# TTP98-04 Singlet Polarization Functions at O(\alpha_s^2)

TTP98-04 Singlet Polarization Functions at O(\alpha_s^2)

TTP98-04 Singlet Polarization Functions at O(\alpha_s^2)

We consider the three-loop singlet diagrams induced by axial-vector, scalar and pseudo-scalar currents. Expansions for small and large external momentum $q$ are presented. They are used in combination with conformal mapping and Pad\'e approximations in order to arrive at results for the polarization functions valid for all $q^2$. Results are presented for the imaginary parts which are directly related to physical quantities like the production of top quarks or the decay of scalar or pseudo-scalar Higgs bosons.

 K.G. Chetyrkin, R. Harlander and M. Steinhauser Phys. Rev. D 58 014012 1998 PDF PostScript arXiv