized for combined data set PDFs: gluon, uv, dv, Sea= usea+ubar+dsea+dbar+s+sbar+c+cbar Sea flavour break-up at Q0: sbar = (dbar+ubar)/4, charm dynamically generated, dbar-ubar fixed to fit E866 data

4. Possible forms of PDF parametrization: ‘inbetween’ Original ‘inbetween’ parametrization Lim x→0 u/d →1 ‘inbetween’ parametrization optimized to combined data set Lim x→0 u/d →1 PDFs: gluon, uv, dv, Ubar=ubar+cbar, Dbar=dbar+sbar+bbar Sea flavour break-up at Q0: s = fs*D, c=fc*U AUbar=(1-fs)/(1-fc)ADbar Can also dynamically generate charm, but need to keep AUbar to ADbar relationship as here

5. For each of the old parametrizations, which have non-zero D parameter for the gluon, there are two minima: ‘straight’ gluon and ‘humpy’ gluon solution. Which look rather like the published ZEUS and H1 gluons respectively! For the H1/ZEUS combined data set the χ2 of the straight solution is always lower by about 10 χ2 points. For the H1 data set alone the ‘humpy’ gluon had the lower χ2, whereas for the ZEUS data set alone the ‘straight’ gluon had the lower χ2 This χ2 table compares humpy and straight gluon solutions for the old parametrizations and the straight solution for the new parametrizations: using a χ2 definition where all 47 systematic errors of the combined data set are added in quadrature. Table from J.Feltesse excellent agreement on all results in this talk 433 We have chosen the new ‘inbetween’ parametrization to be the form of the new h1/zeus combined PDF fit.

6. Now compare methods of treating systematic errors: Quadratic/Hessian/Offset (using published ZEUS-JETS parametrization) 47 systematic errors added to statistical quadratically 47 systematic errors treated by Hessian method 43 original sources of systematic errors added to statistical quadratically and 4 procedural errors Offset Central values very similar (not necessarily obvious for full Hessian treatment) Errors generally largest for OFFSET procedural, but not much difference in treatments since systematic errors not so big now- chose this method.

7. Theoretical framework NLO DGLAP evolution Facttorisation and renormalisation scales Q2 Zero-mass variable flavour number heavy quark scheme Model assumptions Which will be varied to assess model uncertainty Q02 = 4 GeV2 input scale Q2min = 3.5 GeV2 minimum Q2 of input data fs = 0.33D strange sea fraction, means s=0.5d fc = 0.15U charm sea fraction, means c=0.176u mc=1.4 mass of charm quark mb=4.75 mass of beauty quark αs(Mz) = 0.1176 PDG2006 value Form of the parametrization: ‘in between’

8. PDF fit RESULTS

9. New H1/ZEUS combined PDF fit vs combined data- see comparison to ZEUS-JETS 2005 in EXTRAS

10. First consider experimental uncertainties New H1/ZEUS combined PDFs with experimental uncertainty bands from statistical errors plus 43 sources of systematics in quadrature plus 4 procedural systematics OFFSET

11. Compare the experimental error bands of the new analysis using combined data to the experimental error bands of the ZEUS-JETS fit –obviously we are winning!

12. Compare to published ZEUS-JETS PDFs Compare to published H1PDF2000 fit

13. Now consider model uncertainties: Proposal for MAIN results New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands from 6 sources of model variation: mc, mb, fs, fc, Q0, Q2min.

14. Variation with Q2

15. New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands from 6 sources of model variation: AT THE STARTING SCALE Q20 = 4 GeV2

16. New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands from 6 sources of model variation: AT Q20 = 100 GeV2 . Note how uncertainties are decreasing

17. New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands from 6 sources of model variation: AT Q20 = 10000 GeV2 . At scales relevant to LHC physics uncertainties are impressively small.

