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Recap of PDF fitting to the HERA average data Oct 12 th 2007 AMCS

Recap of PDF fitting to the HERA average data Oct 12 th 2007 AMCS. Model dependence from assumptions about averaging procedure Model dependence from PDF parametrisation Model dependence from fitting programme! Free alphas Compare ZEUS and H1-style parametrisation.

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Recap of PDF fitting to the HERA average data Oct 12 th 2007 AMCS

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  1. Recap of PDF fitting to the HERA average data Oct 12th 2007 AMCS • Model dependence from assumptions about averaging procedure • Model dependence from PDF parametrisation • Model dependence from fitting programme! • Free alphas • Compare ZEUS and H1-style parametrisation

  2. Version of the combination agreed as standard in July was: all sources of error relative; y>0.35 for NC 820,920 not combined Had considered variations on this see talk of 04june07 Illustrated here: only normalisations relative and NC 820,920 combined to 920 Conclusion model dependence from averaging procedure not large

  3. Q02=4 GeV2 Q02=7 GeV2 To test model dependence from parametrisation – change Q02 from 7 GeV2 to 4 GeV2 to 2 GeV2 Changes are as expected – gluon gets a bit humpier, reflects instability at Q02=2 d valence is also affected Sea and u valence stable Conclusion: Model dependence not too bad- but certainly as large as changes due to the choices in our procedure – see talk of 22 june07 Q02=2 GeV2

  4. QCDNUM17linear QCDNUM16 compatible QCDNUM17 quadratic Model dependence – why chose Q02 as low as 2 GeV2? Because for QCDNUM17 you have to! It HAS to start below the charm threshold whether you chose NLO or NNLO. These fits show only NLO. There is a choice of linear spline interpolation (as for QCDNUM16) or Quadratic spline interpolation which is more accurate at high-x…and it makes a difference! See talk of 22June07

  5. Free αS(MZ) αS(MZ) =0.121 ± 0.003 χ2=500 Investigate scale dependence Renormalisation scale usually the biggest so start with that Scale= 2 Q2 αS(MZ) =0.123 χ2=502 Scale= 4Q2αS(MZ) =0.124 χ2=507 Scale= Q2/2 αS(MZ) =0.118 χ2=526 Scale= Q2/4 job blows up! Scale dependence 0.002-0.003? Not as bad as I thought!

  6. Q02=4 GeV2 Q02=4 GeV2 ZEUS parametrization H1-style parametrization Nature of the parametrization forces the errors on the low-x valence distributions to be very small- better to compare U,D Central values of the fits are very close- good news I haven’t added the charm into the sea for H1 in the plot, so it’s a bit low Very similar χ2 ~ 500 for 584 points

  7. ZEUS parametrisation xf(x) = A xa (1-x)b (1+ c x) For u,d valence, sea and glue Au,Ad,Ag from sum rules, ad=au, cs=0 H1 parametrisation xf(x) = A xa (1-x)b (1+ c x) (no x3 term) For U=u+c, D=d+s, Ubar, Dbar and glue AU,AD,Ag from sum-rules, aU=aD=aUbar=aDbar,cUbar=cDbar=0 aU= -0.195±0.004 bU=3.5± 0.05 cU=31 ± 2 bD=4.5 ± 0.22 cD=34 ± 8 AUbar=AU, ADbar=AD bUbar = 10.8 ± 0.5 bDbar = 2.7 ± 0.9 ag= -0.115 ± 0.03 bg= 11 ± 5 cg= 12 ± 5 au=0.72 ± 0.04 bu=3.99 ± 0.13 cu=1.5 ±0.71 bd=5.18 ± 0.72 cd=2.54 ± 2.02 As=0.63 ± 0.02 as= -0.197 ± 0.004 bs=6.85 ± 0.71 ag= -0.128 ± 0.02 bg= 11 ± 1 cg= 16 ± 5 Low-x sea similar Gluon similar Looking back at old slides cg was sometimes written negative, sorry it is always positive!

  8. Then we had the final decision to combine all data at 920, with all input errors relative AND the output had extra uncertainties from our procedures Here I combined all output errors in quadrature for the PDF fit Here I treat the 4 procedural errors by the OFFSET method for the PDF fit

  9. Here I compare fits with Q2_min > 2.5 and Q2min > 1.5- since the fits to the lowets Q2 point didn’t look so goof Q2_min=2.5 Q2_min=1.5 No of data points 584 NC e+ data points 371 χ2/dp = 0.93 No of data points 596 NC e+ data points 383 χ2/dp = 1.14 The shape of the low-x gluon is significantly affected BUT the chisq for these low Q2 points is not good

  10. What else ? • Investigate other model dependence changes… • Investigate NNLO • Implement Hessian+Offset as well as quadratic chisq

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