Theoretical Procedures and the effect on PDFs and $\alpha_S(M_Z^2)$

TL;DR

This paper examines how different theoretical procedures, such as flavor schemes and data cuts, impact the determination of PDFs and the strong coupling constant, highlighting significant scheme-dependent differences.

Contribution

It compares fixed and variable flavor schemes in PDF fits, analyzing their effects on PDFs and ppa_S, and discusses the convergence of logarithmic terms in the fixed flavor scheme.

Findings

Fixed flavor scheme increases light quarks at all x

Gluon distribution becomes softer at high x and larger at small x

ppa_S(M_Z^2) decreases, especially at NNLO

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.