Theoretical Procedures and the effect on PDFs and ${\alpha }_S(M_Z^2)$

Abstract

I consider the effect on partons distribution functions (PDFs) of changes in the theoretical procedure used in a PDF fit. I consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at most $x$ values, the gluon distribution becoming softer at high values of $x$ and larger at small $x$, and the coupling constant ${\alpha }_S(M_Z^2)$ falling, particularly at NNLO. The fit quality also deteriorates.I also consider lowering the kinematic cut on $W^2$ for DIS data and introducing higher twist terms which are fit to data. This results in much smaller effects on both PDFs and ${\alpha }_S(M_Z^2)$, with changes generally smaller than uncertainties, except for quarks at very high $x$. I show that the fixed flavour scheme and variable flavour scheme structure functions differ significantly for $x\sim 0.01$ at high $Q^2$. I demonstrate that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form $({\alpha }_S\ln (Q^2/m_c^2){)}^n$ in this regime. I conclude that some major differences in PDF sets are largely due to the choice of flavour scheme used.

Comments: 6 pages, 11 figures, to appear in proceedings of DIS2013 Workshop