Comparison between variable flavor number schemes for charm quark electroproduction

A comparison is made between two variable flavor number schemes which describe charm quark production in deep inelastic electron-proton scattering. In these schemes the coefficient functions are derived from mass factorization of the heavy quark coefficient functions presented in a fixed flavor number scheme. Since the coefficient functions in the variable flavor number schemes have to be finite in the limit →m0 we have defined a prescription for those processes where the virtual photon is attached to a light quark. Furthermore one has to construct a parton density set with four active flavors $(u,d,s,c)$ out of a set which only contains three light flavors $(u,d,s).$ In order αₛ² the two sets are discontinuous at μ=mc which follows from mass factorization of the heavy quark coefficient functions. The charm component of the structure function F2,c is insensitive to the different variable flavor number schemes. In particular in the threshold region they both agree with the description in fixed order perturbation theory presented in a three flavor scheme. However one version does not lead to a correct description of the threshold behavior of the longitudinal structure function FL,c. This happens when one requires a non-vanishing zeroth order longitudinal coefficient function.