Two-Loop QCD Corrections to the Heavy Quark Pair Production Cross Section in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>Annihilation near Threshold

Abstract

We present the O(alpha_s) corrections to the cross section for the reaction\ne+e- --&gt; gamma^* --&gt; Q \\bar Q in the energy region close to the threshold. We\nassume that the energy of the reaction is such that both the perturbative\nexpansion in the strong coupling constant and expansion in the relative\nvelocity of the heavy quarks can be used. We explicitly obtain terms\nO(alpha_s^2/beta^2, alpha_s^2/beta, alpha_s^2) in the relative correction to\nthe threshold cross section. Using the ideas of asymptotic expansions, we\ndemonstrate how an expansion of Feynman diagrams in the threshold region is\nconstructed. From this analysis we obtain a matching relation between the\nvector current in full QCD and the quark-antiquark current in NRQCD at leading\norder in 1/m and the second order in the strong coupling constant.\n