Abstract
Using the non-abelian exponentiation theorem with eikonalized quarks, we have calculated to fourth order in perturbative QCD the exponent which contains the contribution of the annihilation process into a quark-antiquark pair, including soft gluon production up to a maximum energy Δ. We suggest a generalization of these results to all orders, which contains all leading as well as non-leading logarithms of m/ S , where m denotes the quark mass and √ S represents the center of mass energy of the electron-positron pair. We show in particular that the dependence of the exponent on these parameters is governed, in leading order, by the effective coupling g(Δm/μ√S) as given by the renormalization group.
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