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

K.G. Chetyrkin; A.H. Hoang; J.H. Kühn; M. Steinhauser; T. Teubner

doi:doi:10.1007/s100520050128

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2019 Impact factor 4.389

Particles and Fields

Eur. Phys. J. C 2, 137-150

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

K.G. Chetyrkin^1,2 - 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 M_Z, are given. The dominant terms close to threshold, i.e. in an expansion for small quark velocity $\beta$ , are presented