1. May 14th 2008 averaging meeting A M Cooper-Sarkar
Look at the HERA-I PDFs in new ways
Flavour break-up
High-x
Compare to ZEUS data alone/ H1 data alone fitted in the same way
Look at predictions for W/Z production at the LHC

2. Flavour break-up

3. Flavour break-up ubar, dbar, sbar. cbar
The blue lines are just showing that ‘humpy’ param and massive heavy quarks (rtvfn) don’t make much difference
Flavour break-up ubar, dbar, sbar. cbar
The model uncertainty in sbar and cbar is quite big- not suprisingly
Fc varies 0.15±0.05 (30%) and fs varies 0.33±0.08 (24%)

4. Flavour break-up ubar, dbar, sbar. cbar
The blue lines are just showing that zeus-jets style or h1-style parametrizations don’t make much difference
Flavour break-up ubar, dbar, sbar. cbar
I have not shown the variations with different alphas values- because this really does just affect the gluon

5. Now considering what contributes to the model dependence
Flavour break-up ubar, dbar, sbar. cbar
Just vary the low Q2 cut again no effect on sea flavours
Just vary mc and mb no effect on sea flavours

6. Flavour break-up ubar, dbar, sbar. cbar
Change fs: mostly affects sbar
Change fc: mostly affects cbar
Remember fs and fc are used for normalising ubar and dbar, so there is some small cross-talk

7. Flavour break-up ubar, dbar, sbar. cbar
Now vary the value of Q2_0
This affects all flavours:
ubar and dbar because it amounts to a change in parametrization and
sbar and cbar because it amounts to changing fs and fc-
(what we have done is vary Q2_0 keeping the same fs and fc when these fractions would obviously change with Q2)
should we do something about this?

8. Look at high-x make the y axis log!

9. Here MSTW08 is underneath
Here MSTW08 is on top
Here are our PDFs at high-x compared to those of MSTW08
Red is our experimental error, yellow is the model band, green is MSTW08.
You can see pretty good agreement of sea quark and d-valence, and of u-valence until x > 0.7, where there’s no data so either of us could be right
BUT our gluon at x > 0.2 is softer and its uncertainties do not reflect our lack of knowledge in this region. Also it is softer than our sea for x > 0.3 which seems a bit weird.

10. Here’s the same comparison for CTEQ65, where I haven’t separated our model uncertainty from our experimental error
The comments are identical as for MSTW08

11. Here’s the same comparison for ZEUS-JETS 2005
Here’s the same comparison for ZEUS-JETS ZEUS-JETS is much closer to the HERA PDF, but it is a BIT harder and a BIT less precise, such that it is in striking distance of the CTEQ65 error band.
This means that ZJ2005 can almost fit Tevatron jet data- χ2/d.p = 122/82 (for Run-I D0) for the central value of ZJ2005. IF I take the extremal values of the ZJ2005 high-x gluon then I get 156/82 (soft) and 87/82(hard)
So our HERA PDF will have something like 156/82 because its on the soft edge of ZJ

12. Here’s just a plot of our PDFs which has on only our experimental uncertainties.
So far our model uncertainties have not succeeded in making the high-x gluon significantly larger.
We will be criticized for being unable to fit Tevatron jet data well.
But the point is not that we have to fit it, it is that our present uncertainties seem a bit unrealistically low.
So (a la Pumplin at DIS08) can one
Make it more uncertain by adding parameters?

13. So far I have tried looking at ‘humpy’ which has more gluon parameters, and at a fit with Cg.ne.0 but NOT the humpy solution. Neither of these solve the problem. Do we need to do something about this?

14. Comparison of new fit to fits to ZEUS data only or H1 data only fits done in the same way i.e. optimized ‘inbetween’ parametriation with all the same assumptions.

15. Fit to ZEUS data only fitted in the same way
Fit to ZEUS data only fitted in the same way. Errors OFFSET (as for ZEUS-JETS)
New HERA-I PDFs experimental error only
Fit to ZEUS data only fitted in the same way. Errors in quadrature Norms fitted.
There is still the choice as to how to do the errors, I have chosen OFFSET but also show quadrature. I think our message is best illustrated by the comparison to OFFSET

16. Fit to H1 data only fitted in the same way
Fit to H1 data only fitted in the same way. Errors OFFSET hence Not as for H1PDF2K
New HERA-I PDFs experimental error only

17. Fit to ZEUS and H1 data as two separate data sets, but fitted in the same way.
Errors OFFSET
New HERA-I PDFs experimental error only
I am quite aware that I could have chosen to do the errors Hessian on these ZEUS only, H1 only and ZEUS+H1 as separate data set fits.
I did this exercise before on an earlier version of our combination and our fit. See hep-ph/ from one of the HERALHC workshops. The conclusion was that by putting ZEUS and H1 data separately through a Hessian fit you can get a fit with the same impressively small errors as our combination fit BUT the central values of the gluon and the d-valence were very different. The QCD fit imposes many assumptions when setting the correlated experimental shift parameters, by contrast our combination is ‘assumption free’. Hence I prefer to make the comparisons to the more conservative OFFSET method. This gives a clearer message about improvement to the outside world.

