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

Flavour break-up

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%)

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

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

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

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?

Look at high-x make the y axis log!

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.

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

Here’s the same comparison for ZEUS-JETS 2005 Here’s the same comparison for ZEUS-JETS 2005. 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

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?

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?

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.

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

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

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/0508304 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.

Predictions for W/Z production at the LHC

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

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

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.

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

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

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

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

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

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

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

Comparsion to other PDFs just CTEQ for now

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

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

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

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

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)

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.

extras

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

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

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

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

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

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

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

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

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