18. Examine model uncertainties

19. Include only variation of charm mass and beauty mass mc:1.35→1.5 GeV and mb: 4.3 →5.0 GeV This model dependence is invisible

20. Include only variation of strange fraction fs: 0.25 →0.40 Makes very little difference in the total Sea, but affects sea flavour break-up

21. Include only variation of charm fraction fc: 0.10 →0.20 A smaller effect than fs: makes very little difference in the total Sea, but affects sea flavour break-up

22. Include only variation of starting scale Q02: 2 → 6 GeV2 Has a small asymmetric effect on PDF ucertainties

23. Include only variation of minimum Q2 of fitted data Qmin2: 2.5 → 5 GeV2 Has an even smaller asymmetric effect on PDF ucertainties

24. Other possible model uncertainties

25. And we could have added in Include only variation of αs (Mz): 0.1156 → 0.1196 (PDG2006) Looking at this uncertainty alone it affects only the gluon PDF

26. And if we add in the variation of αs (Mz) to the other 6 model uncertainties. I chose not to add this in since MRST(MSTW) and CTEQ both use fixed alphas and I want the public to compare ‘like with like’.

27. There is another model uncertainty that we could add in- the variation if one uses different forms of parametrization: H1 style newly optimized paremetrization and ZEUS-JETs style newly optimized parametrization. Looking at this uncertainty alone there is a small asymmetric effect, most visible in valence distributions.

28. Illustration of the difference between using 6 or 7 sources of model uncertainty: On the right the 7th uncertainty from form of parametrization: h1 vs zeus-jet is added in. There is excellent agreement with J Feltesse. I chose not to add this in because its not the same kind of variation as the others- varying our new parametrization to two others is not an ‘up and down’ variation!

29. We could illustrate some of these other choices as variations rather than adding them into model uncertainty.

30. Comparison of central fit plus total experimental errors to variations with αs(Mz)=0.1156 (left) and 0.1196 (right) Confirms what we’ve already seen-variation is outside the gluon error bands even when other model dependence is accounted.

31. Comparison of central fit plus total experimental errors to parametrization variation using: New H1 optimised parametrization Marginally outside normal error bands for valence even when other model dependence is accounted(but note this is at low x where valence isn’t very significant)

32. Comparison of central fit plus total experimental errors to parametrization variation using: New ZEUS-JETS optimised parametrization Inside error bands if other model dependence is accounted

33. Comparison of central fit plus total experimental errors to parametrization variation using: the ‘humpy’solution for the h1/zeus parametrization. At Q2=10 (left) and Q2=4 (right)GeV2 where the humpy structure is more visible. Marginally outside normal error bands for valencemore than for gluoneven when other model dependence is accounted(but note this is at low x where valence isn’t very significant)

34. Finally we may be criticized for the use of a zero-mass scheme. Comparison of central fit plus total experimental errors to variation of heavy quark scheme: using massive variable flavour number scheme of Thorne. This cannot yet be checked by both H1 and ZEUS

35. Time to decide what we want to show the world

36. EXTRAS

37. Here’s how the new H1Z PDF fit fits the data e-CC (left) e+CC (right) but with ZJ2005 also superimposed H1Z fit is slightly lower.

38. Here’s how H1Z fits the data e-NC (left) e+NC (right) with ZJ2005 also superimposed – no I cant see it either!

39. Now in terms of ubar, dbar, sbar, cbar xubar xcbar xdbar xsbar ZEUS-Jets Parametrization in between H1 parametrization The similarity of these is perhaps even more remarkable given the different treatment of charm- clearly the fixed fraction fc=0.15 is about right compared to dynamical turn on at Q2=mc2

40. Model dependence: just fs and fc variations together

41. Model dependence: mc.mb,fs.fc.Q0

42. Illustration of the difference between using 6 or 7 sources of model uncertainty: mc,mb, fs, fc, Q0, Q2min (and parametrization form h1 vs zeus-jets). Excellent agreement with J Feltesse.

43. Comparison of central fit plus total experimental errors to variations with alphas=0.1156 (left) and 0.1196 (right)

44. Comparison of central fit plus total experimental errors to parametrization variation using: the ‘humpy’solution for the h1/zeus parametrization

45. Bg= -0.03 ± 0.02 Cg= 7.8 ± 0.7 Buv= 0.69 ± 0.07 Cuv= 5.1 ± 0.2 Duv= 12.1 ± 2.3 Euv= -0.66 ±0.91 Cdv= 3.8 ± 0.4 BUbar = -0.206 ± 0.005 CUbar = 5.1 ± 0.9 ADbar = 0.159 ± 0.006 CDbar = 4.0 ± 1.1 Feltesse Cooper-Sarkar Chi2 old = 437.9 Chi2 new = 428.0 Look at parameters, agree that gluon distribution must be flatter at low-x Chi2 are for all 47 systematic sources added in quadrature