18. Predictions for W/Z production at the LHC

19. What has HERA data ever done for us? A little history…
W+ from ZEUS-S PDF
W+ pre HERA PDF
W+ from ZEUS-J PDF
So looking at the predictions for W+ rapidity distributions (NLO code J.Stirling) we see a terrific improvement in putting in the HERA data (these are ZEUS-S style global fits without and with the ZEUS 97/97 data). The ZEUS-JETS fit gives more or less as good a precision as the ZEUS-S global fit because at high scale (Q2=MW2) in the central rapidity region the W+ (and W-, Z distributions) are driven by the low-x gluon (by g→qqbar splitting)
In these plots there are experimental errors only
No model dependence

20. A couple of years ago we even made a plot of how good it could get with HERA-II data.
But we were pessimistic
We were not expecting the improvement in systematic error that our combination has made.
The predictions are very precise ~1% error
W+ from HERA-I PDF
Ta-Dah!!
W+ from HERA-II projections
PDF set
σW+ BW→lν (nb)
σW- BW→lν (nb)
σz Bz→ll (nb)
ZEUS-2005
11.87±0.45
8.74±0.31
1.97±0.06
MRST01
11.61±0.23
8.62±0.16
1.95±0.04
HERA-I
12.13±0.13
9.13±0.15
2.01±0.025
CTEQ65
12.47±0.47
9.14±0.36
2.03±0.07
CTEQ61
11.61±0.56
8.54±0.43
1.89±0.09
But wait.. this does NOT have model dependence

21. Fc variation is on the edge of the errors
PDF set
σW+ BW→lν (nb)
σW- BW→lν (nb)
σz Bz→ll (nb)
HERA-I
12.13±0.13
9.13±0.15
2.01±0.025
Fs=0.25
12.12
9.09
2.00
Fs=0.4
12.15
9.16
2.02
Fc=0.10
12.26
9.23
2.04
Fc=0.20
12.00
9.03
1.99
Q2min=2.5
12.13
9.12
2.01
Q2min=5.0
12.17
9.17
Q2_0=2
11.77
8.85
1.95
Q2_0=6
12.37
9.29
2.06
αs=0.1156
12.02
9.01
1.98
αs=0.1196
9.19
humpy
11.95
9.00
Zeus-style
12.45
9.36
2.07
Model dependences
Varying mc and mb (not shown) gives results well within errors, similarly for fs
Fc variation is on the edge of the errors
Q2min variation is well within
Q2_0 variation is the biggest effect outside errors
Varying αs is on the edge of the errors
Varying the parametrization is also outside errors.

22. Look at plots of W+ (W- and Z have the same features see EXTRAS)
W+ experimental only
Variation of alphas ~ same size as experimental error
Variation of fc ~ same size as experimental error
Variation of parmetrization ZJ or humpy style
The total production cross-sections do not tell the full story about the shape in rapidity. Errors tend to be slightly larger in the central region
Variation of Q2_0 is the most significant model error in the measurable range

23. And we actually measure leptons: let’s look at lepton+
e+ experimental only
Variation of alphas ~ same size as experimental error
Variation of fc- ~ same size as experimental error
Variation of parmetrization ZJ or humpy style
The pattern repeats in the lepton sector with small differences in detail
Variation of Q2_0 is the most significant model error in the measurable range

24. And we actually measure leptons: let’s look at lepton-
e+ experimental only
Variation of alphas ~ same size as experimental error
Variation of fc- ~ same size as experimental error
Variation of parmetrization ZJ or humpy style
The pattern repeats in the lepton sector with small differences in detail
Variation of Q2_0 is the most significant model error in the measurable range

25. Now let’s look at ratios
Variation of parmetrization ZJ or humpy style
AW experimental only
Variation of alphas
Variation of fc
First AW = (W+ - W-)/(W+ + W-)
The model dependences cancel out at central rapidity
See EXTRAS for the full rapidity range where you can see that ‘humpy’ does give differences at the edges of y.
Variation of Q2_0

26. And we actually measure leptons: let’s look at lepton asymmetry
Variation of parametrization ZJ or humpy style
Alep experimental only
Variation of alphas
Variation of fc
For the lepton asymmetry the wash out of model dependence in the measurable region is not quite so perfect but it is still quite impressive
See EXTRAS for full rapidity range
Variation of Q2_0

27. Now let’s look at ratios
Variation of parametrization ZJ or humpy style
Z/W experimental only
Variation of alphas
Variation of fc
Another important ratio is
Z/(W+ + W-)
The experimental error on this is VERY small.
For model dependences: fc, Q2_0 and parametrization do not matter much but
Alphas has a noticeable effect
Variation of Q2_0

