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May 14 th 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

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Flavour break-up

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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%) The blue lines are just showing that ‘humpy’ param and massive heavy quarks (rtvfn) don’t make much difference

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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 I have not shown the variations with different alphas values- because this really does just affect the gluon

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

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Change fs: mostly affects sbarChange 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

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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? Flavour break-up ubar, dbar, sbar. cbar

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Look at high-x make the y axis log!

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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 MSTW08 is on top Here MSTW08 is underneath

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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

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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

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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?

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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?

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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.

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New HERA-I PDFs experimental error only Fit to ZEUS data only fitted in the same way. Errors OFFSET (as for ZEUS-JETS) 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

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

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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 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.

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Predictions for W/Z production at the LHC

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W+ from ZEUS-S PDF W+ pre HERA PDFW+ from ZEUS-J PDF In these plots there are experimental errors only No model dependence What has HERA data ever done for us? A little history… 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)

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W+ from HERA-II projections W+ from HERA-I PDF Ta-Dah!! 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 PDF set σ W+ B W →lν (nb) σ W- B W →lν (nb) σ z B z →ll (nb) ZEUS-200511.87±0.458.74±0.311.97±0.06 MRST0111.61±0.238.62±0.161.95±0.04 HERA-I12.13±0.139.13±0.152.01±0.025 CTEQ6512.47±0.479.14±0.362.03±0.07 CTEQ6111.61±0.568.54±0.431.89±0.09 But wait.. this does NOT have model dependence

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PDF set σ W+ B W →lν (nb) σ W- B W →lν (nb) σ z B z →ll (nb) HERA-I12.13±0.139.13±0.152.01±0.025 Fs=0.2512.129.092.00 Fs=0.412.159.162.02 Fc=0.1012.269.232.04 Fc=0.2012.009.031.99 Q2min=2.512.139.122.01 Q2min=5.012.179.172.01 Q2_0=211.778.851.95 Q2_0=612.379.292.06 αs=0.115612.029.011.98 αs=0.119612.269.192.04 humpy11.959.001.98 Zeus-style12.459.362.07 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.

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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 Variation of Q2_0 is the most significant model error in the measurable range Look at plots of W+ (W- and Z have the same features see EXTRAS) 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

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The pattern repeats in the lepton sector with small differences in detail 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 And we actually measure leptons: let’s look at lepton+ Variation of Q2_0 is the most significant model error in the measurable range

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The pattern repeats in the lepton sector with small differences in detail 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 Variation of Q2_0 is the most significant model error in the measurable range

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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. AW experimental only Variation of alphas Variation of parmetrization ZJ or humpy style Variation of Q2_0 Variation of fc Now let’s look at ratios

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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 And we actually measure leptons: let’s look at lepton asymmetry Alep experimental only Variation of alphasVariation of fc Variation of parametrization ZJ or humpy style Variation of Q2_0

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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 Z/W experimental only Variation of alphasVariation of fc Variation of parametrization ZJ or humpy style Variation of Q2_0 Now let’s look at ratios

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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 And we actually measure leptons: let’s look at Z/(e+ + e-) Z/leptons experimental only Variation of alphasVariation of fc Variation of parametrization ZJ or humpy style Variation of Q2_0

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Comparsion to other PDFs just CTEQ for now

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Hera-I pdfs expcteq61cteq65 Now we need some comparsion to other PDFs: Z (W+,W- in extras) 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

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But we measure leptons: comparison to other PDFs: lepton+ (lepton- in EXTRAS) Hera-I pdfs exp Hera-I pdfs: Q2_0 model dependence 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

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

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cteq61cteq65 Lepton asymmetry in full kinematic range is in EXTRAS But we measure leptons: comparison to other PDFs: lepton asymmetry Mrst01(4) Small model dependence in HERA PDF from both Q2_0 and alternative parametrizations Hera-I pdfs: Q2_0 model dependence Hera-I pdfs: alternative parametrization Hera-I pdfs exp

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Mrst01(4) This is a bit wider than 65 because of strangeness uncertainty Hera-I pdfs: alphas model dependence Now we need some comparison to other PDFs: ratios: Z/W Hera-I pdfs expcteq61 cteq65cteq66 Small model dependence in HERA PDF from alphas 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

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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: 1.Very small experimental errors. 2. Model uncertainty from choice of Q2_0 (effectively parametrization) is significant for W,Z and decay lepton spectra. 3.Model uncertainty cancels out of W asymmetry in central rapidity range, small model uncertainty is left in lepton asymmetry 4.Small model uncertainty from alphas in Z/W ratio and Z/lepton ratio. 5.Interesting for PDF4LHC.

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extras

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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 Variation of Q2_0 is the most significant model error in the measurable range

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

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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 alphasVariation of fc Variation of parmetrization ZJ or humpy style Variation of Q2_0 AW experimental only

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

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

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Hera-I pdfs exp Hera-I pdfs: Q2_0 model dependence cteq61cteq65 Now we need some comparsion to other PDFs: W- Note CTEQ61 is lower and less precise than CTEQ65

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Hera-I pdfs exp Hera-I pdfs: Q2_0 model dependence cteq61cteq65 But we measure leptons: comparison to other PDFs: lepton-

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HERA-I PDFS cteq61cteq65 Lepton asymmetry across full kinematic range

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But we measure leptons: comparison to other PDFs: Z/leptons Hera-I pdfs expcteq61 cteq65 Small model dependence in HERA PDF from alphas Hera-I pdfs: alphas model dependence

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