The difference between n-dimensional regularization and n-dimensional reduction in QCD

Abstract

We discuss the difference between n-dimensional regularization and n-dimensional reduction for processes in QCD which have an additional mass scale. Examples are heavy flavour production in hadron-hadron collisions or on-shell photon-hadron collisions where the scale is represented by the mass $m$. Another example is electroproduction of heavy flavours where we have two mass scales given by $m$ and the virtuality of the photon $Q=\sqrt{-q^2}$. Finally we study the Drell-Yan process where the additional scale is represented by the virtuality $Q=\sqrt{q^2}$ of the vector boson (${\gamma }^{\ast },W,Z$). The difference between the two schemes is not accounted for by the usual oversubtractions. There are extra counter terms which multiply the mass scale dependent parts of the Born cross sections. In the case of the Drell-Yan process it turns out that the off-shell mass regularization agrees with n-dimensional regularization.

12 pages Latex

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