28. And we actually measure leptons: let’s look at Z/(e+ + e-)
Variation of parametrization ZJ or humpy style
Z/leptons experimental only
Variation of alphas
Variation of fc
In the Z to leptons ratio the same features appear
The experimental error is VERY small.
For model dependences: fc, Q2_0 and parametrization do not matter much but
Alphas has a noticeable effect
Variation of Q2_0

29. Comparsion to other PDFs just CTEQ for now

30. Now we need some comparsion to other PDFs: Z (W+,W- in extras)
Hera-I pdfs exp
cteq61
cteq65
Hera-I pdfs: Q2_0 model dependence
Note CTEQ61 is lower and less precise than CTEQ65
HERA-I PDFs are very precise BUT model dependence IS significant.
Still winning wrt CTEQ

31. But we measure leptons: comparison to other PDFs: lepton+ (lepton- in EXTRAS)
Hera-I pdfs exp
cteq61
cteq65
Note CTEQ61 is lower and less precise than CTEQ65
HERA-I PDFs are very precise BUT model dependence IS significant.
Still winning wrt CTEQ
Hera-I pdfs: Q2_0 model dependence

32. Now we need some comparison to other PDFs: ratios: AW
Hera-I pdfs exp
cteq65
cteq61
Mrst01(4)
Negligible model dependence in HERA PDF.
Below see AW across full kinematic range

33. But we measure leptons: comparison to other PDFs: lepton asymmetry
Hera-I pdfs exp
Mrst01(4)
cteq61
cteq65
Small model dependence in HERA PDF from both Q2_0 and alternative parametrizations
Lepton asymmetry in full kinematic range is in EXTRAS
Hera-I pdfs: Q2_0 model dependence
Hera-I pdfs: alternative parametrization

34. Now we need some comparison to other PDFs: ratios: Z/W
Hera-I pdfs exp
cteq61
cteq65
cteq66
This is a bit wider than 65 because of strangeness uncertainty
Small model dependence in HERA PDF from alphas
Hera-I pdfs: alphas model dependence
No matter what their other discrepancies all PDFs are agreed on this ratio.
Recently strangeness uncertainty has been introduced and this affects it- but it is NOT a big deal, see CTEQ66
Mrst01(4)

35. Summary
Flavour break up behaves as expected, not sure whether to ‘go public’ with plots. Probably should sort out Q2_0, fc, fs double counting in model dependence.
High-x gluon is soft, but worse than this is that it does not have a large enough uncertainty- work on this more?
Comparison to ZEUS-ONLY or H1-ONLY seems OK, probably won’t ‘go public’
Prediction of W/Z at LHC:
Very small experimental errors.
Model uncertainty from choice of Q2_0 (effectively parametrization) is significant for W,Z and decay lepton spectra.
Model uncertainty cancels out of W asymmetry in central rapidity range, small model uncertainty is left in lepton asymmetry
Small model uncertainty from alphas in Z/W ratio and Z/lepton ratio.
Interesting for PDF4LHC.

36. extras

37. The pattern repeats in W-
W- experimental only
Variation of alphas ~ same size as experimental error
Variation of fc- ~ same size as experimental error
Variation of parmetrization ZJ or humpy style
The pattern repeats in W-
Variation of Q2_0 is the most significant model error in the measurable range

38. The pattern repeats in Z
Z experimental only
Variation of alphas ~ same size as experimental error
Variation of fc- ~ same size as experimental error
Variation of parmetrization ZJ or humpy style
The pattern repeats in Z
Variation of Q2_0 is the most significant model error in the measurable range

39. AW asymmetry over the full rapidity range alphas has no effect
Variation of parmetrization ZJ or humpy style
AW experimental only
Variation of alphas
Variation of fc
AW asymmetry over the full rapidity range
alphas has no effect
Fc has no effect
Zj/humpy has effect only at high-y
Q20 is not a big effect..model dependences cancel out at central rapidity.
Variation of Q2_0

40. Alep experimental only
Variation of parmetrization ZJ or humpy style
Alep experimental only
Variation of alphas
Variation of fc
the lepton asymmetry over the full rapidity range
Variation of Q2_0

41. Now we need some comparsion to other PDFs: W+
Hera-I pdfs exp
cteq61
cteq65
Hera-I pdfs: Q2_0 model dependence
Note CTEQ61 is lower and less precise than CTEQ65

42. Now we need some comparsion to other PDFs: W-
Hera-I pdfs exp
cteq61
cteq65
Hera-I pdfs: Q2_0 model dependence
Note CTEQ61 is lower and less precise than CTEQ65

43. But we measure leptons: comparison to other PDFs: lepton-
Hera-I pdfs exp
cteq61
cteq65
Hera-I pdfs: Q2_0 model dependence

44. Lepton asymmetry across full kinematic range
cteq61
cteq65
HERA-I PDFS

45. But we measure leptons: comparison to other PDFs: Z/leptons
Hera-I pdfs exp
cteq61
cteq65
Small model dependence in HERA PDF from alphas
Hera-I pdfs: alphas model dependence