Production of Heavy Quarks in Deep-Inelastic Lepton-Hadron Scattering scattering

We will give a review of the computation of exact next-to-leading order corrections to heavy quark production in deep inelastic lepton-hadron scattering and discuss the progress made in this field over the past ten years. In this approach, hereafter called EXACT, where the heavy quark mass is taken to be of the same order of magnitude as the other large scales in the process, one can apply perturbation theory in all orders of the strong coupling constant alpha_s. The results are compared with another approach, called the variable flavor number scheme (VFNS), where the heavy quark is also treated as a massless quark. It turns out that the differences between the two approaches are very small provided both of them are carried out up to next-to-next-to-leading order.