1. HERA I - Preliminary H1 and ZEUS QCD Fit
28/03/08
A.Cooper-Sarkar, R.Devenish, C.Gwenlan, K.Nagano, J.Ferrando, Y.Ri, E.Tassi,
J.Feltesse, A.Glazov, M.Klein, G.Li, B. Olivier, V.Radescu,
E.Rizvi, V.Shekelian, Z.Zhang
Choice of data set
Central fit: choice of parametrization
Central fit: choice of error treatment
Central fit: choice of model assumptions
Quality of fit to data
PDFs plus experimental errors
PDFs plus model uncertainties
Comparison to older H1/ZEUS fits, comparison to CTEQ, MRST
Model uncertainty investigations
Model Variations

2. Preliminary QCD Fit to Combined H1-ZEUS HERA-I data
A.Cooper-Sarkar, R.Devenish, C.Gwenlan, K.Nagano, J.Ferrando, Y.Ri, E.Tassi,
J.Feltesse, A.Glazov, M.Klein, G.Li, B. Olivier, V.Radescu,
E.Rizvi, V.Shekelian, Z.Zhang

3. QCD Fits of the preliminary combined data set presented at LP07
Input data sets : Published HERA I cross sections
NC and CC e+, e < Q2 < GeV2 → 240 pb-1
1.5
With H1 NC MB (Q2 < 12 GeV2) moved up by 3.4 % after reanalysis of luminosity

4. 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

5. Possible forms of PDF parametrization: ZEUS style
ZEUS-JETS published
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

6. 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

7. Which look rather like the published ZEUS and H1 gluons respectively!
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
433.6

8. Choice of parameterization
All parametrizations give an excellent χ2 /degree of freedom :
Inbetween : 431.9/563=(573-10)
H1 param : 434.7/563=(573-10)
ZEUS_Jet : 433.6/562=(573-11)
Chosen central parameterization : ‘optimized Inbetween’
Motivations :
Less model dependence on B parameters than in H1 param.
No need for an additional input (ubar-dbar) x distribution as in ZEUS-Jet param
Most conservative errors.
It is inspired by both H1 and ZEUS parameterizations.
The two other parameterizations AND humpy solution for inbetween the are considered in the model variations

9. Choice of treatment of systematic errors
Reminder: combining H1 & ZEUS cross-sections
Full account taken of systematic uncertainties of H1 and ZEUS
measurements, including correlations:
43 separate sources
plus 4 ‘procedural uncertainties’
44:   photoproduction assumed correlated in H1-ZEUS 45:  FL is set to 0 for Centre-of-Mass Energy shift 46:  Difference between "all relative" -- "global normalisations relative"
treatement 47:  Extra 1% for y<0.02 NC data to take into account correlated
HFS simulation   (based on hadronic energy scale correlations study)

10. 47 systematic errors added to statistical quadratically χ2= 428.0
47 systematic errors treated by Hessian method χ2=553.1
43 original sources of systematic errors added to statistical quadratically and 4 procedural errors Offset χ2=476.7
Central values very similar, uncertainties largest for OFFSET method, we chose this because it is most conservative. Note there is not much difference between these different error treatments since systematic errors not so big
Proposal that these χ2 values be made preliminary, all are for 563 degrees of freedom

11. 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) = PDG2006 value
Form of the parametrization: ‘in between’/ H1/ ZEUS-JETS/ ‘humpy’

12. PDF fit RESULTS let’s call it the HERA-I PDF Comparison to HERA combined data

13. Preliminary status requested
HERA I - Preliminary H1 and ZEUS QCD Fit
Preliminary status requested
Blow up just three x values to see older ZEUS-JETS PDF and H12000 PDF plus new HERA-I PDF
New HERA-I PDF fit predictions vs. H1/ZEUS combined data for NC e+p. Experimental uncertainties on the PDF fit predictions are included but can barely be be resolved.

14. Preliminary status requested
HERA I - Preliminary H1 and ZEUS QCD Fit
Preliminary status requested
New H1/ZEUS combined PDF fit predictions vs. H1/ZEUS combined data for NC e+p and e-p at low Q2. Experimental and model uncertainties on the PDF fit predictions are included but barely be resolved

15. Preliminary status requested
HERA I - Preliminary H1 and ZEUS QCD Fit
Preliminary status requested
New H1/ZEUS combined PDF fit predictions vs. H1/ZEUS combined data for NC e+p and e-p at high Q2. Experimental and model uncertainties on the PDF fit predictions are included but cannot be resolved

16. Preliminary status requested
HERA I - Preliminary H1 and ZEUS QCD Fit
Preliminary status requested
New H1/ZEUS combined PDF fit predictions vs. H1/ZEUS combined data for NC e+p and e-p at high Q2. Experimental and model uncertainties on the PDF fit predictions are included

17. HERA I - Preliminary H1 and ZEUS QCD Fit
CC e+p (left) e-p (right) compared to older ZEUS-JETS PDF and H12000 PDF plus new HERA-I PDF.

