Re-implement official HERAPDF parameterisation
Since the PionCeres merge in 2019, the implemented HERAPDF parameterisation is different from the one used in the papers. It differs in two regards:
-
The functional form of the negative gluon term has changed
The canonical form is
xg(x) = A_g x^{B_g} (1-x)^{C_g} - A_g' x^{B_g'} (1-x)^{C_g'},
but the actual implementation was
xg(x) = A_g (x^{B_g} (1-x)^{C_g} - A_g' x^{B_g'} (1-x)^{C_g'}).
While these forms can express the same set of functions, the correlations between parameters are different and thus the shape of the χ² function changes. It turns out that the second form makes the fit more unstable.
The
NegativeGluon
parameterisation class has been changed to adapt the first form again. The sum rule is implemented accordingly. In all affected examples, the Ag' parameter has been adjusted to keep the PDFs unchanged. If necessary, the second form can still be obtained, using theExpression
parameterisation. -
Sea quark parameters
In HERAPDF the Ubar and Dbar distributions are parameterised. However, the
UvDvUbarDbarS
decomposition parameterises ubar and dbar instead. By HERAPDF assumption, ubar=Ubar, but dbar=(1-fs)Dbar. This change does not affect convergence, but the fitted parameters are not identical to the ones quoted in the paper. The parameterisation has been adjusted in the defaultNLO and defaultNNLO examples.
With both of these changes implemented, the current xFitter version is again able to reproduce the HERAPDF2.0NLO, NNLO and Jets NLO fits.