PDF parametrization issues

In the standard PDF fitting paradigm, one parametrizes each flavor fa(x, Q0) at a small Q0 using currently a total of about 20 parameters. One then computes the PDFs fa(x, Q) for Q > Q0 by DGLAP evolution; followed by the cross section predictions for DIS(e,μ,ν), DrellYan, inclusive jets, . . . by perturbation theory; followed by a “χ” measure of agreement between the predictions and measurements. One minimizes χ with respect to the parameters at Q0 to find Best Fit PDFs, and explores the neighborhood of the minimum via eigenvector sets to estimate an uncertainty range in which all of the data sets are described tolerably well. (Weight factors are included in the definition of χ to keep experiments with a small number of data points from being unduly neglected.) Parametrization dependence is the systematic error caused by making specific choices of the functional forms in fa(x, Q0). It was interesting to observe at this meeting that the major fitting groups all use significantly different parametrizations, so at least the community is not being mislead by a single choice. Meanwhile, Neural Net methods may be able to avoid this problem entirely. Previous CTEQ PDF analyses generally assumed s(x) = s̄(x) ∝ d̄(x) + ū(x) at Q0. We dropped that ansatz in CTEQ6.6. A preliminary version used the innocent-looking form s(x) = s̄(x) = a0 x a1 (1−x)2 , with a1 the same as for d̄ and ū, as predicted by Regge theory. The resulting strangeness looked OK by itself; but gave s̄(x) > ū(x), d̄(x) at small x, which violates theory prejudice and perhaps Hermes data. A more elaborate parametrization was chosen in a somewhat ad hoc manner for the final CTEQ6.6 to avoid this.