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Update of comparison of QCD fits

Update of comparison of QCD fits. 29/01/2008. Outlook. Double minimum with H1 param Double (triple) minimum with ZEUS-Jet and Inbetween parametrisations Last comparisons between results of JF (H1fitter) and ACS programmes. H1-ZEUS data set. Gluon at Q 2 = 4 GeV 2 for various input param.

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Update of comparison of QCD fits

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  1. Update of comparison of QCD fits 29/01/2008 Joël Feltesse

  2. Outlook • Double minimum with H1 param • Double (triple) minimum with ZEUS-Jet and Inbetween parametrisations • Last comparisons between results of JF (H1fitter) and ACS programmes. Joël Feltesse

  3. H1-ZEUS data set. Gluon at Q2 = 4 GeV2 for various input param. Ref Inbetween H1-Par. data set H1-Z With error band Zeus-S Zeus-J Large difference with H1-par. Gluon!! Joël Feltesse 20/11/2007

  4. Reminder • JF :Two types of solutions pending on the parameteristion: • Humpy gluon with H1param and Inbetween • Straight gluon at low x with ZEUS-J and ZEUS-S • Mandy : one only type of solution for all 4 parameterisations: • Straight(smooth) gluon at low x Joël Feltesse

  5. New test • Use H1 parametrisation but giving as input to Minuit the initial values of the parameter of a straight gluon. • Surprising results • Initial straight gluon gives after minimisation a straight gluon : Chi2 = 446 [fit_2] • Initial humpy gluon gives after mininisation a humpy gluon : Chi2 = 456 [[fit_1] • No way (so far) to jump by minimisation from the humpy gluon to to the other !! • Double minimum also observed with QCDFIT (Li) and with ZEUS package (Mandy) Joël Feltesse

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  9. Comparison of output values of parameters at Q02 = 4 GeV2 JF output, H1 Param. H1PDF2k init. values Fit_1, chi2 = 456.4 NO. NAME VALUE ERROR 1 Bg -0.93489 0.38909E-01 2 Cg 9.2298 0.73734 3 Dg 11398. 8871.4 4 BU -0.21035 0.79069E-02 5 CU 4.8602 0.17934 6 FU 274.36 52.835 7 AD 0.15956 0.88072E-02 8 CD 4.0076 0.33801 9 CUbar 6.2007 0.63037 10 CDbar 5.8054 1.3173 JF output, H1-Param with mandy init.values Fit_2, chi2 = 446.0 NAME VALUE ERROR 1 Bg -0.85283E-01 0.35957E-01 2 Cg 0.13562E+02 0.12354E+01 3 Dg 0.16840E+02 0.65782E+01 4 BU -0.20143E+00 0.40238E-02 5 CU 0.48627E+01 0.19240E+00 6 FU 0.26490E+03 0.54386E+02 7 AD 0.17032E+00 0.53413E-02 8 CD 0.40289E+01 0.32759E+00 9 CUbar 0.72805E+01 0.50364E+00 10 CDbar 0.47830E+01 0.11619E+01 Where PDF parametrisation : x f(x) = A xB(1 - x)C (1 + D x + F x3 ) Joël Feltesse

  10. Obvious questions • Is the double minimum feature unique to H1 parameterisation ? • Is the double minimum unique to H1/ZEUS combined data set ? • Is the chi2 difference always in favor of a straight gluon ? Joël Feltesse

  11. Double minimum with ZEUS-Jet parameterisation (and ZEUS HQ treatment) ? • Initial straight gluon gives after minimisation a straight gluon : Chi2 = 443.9 • Initial humpy gluon gives after minimisation a humpy gluon : Chi2 = 456.3 → Results similar to H1 parametrisation Joël Feltesse

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  13. Double minimum with Inbetween parameterisation (and H1 HQ treatment) ? • Initial straight gluon gives after minimisation a straight gluon : Chi2 = 442.3 • Initial humpy gluon gives after mininisation a humpy gluon : Chi2 = 433.8 ! the smallest Chi2 so far BUT → • Dvalence negative at large x is an unphysical solution (Mandy). It even gives a negative CC x-sec at large x ! • Initial humpy gluon and dvalence density forced to be positive gives after minimisation a new minimum with a humpy gluon : Chi2 = 450.1 ! Joël Feltesse

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  16. Double minimum with only H1 data (from H1PDF2k) and H1 parameterisation ? • Initial straight gluon gives after minimisation a straight gluon : Chi2 = 547.3 • Initial humpy gluon gives after mininisation a humpy gluon : Chi2 = 536.8. Smaller than the straight gluon minimum (relief). • Remark : as for the publication the fit has been performed with full correlation taken into account. Joël Feltesse

