A Practical Procedure for Evolving Heavy Flavour Structure Functions

The transition from the low $Q^2$ region in deep inelastic scattering where charm production is described by photon-gluon fusion to a region where the charm structure function $F_2^c$ is largely generated by a charm quark density should be a smooth passage. The all orders prescription for matching between the two schemes does not uniquely determine all the relevant coefficient functions (CF's) or guarantee the correct threshold behaviour at fixed order in $\alpha_s$. The constraints of matching not only the value but also the evolution of $F_2^c$ order by order allows all CF's to be determined at any order, each of which reduces to the appropriate massless $\msb$ expression as $Q^2 \to \infty$, and leads to a smooth transition in the threshold region. This procedure gives an excellent description of the $F_2^c$ data for all $Q^2$.