18. PDF fit RESULTS PDFs: experimental and model errors Comparison to other PDFs

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

20. Now add 6 sources of model dependence
mc 1.3 → 1.55 GeV variation of mass of c quark
mb 4.3 → GeV variation of mass of b quark
fs → variation of strange sea fraction at Q0
fc → variation of charm sea fraction at Q0
Q →6.0 GeV2 variation of starting scale
Qmin2 2.5→5.0 GeV2 variation of cuts on the data included

21. Now add 6 sources of model dependence
HERA I PDFs
HERA I PDFs
New H1/ZEUS combined PDFs with total experimental uncertainty plus model uncertainty

22. Preliminary status requested
Compare to previous ZEUS/H1 results
Preliminary status requested
HERA I PDFs
Resolution of previous discrepancies, improvement in level of uncertainty

23. Compare to CTEQ and MRST analyses
Do we want preliminary status for these?

24. Compare to CTEQ and MRST analyses: 2008
Note MSTW08 is as yet unpublished- I have a pre-release

25. Look at our results in more detail: vs Q2

26. Preliminary status requested
HERA I PDFs
HERA I PDFs
Preliminary status requested
New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands
AT THE STARTING SCALE Q20 = 4 GeV2

27. Preliminary status requested
HERA I PDFs
HERA I PDFs
Preliminary status requested
New H1/ZEUS combined PDFs with total experimental uncertainty bands plus model uncertainty bands
At Q2 =10 GeV2

28. Preliminary status requested
HERA I PDFs
HERA I PDFs
Preliminary status requested
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

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

30. Checks between ZEUS and H1

31. Check analysis
H1 Package
ZEUS Package

32. Investigate model uncertainties

33. 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

34. 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

35. 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

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

37. Include only variation of minimum Q2 of fitted data Qmin2: 2
Include only variation of minimum Q2 of fitted data Qmin2: 2.5 → 5 GeV2
Has an even smaller asymmetric effect on PDF ucertainties

38. We illustrate some of the other choices as variations compared to our central value:
αS(Mz) = →
New H1 ‘optimized’ parametrization
New ZEUS-JETS ‘optimized parametrization
Old ‘in-between’ parametrization with ‘humpy’ gluon solution
Use of massive variable flavour number scheme- cannot be checked by both ZEUS and H1 yet, so no preliminary request

39. Preliminary status requested
HERA I PDFs
HERA I PDFs
Preliminary status requested
Comparison of central fit plus total uncertainties to variations with αs(Mz)= (left) and (right)
Confirms what we’ve already seen-variation is outside the gluon error bands even when other model dependence is accounted.

40. Preliminary status requested
HERA I PDFs
HERA I PDFs
Preliminary status requested
Comparison of central fit plus total uncertainties 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)

41. Preliminary status requested
HERA I PDFs
HERA I PDFs
Preliminary status requested
Comparison of central fit plus total uncertainties to parametrization variation using: New ZEUS-JETS optimised parametrization
Inside error bands if other model dependence is accounted

42. Preliminary status requested
HERA I PDFs
HERA I PDFs
Preliminary status requested
Comparison of central fit plus total uncertainties 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 valence more than for gluon! even when other model dependence is accounted (but note this is at low x where valence isn’t very significant)

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

44. Summary
An immense amount of work has been done to resolve differences between ZEUS and H1 PDF fitting analyses
Agreement has been reached on procedure AND
Agreement has been reached on fit results
We wish to make preliminary:
Plots of the new HERA-I PDF fit compared to the new HERA-I combined data
Plots of the PDFs: u-valence, d-valence, gluon and total Sea
: U, D, Ubar, Dbar
with experimental uncertainty bands and model uncertainty bands
and additional plots showing variations NOT added into model uncertainty
Plots of the PDFs in comparison to previous ZEUS and H1 analyses
Plots of the PDFs in comparison to CTEQ6 and MRST04 analyses

45. EXTRAS: Questions asked by ZEUS and H1 already

46. Compare to previous ZEUS-JETS fit : with errors on both
The extra data and reduction of systematics constrains gluon better at low-x, which by the momentum sum-rule constrains it better at high-x. Hence it is precise even without jets.

47. What would it look like with the parametrization uncertainty added in
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.

48. How much of the change is data and how much is the parametrization: the plots below are ALL with the new combined data- parametrization make a large difference to the error estimate
ZEUS-Jets Parametrization in between H1 parametrization
Central values are really very similar- quite remarkable since ZEUS and H1 parametrizations are not- however the size of errors differs, with ‘in between’ being the most conservative

49. Other extras

50. 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

51. Compare to previous ZEUS and H1 analyses in a different style

52. And we could have added in Include only variation of αs (Mz): 0
And we could have added in Include only variation of αs (Mz): → (PDG2006)
Looking at this uncertainty alone it affects only the gluon PDF

53. 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’.

54. Comparison of central fit plus total uncertainties to variations with alphas= (left) and (right) : U D plots

55. 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.

56. 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!

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

58. NC e+p low and high Q2 from Enrico, only experimental errors

59. NC e-p high Q2 from Enrico, only experimental errors

60. CC e-p and e+p from Enrico, only experimental errors

61. Check analysis
H1 Package
ZEUS Package
Gluon PDF

62. Check analysis
H1 Package
ZEUS Package
u-valence

63. Check analysis
H1 Package
ZEUS Package
d-valence