  17. In short When fitting H1Z combined data sets Minuit minimisation finds two minimum independently of the parameterisation (H1-param., Inbetween, ZEUS-Jet). Each time, the straight gluon minimum is slightly favored (Chi2 smaller by 6 to 13 units) provided unphysical solutions are removed. Is the double minimum a problem ? Is there a third minimum ? I feel uneasy than Minuit is not capable to jump alone from a minimum to a better one. The double minimum is also observed when using H1 published data sets but then favoring the humpy solution. → Better find a way to get one only robust minimum (Li’s talk) Joël Feltesse

  18. Considering only the straight gluon solutions. How different are the 3 fits ? Reminder. All fits with : Q2min = 3.5 GeV2, 573 data points and all errors uncorrelated. H1 param (10 parameters), chi2 = 446.1 Inbetween (12 parameters), chi2 = 442.3 ZEUS-JET (11 parameters), chi2 = 443.9 Chi2 are very close, but PDFs are not so close → Joël Feltesse

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  22. Staight Gluon. Technical comparison between JF and Mandy ZEUS J Parameterisation Chi2_J = 443.9 Chi2_M = 440.8 Val_J Err_J Val_M Err_M Dif/Err Gluon Bg -0.092 0.028 -0.104 0.034 0.396 Gluon Cg 12.934 0.844 13.323 0.925 -0.440 Gluon Dg 15.036 4.350 17.633 5.879 -0.508 u valence Buv 0.590 0.037 0.616 0.039 -0.693 u valence Cuv 3.817 0.121 3.825 0.138 -0.067 u valence Duv 2.450 0.755 2.103 0.744 0.463 d valence Cdv 4.866 0.726 4.803 0.910 0.077 d valence Ddv 2.597 2.030 2.089 2.362 0.677 Sea Asea 0.567 0.019 0.582 0.022 -0.735 Sea Bsea -0.210 0.004 -0.206 0.004 -0.712 Sea Csea 3.662 0.541 3.743 0.655 -0.135 Joël Feltesse

  23. Staight Gluon. Technical comparison between JF and Mandy H1 Parameterisation Chi2_J = 446. Chi2_M = 439.3 Val_J Err_J Val_M Err_M Dif/Err Gluon Bg -0.085 0.036 -0.090 0.035 0.139 Gluon Cg 13.562 1.235 13.372 0.290 0.154 Gluon Dg 16.840 6.578 16.648 0.425 0.029 B_U -0.201 0.004 -0.201 0.004 -0.218 C_U 4.863 0.192 4.882 0.096 -0.098 F_U 264.900 54.386 268.61 6.951 -0.068 A_D 0.170 0.005 0.172 0.005 -0.271 C_D 4.029 0.328 4.016 0.323 0.038 C_Ubar 7.280 0.504 7.724 0.520 -0.881 C_Dbar 4.783 1.162 4.584 0.157 0.172 Joël Feltesse

  24. Staight Gluon. Technical comparison between JF and Mandy Inbetween Parameterisation Chi2_J = 442.3. Chi2_M = 437.9 Val_J Err_J Val_M Err_M Dif/Err Gluon Bg -0.091 0.028 -0.098 0.034 0.242 Gluon Cg 11.433 1.026 11.406 1.310 0.023 Gluon Dg 11.341 3.970 11.952 5.463 -0.129 u valence Buv 0.545 0.047 0.556 0.058 -0.211 u valence Cuv 3.831 0.107 3.853 0.112 -0.206 u valence Duv 3.496 1.028 3.501 1.230 -0.004 d valence Cdv 5.042 0.605 5.054 0.713 -0.019 d valence Ddv 6.006 3.279 6.559 4.585 -0.490 Sea BDbar -0.210 0.004 -0.209 0.005 -0.368 Sea CDbar 4.958 1.722 4.615 0.869 0.264 Sea CDbar 3.895 0.851 4.615 0.869 -0.837 Joël Feltesse

  25. Conclusion • The largest difference between JF and Mandy on fit results has been understood. • Technical comparison between JF and Mandy : agreement at the ~ 0.3 sigma level on parameter values for all choices of parameterisation, although Chi2 of Mandy are always a bit smaller. • At present, should concentrate on understanding (improving) the remaining differences between parameterisations and move to more elaborate fits, for example on HQ treatment and with treatment of correlations between errors. Joël Feltesse

  26. APPENDIX Joël Feltesse

  27. PDF parametrisation : x f(x) = A xB(1 - x)C(1 + D x + F x3 ) Quite simple but questionable assumption on ubar -dbar Joël Feltesse Where U = u +c and D = d+ s + b

  28. PDF parametrisation : x f(x) = A xB(1 - x)C(1 + D x + F x3 ) Very strong assumptions on B’s, questionable assumption on ubar/dbar as x → 0. Joël Feltesse

  29. PDF parametrisation : x f(x) = A xB(1 - x)C(1 + D x + F x3 ) Weaker assumptions on B’s. Less model dependence questionable assumption on ubar/dbar as x → 0. Joël Feltesse

  30. EXTRAS Joël Feltesse

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