Effect of changes of variable flavor number scheme on parton distribution functions and predicted cross sections

I consider variations in the definitions, at next-to-leading order and at next-to-next-to leading order, of a general-mass variable flavor number scheme (GM-VFNS) for heavy flavor structure functions. I also define a new optimal scheme choice improving the smoothness of the transition from one flavor number to the next. I investigate the variation of the structure function for a fixed set of parton distribution functions (PDFs) and also the change in the PDFs when a new MSTW2008-type global fit to data is performed for each GM-VFNS. At next-to-leading order the parton distributions, and predictions using them at hadron colliders, can vary by similar to 2-3% from the mean value. At next-to-next-to leading order there is far more stability with varying GM-VFNS definitions, and changes in PDFs and predictions are less than 1%, with most variations at very small x values. Hence, mass-scheme variation is an additional and significant source of uncertainty when considering parton distributions, but as with all perturbative uncertainties, it diminishes quickly as higher orders are included.