EPJ

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EPJ C - Particles and Fields
Particles and Fields
Eur. Phys. J. C 2, 137-150

Massive quark production in electron positron annihilation to order $\alpha_s^2$

K.G. Chetyrkin1,2 - A.H. Hoang3 - J.H. Kühn1 - M. Steinhauser4 - T. Teubner5

1 Institut für Theoretische Teilchenphysik, Universität Karlsruhe, D-76128 Karlsruhe, Germany
2 Institute for Nuclear Research, Russian Academy of Sciences, Moscow 117312, Russia
3 Department of Physics, University of California, San Diego, La Jolla, CA 92093-0319, USA
4 Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 Munich, Germany
5 Deutsches Elektronen-Synchrotron DESY, D-22603 Hamburg, Germany

Received: 12 November 1997

Abstract
Recent analytical and numerical results for the three-loop polarization function allow to present a phenomenological analysis of the cross section for massive quark production in electron positron annihilation to order $\alpha_s^2$. Numerical predictions based on fixed order perturbation theory are presented for charm and bottom production above 5 and 11.5 GeV, respectively. The contribution from these energy regions to $\alpha(M_Z^2)$, the running QED coupling constant at scale MZ, are given. The dominant terms close to threshold, i.e. in an expansion for small quark velocity $\beta$, are presented

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