Heavy quark coefficient functions at asymptotic values $Q^2\gg m^2$

Abstract

In this paper we present the analytic form of the heavy-quark coefficient functions for deep-inelastic lepton-hadron scattering in the kinematical regime $Q^2\gg m^2$ . Here $Q^2$ and $m^2$ stand for the masses squared of the virtual photon and heavy quark respectively. The calculations have been performed up to next-to-leading order in the strong coupling constant ${\alpha }_s$ using operator product expansion techniques. Apart from a check on earlier calculations, which however are only accessible via large computer programs, the asymptotic forms of the coefficient functions are useful for charm production at HERA when the condition $Q^2\gg m_c^2$ is satisfied. Furthermore the analytical expressions can also be used when one applies the variable heavy flavour scheme up to next-to-leading order in ${\alpha }_s$.

56 pages plain LATEX, 11 Postscript figures

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