# Additive option for RT scaling of FL and F2

The chi-square minimum of the default NNLO fit with RTOPT as VFN scheme shows some hyperbolic discontinuities. The reason of such discontinuities is the scaling of the RT correction to FL from the pure gamma contribution to the sum of gamma, Z and gamma/Z interference terms. Such scaling is ill-defined when the massless FL cross zeros, and gives raise to hyperbolic discontinuities which can generate false minima and not positive-definite covariance matrix at the minimum.

As a temporary solution, I have added an option which implements and additive correction. For consistency the same additive corrections is implemented also for F2. A better solution would consist in evaluating FL and F2 separately for u and d quarks, and compute the gamma, Z and gamma/Z terms from the u and d quark contributions.

The discontinuities at minimum can be checked in the test: temp/checkmin-default/output/minuit.out.txt default-minuit.out.txt The smooth minimum with the additive correction is in temp/checkmin-additive/output/minuit.out.txt additive-minuit.out.txt