Two loop matching conditions on $\overline{\mathrm{MS}}$ parton densities

Abstract

We discuss how the operator product expansion (OPE) can be used to derive asymptotic expressions for certain integrals. This yields operator matrix elements (OME's) which determine the matching conditions for $\overline{\mathrm{MS}}$ parton densities across heavy flavour thresholds. Then we construct four and five-flavour densities from a three-flavour set via the AP equation using LO and NLO splitting functions.

Latex with six figures